ALBERT

Beschreibung: This article performs an exact analysis for a frictional triangular or cylindrical punch acting on the surface of magneto-electro-elastic materials. The punch moves relative to the surface of magneto-electro-elastic materials. Inside the contact area, the Coulomb friction law is applied. Eigenvalue distribution is analyzed, and then appropriate fundamental solutions are given. The stated problem is reduced to a system of singular integral equations of the second kind. The exact solution of the obtained singular integral equations makes it easy to get the explicit expressions of the surface physical quantities. Through plotting figures, the influences of the friction coefficient on contact behavior are shown and interesting results are observed. The in-plane stress, electric displacement and magnetic induction tend to be infinite near the leading edge of the frictional triangular punch, while having spikes at one edge of the frictional cylindrical punch, which may explain why surface damage occurs on the surface of magneto-electro-elastic materials.

Beschreibung: Conversion of cellulosic biomass to useful products involves pumping and mixing of fiber suspensions. Depending upon the concentration, the fibers may entangle to form flocs and networks. The fibers in these suspensions may settle both as individual fibers and fiber flocs. The flow of cellulosic suspensions has been previously modeled using generalized Newtonian rheological models. Under some flow conditions, those models do not apply due to strong gravitational effects that result in concentration gradients. Magnetic resonance flow imaging was used to obtain velocity profiles of fiber suspensions in horizontal pipe flow as a function of fiber length, concentration, and flow rates. Measures of flatness and asymmetry are used to characterize the shape of the velocity profiles. The largest asymmetry is found near a crowding number of roughly three. At higher crowding numbers, the velocity profiles tended to become flat, more symmetric, and pressure drops per unit length depend strongly on concentration.

Beschreibung: The present work studies the interfacial fracture in a piezoelectric cylindrical shell patch. The problem is solved by the methods of infinite trigonometric series and Cauchy singular integral equation, and the numerical results of the stress intensity factor (SIF) are obtained. The effects of the interfacial radius and crack’s location on the SIF are explained through the effects of the free surface, interfacial curvature, crack length, and interface end, respectively. An optimal stiffness matching relationship between the piezoelectric layer and dielectric substrate is suggested. The effects of the piezoelectric and dielectric coefficients are explained through the mechanism of piezoelectric stiffening.

Beschreibung: The interaction between a screw dislocation and a circular nano-inhomogeneity with a semi-infinite wedge crack penetrating the interface is investigated. By using Riemann-Schwartz’s symmetry principle integrated with the analysis of singularity of complex functions and the conformal mapping technique, the analytical expressions of the stress field in both the circular nano-inhomogeneity and the infinite matrix, the image force acting on the screw dislocation and the stress intensity factor at the crack tip are obtained. The influence of elastic mismatch of materials, inhomogeneity size, interface stress, wedge crack opening angle and the relative location of dislocation on the image force and on the equilibrium position of the screw dislocation and the shielding effect of the screw dislocation are discussed in detail. The results show that interface stress has a significant impact on the movement of dislocations near the interface, and the effect of interface stress enhances when the inhomogeneity radius decreases. With the decrease in the wedge crack opening angle, the influence of interface stress on the movement of the screw dislocation and on the SIF enhances. With the increment of the relative shear modulus, the influence of interface stress weakens with the screw dislocation locating in the inhomogeneity and strengthens with the screw dislocation locating in the matrix. When the screw dislocation is located in the inhomogeneity, the positive (negative) interface stress increases (decreases) the shielding effect, while this phenomenon is opposite when the screw dislocation locates in the matrix.

Beschreibung: In the paper, the reinforcement of no-tension structures by the application of superposed high-strength sheets, or by the insertion of tensile bars, has been considered with the purpose to set up a design path aiming at the positioning of the new material according to some optimal criterion. In detail, no-tension models are adopted which are recognized as an effective tool for analyzing a wide class of structures (e.g., masonry and reinforced concrete members), and the equilibrium and the failure analysis of the reinforced body are developed with particular reference to its ultimate limit state of collapse. Finally, an approach through the “topologic optimization” is proposed for the identification of the optimal distribution of the reinforcement, and some of the obtained results are shown.

Beschreibung: The dynamics of individual flexible fibers in a turbulent flow field have been analyzed, varying their initial position, density and length. A particle-level fiber model has been integrated into a general-purpose, open source computational fluid dynamics code. The fibers are modeled as chains of cylindrical segments connected by ball and socket joints. The equations of motion of the fibers contain the inertia of the segments, the contributions from hydrodynamic forces and torques, and the connectivity forces at the joints. Direct numerical simulation of the incompressible Navier–Stokes equations is used to describe the fluid flow in a plane channel, and a one-way coupling is considered between the fibers and the fluid phase. We investigate the translational motion of fibers by considering the mean square displacement of their trajectories. We find that the fiber motion is primarily governed by velocity correlations of the flow fluctuations. In addition, we show that there is a clear tendency of the thread-like fibers to evolve into complex geometrical configurations in a turbulent flow field, in fashion similar to random conformations of polymer strands subjected to thermal fluctuations in a suspension. Finally, we show that fiber inertia has a significant impact on reorientation timescales of fibers suspended in a turbulent flow field.

Beschreibung: Non-smooth strain gradient fields are studied in bending beams, in the context of strain gradient elasticity. It is found that strain fields with continuous curvature, but discontinuous curvature derivatives (evolutes) are possible. The pure bending and buckling problems of a simply supported beam are investigated.

Beschreibung: This paper deals with the linear and nonlinear vibrations of a truncated conical shell; both internal and external surfaces are covered by functionally graded coatings (FGCs). The theoretical formulation is based on the von Karman–Donnell-type nonlinear kinematics. The material properties of FGCs are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The fundamental relations, the modified Donnell-type nonlinear motion, and compatibility equations of the truncated conical shell with FGCs are derived. The basic equations are reduced to the ordinary differential equation depending on time with geometric nonlinearity using the Superposition and Galerkin methods. By applying the homotopy perturbation method to the foregoing equation, the relation between nonlinear frequency parameters with the dimensionless amplitude of a truncated conical shell with FGCs is obtained. Parametric studies are performed to illustrate the effect of different values of thickness and material composition of the FGCs on the frequency-amplitude relationships. The validity of the present solution is demonstrated by comparison with solutions available in the literature.

Beschreibung: A two-dimensional linearly elastic model of shells made of an anisotropic material described by 21 elastic moduli is developed. For this aim, the generalized Timoshenko–Reissner hypotheses are used. In contrast to the ordinary shell models, the tangential stress-resultants here depend not only on the tangential strains but also on the transverse shear. An asymptotic analysis of the obtained equations is fulfilled. The typical stress-strain states, namely the membrane state, the edge effect state, and the boundary layer, are constructed. The system of the Donnell type is delivered. As an example of general anisotropy, a composite material consisting of a matrix reinforced by the system of fibers inclined to the mid-surface is studied. Certain simple static problems and free vibration problems are solved for a cylindrical shell made of this material.

Beschreibung: A unified analytical approach is applied for investigating the vibrational behavior of grid-stiffened composite cylindrical shells considering the flexural behavior of the ribs. A smeared method is employed to superimpose the stiffness contribution of the stiffeners with those of the shell in order to obtain the equivalent stiffness parameters of the whole panel. The stiffeners are modeled as a beam and considered to support shear loads and bending moments in addition to the axial loads. Therefore, the corresponding stiffness terms are taken into consideration while obtaining the stiffness matrices due to the stiffeners. Theoretical formulations are based on first-order shear deformation shell theory, which includes the effects of transverse shear deformation and rotary inertia. The modal forms are assumed to have the axial dependency in the form of Fourier series whose derivatives are legitimized using Stokes’ transformation. In order to validate the obtained results, a 3-D finite element model is also built using ABAQUS CAE software. Results obtained from two types of analyses are compared with each other, and good agreement has been achieved. Furthermore, the influence of variations in the shell thickness and changes of the boundary conditions on the shell frequencies is studied. The results obtained are novel and can be used as a benchmark for further studies.

Beschreibung: In this paper, a new analytical solution for the optimal shape of a plane-statically determined arch subjected to uniform vertical loads is presented. The classical problem of a catenary subjected to the self-weight is extended to an inverted catenary subjected to the self-weight and to a constant vertical load distribution. In this condition, the authors demonstrate that a class of analytical solutions exists and that unlike previously proposed solutions it corresponds to the minimum ratio of the self-weight of the arch to the total applied load. Finally, existence conditions for such a solution are derived.

Beschreibung: A theoretical study has been carried out to determine the thickness of the bedload layer in an open channel turbulent flow with non-cohesive sediment, which is very crucial in sediment transport problems as this is treated as saltation height of a sediment particle and the reference level in suspension studies. A new expression of viscous shear stress is proposed, which is a function of effective viscosity of sediment–fluid mixture, velocity gradient and volumetric concentration of sediment particles. During particle collisions, impact shear stress is generated, which is another important parameter near the sediment bed. By including both the shear stresses, an expression for the thickness of the bedload layer is developed. The predicted bedload layer thickness is a function of viscous coefficient, impact coefficient, particle diameter, relative mass density of sediment particle, maximum bed concentration and non-dimensional shear stress. It agrees reasonably well when compared with a wide class of experimental data under different hydraulic conditions.

Beschreibung: This paper is devoted to a new approach for the derivation of main thermoelastic Green’s functions (MTGFs), based on their new integral representations via Green’s functions for Poisson’s equation. These integral representations have permitted us to derive in elementary functions new MTGFs and new Poisson-type integral formulas for a thermoelastic octant under mixed mechanical and thermal boundary conditions, which are formulated in a special theorem. Examples of validation of the obtained MTGFs are presented. The effectiveness of the obtained MTGFs and of the Poisson-type integral formula is shown on a solution in elementary functions of a particular BVP of thermoelasticity for octant. The graphical and numerical computer evaluation of the obtained MTGFs and of the thermoelastic displacements of the particular BVP for an octant is also presented. By using the proposed approach, it is possible to derive in elementary functions many new MTGFs and new Poisson-type integral formulas for many canonical Cartesian domains.

Beschreibung: The presence of in-homogeneity or defects in materials cannot be ignored. There is great need to understand the influence of defects on the mechanical response of nano-materials. In this study, atomistic simulations have been used to investigate the mechanical response of gold nano-wires under twisting. Simulations show that nano-wires have different elastic properties when defects are present. Embedded cracks of different sizes have been created in nano-wires to quantify in-homogeneity. The inter-atomic interactions are represented by employing an embedded-atom potential. The effect of different sizes of crack on potential energy, torque and stresses for investigating the mechanical response of a nano-wire is part of the whole investigation. It is predicted from our simulation that the presence of a crack and dimensions of the crack control the torsional response of gold nano-wires. Deviation in the behavior of gold nano-wires from continuum expectations is also discussed. The comparison of results of atomistic simulations is made with a linear elasticity model (of healthy and cracked nano-wires) to get deep insights into the nano-scale behavior of nano-wires.

Beschreibung: The criterion for the onset of Bénard–Marangoni ferroconvection in an initially quiescent magnetized ferrofluid saturated horizontal Brinkman porous layer is investigated in the presence of a uniform vertical magnetic field. The viscosity is considered to be varying exponentially with temperature. The lower rigid boundary and the upper free boundary at which the surface tension effects are accounted for are assumed to be perfectly insulated to temperature perturbations. The eigenvalue problem is solved numerically using the Galerkin technique and analytically by regular perturbation technique with wave number a as a perturbation parameter. It is observed that the analytical and numerical results are very well comparable. The characteristics of stability of the system are strongly dependent on the viscosity parameter B . The effect of B on the onset of Bénard–Marangoni ferroconvection in a porous layer is dual in nature depending on the choices of the physical parameters, and a sublayer starts to form at higher values of B . The nonlinearity of fluid magnetization M 3 is found to have no influence on the onset of ferroconvection, whereas an increase in the value of the magnetic number M 1 and the Darcy number Da is to advance the onset of Bénard–Marangoni ferroconvection in a porous layer.

Beschreibung: A numerical method of constructing eigensolutions for arbitrary elastic conical bodies with smooth and non-smooth lateral surfaces is considered. Different variants of its numerical implementation based on the finite element method are discussed. The results of numerical experiments demonstrating the efficiency and reliability of the proposed method are presented. The character of stress responses (the character of stress singularities) in the vicinity of vertices of circular and non-circular cones, composite and hollow cones, cones with non-smooth lateral surfaces, trihedral wedge, one and two intersecting wedge-shaped cracks is estimated based on the obtained solutions.

Beschreibung: The conformal invariance of the Mei symmetry and the conserved quantities are investigated for discrete Lagrangian systems under the infinitesimal transformation of the Lie group. The difference Euler–Lagrange equations on regular lattices of the discrete Lagrangian systems are presented via the transformation operators in the space of the discrete variables. The conformal invariance of the Mei symmetry is defined for the discrete Lagrangian systems. The criterion equations and the determining equations are proposed. The conserved quantities of the systems are derived from the structure equation governing the gauge function. Two examples are given to illustrate the application of the results.

Beschreibung: This paper introduces an efficient method for the finite element analysis of models comprised of higher order triangular elements. The presented method is based on the force method and benefits graph theoretical transformations. For this purpose, minimal subgraphs of predefined special patterns are selected. Self-equilibrating systems are then constructed on these subgraphs leading to sparse and banded null basis. Finally, well-structured flexibility matrices are formed for efficient finite element analysis.

Beschreibung: Based on analytical solutions of elastic waves scattered by a coated cylinder in an infinite elastic matrix, we construct the localization relations for averaged displacement and stress fields in each phase. Dynamic effective mass, in-plane bulk modulus and shear modulus are defined, respectively, as the ratio between the force and acceleration, bulk stress and bulk strain, maximum shear stress and maximum shear strain. Analytic expressions for dynamic effective parameters of two-dimensional acoustic metamaterials are derived. Numerical examples are given to analyze dynamic effective properties of composites with coated inclusions. It is demonstrated that the proposed model can predict negative values of effective mass and effective bulk and shear modulus, and discover the underlying mechanisms of negative effective material parameters. The proposed model will be helpful in designing new acoustic metamaterials.

Beschreibung: One continues the qualitative analysis started in Part I (Făciu and Molinari in Acta Mech) concerning the thermomechanical characteristics of a steady, structured moving phase boundary in a shape memory alloy (SMA) by a quantitative investigation. The internal structure of these interphase layers is governed by a Maxwellian rate-type constitutive equation coupled or not with the Fourier heat conduction law. We consider as equilibrium stress–strain–temperature response function for the Maxwellian model an explicit piecewise linear thermoelastic relation for an SMA bar which can exist in the austenite phase A and in two variants of martensite M ± . Its thermal properties are built in agreement with experimental results on NiTi. This equilibrium relation has the atypical property that not only the derivative of the stress response function with respect to the strain changes its sign, but also the derivative with respect to the temperature. Considerable temperature variation is generated by impact-induced phase transformations due to the large amount of latent heat released (absorbed) inside the transition layer. One gets strong heating (cooling) across a compressive A → M − (expansive M − → A ) propagating interphase layer. A significant lower (larger) temperature than that at the front and Hugoniot back state is obtained inside an impact-induced M + → M − ( M − → M + ) interphase layer. The experimental finding of this phenomenon of temperature undershoot (overshoot) could be a valuable indication for the existence of an interphase layer.

Beschreibung: The paper focuses on the problem of the assessment of the response of structures behaving like rocking rigid blocks with unilateral constraints under dynamic loading. Although the motion of rigid blocks simulated by means of ad hoc built calculus codes shows good agreement between the numerical results and the data recorded in the laboratory tests, the response of such a system is poorly robust, and results can be very different in dependence of a number of factors, thus making final assessment rather uncertain. The developments presented and discussed represent the premise pushing towards the adoption of approaches aimed at searching for the worst possible rocking response and eventually based on iterative optimisation procedures.

Beschreibung: Fundamental principles of mechanics were primarily conceived for constant mass systems. Since the pioneering works of Meshcherskii, efforts have been made in order to elaborate an adequate mathematical formalism for variable mass systems. This is a current research field in theoretical mechanics. In this paper, attention is focused on the derivation of the generalized Hamilton’s principle for a non-material volume. First studies on the subject go back at least four decades with the article of McIver (J Eng Math 7(3):249–261, 1973 ). However, it is curious to note that the extended form of Hamilton’s principle that is derived by McIver does not recover the Lagrange’s equation for a non-material volume which is demonstrated by Irschik and Holl (Acta Mech 153(3–4):231–248, 2002 ). This does suggest additional theoretical investigations. In the upcoming discussion, Reynolds’ transport theorem is consistently considered regarding the original form of the principle of virtual work, and so the generalized Hamilton’s principle for a non-material volume is properly derived. It is finally shown that the generalization of Hamilton’s principle that is here proposed is in harmony with the Lagrange’s equation which is demonstrated by Irschik and Holl.

Beschreibung: We analytically analyze finite plane strain twisting deformations of a hollow cylinder made of an isotropic and inhomogeneous Mooney-Rivlin material with material moduli varying in the radial direction. The cylinder is deformed by applying either tangential tractions on the inner surface and tangential displacements on the outer surface or vice versa. The radial variation of the moduli is found that will minimize the tangential displacement of the bounding surface where tangential traction is specified. Furthermore, the modulus of a homogeneous neo-Hookean cylinder is found that is energetically equivalent to the inhomogeneous cylinder.

Beschreibung: In this study, new exact Green’s functions and a new exact Green-type integral formula for a boundary value problem (BVP) in thermoelasticity for some spherical wedges with mixed homogeneous mechanical boundary conditions are derived. The thermoelastic displacements are subjected to a heat source applied in the inner points of the spherical wedges and to a mixed non-homogeneous boundary heat conditions. When the thermoelastic Green’s function is derived, the thermoelastic displacements are generated by an inner unit point heat source, described by Dirac’s δ -function. All results are obtained in elementary functions that are formulated in a special theorem. Exact solutions in elementary functions for two particular BVPs of thermoelasticity for spherical wedges also are included. In these particular BVPs, the thermoelastic displacements are subjected to a constant temperature (in the first particular BVP) or to a constant heat source (in the second particular BVP). In both BVPs, the constant temperature or the constant heat source is given on the segment of the radius of the quarter-space. On the boundary half-planes of the quarter-space zero temperature and zero heat flux are prescribed.

Beschreibung: In this paper, the whirling frequencies of simply supported and clamped rotating cylindrical shells surrounded by an elastic foundation are investigated. The Love’s shell theory is used along with the Winkler foundation to obtain the governing equations of motion. An exact power series solution is obtained for arbitrary boundary conditions and the results are verified with the literature. Several case studies are performed, and the effect of spinning speed, foundation stiffness, and geometrical dimensions of the cylinder on the whirling frequencies are investigated.

Beschreibung: The transient response of an interface crack between two dissimilar functionally graded piezoelectric material (FGPM) layers under anti-plane shear impact loading is analyzed using the integral transform method. The properties of the FGPM layers vary continuously along the thickness, and the two layers are connected weak-discontinuously. Laplace transform and Fourier transform are used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate are presented for the FGPM to show the effects on the electric loading, variation and gradient of material properties, and thickness of layers. Following things are helpful to increase the resistance of transient fracture of interface crack in FGPMs: (a) increase of the material properties from the interface to the upper or lower free surface; (b) decrease of weak discontinuity at the interface; (c) increase of the gradient of material properties; (d) certain direction and magnitude of the electric loading; and (e) increase of the thickness of the FGPM layer.

Beschreibung: This paper investigates the free vibrations of a cantilever micro-beam submerged in a bounded frictionless and incompressible fluid cavity. Based on the Fourier–Bessel series expansion and using linear potential theory, an analytical method is proposed to analyze the eigenvalue problem, where the fluid effect emerges as an added mass. Wet beam vibration mode shapes together with the sloshing modes of the oscillating liquid are depicted. Moreover, effects of geometrical configuration and fluid density on the natural frequencies of the coupled system are evaluated. Results show that in spite of the high added mass values related to lower modes, presence of the fluid changes the higher modes more effectively.

Beschreibung: In this paper, for obtaining an overall size-dependent yield function for nanocomposites containing aligned cylindrical nanofibers, the effects of interface residual stress and interface elasticity are taken into account within a micromechanical framework. Toward this goal, the modified Hill’s condition is used, and then, in order to consider effects of the interface residual stress, strains are decomposed into two parts, a part due to the external loadings and the other due to the interface residual stress. Next, utilizing the field fluctuation method, an overall yield function containing effective elastic constants of the material is derived and then simplified for practical loading conditions. Moreover, a secant modulus scheme is adopted to examine the overall nonlinear behavior of the material in plastic deformation. Finally, by some numerical examples, it is shown that the interface stress, including the interface residual stress, makes the yield strength and plastic deformation of the metal matrix nanocomposites dependent on the nanofiber size, in contrast to the classical results.

Beschreibung: The propagation of SH-type wave is studied in a composite structure consisting of alternating polymeric layers and porous piezoelectric layers. The porous piezoelectric materials of the composite structure are assumed to have 6mm symmetry and their poling direction is along z -axis. Layers of the polymer are considered as isotropic dielectric elastic material. Solutions of the field equations for the porous piezoelectric material and for the polymeric material are obtained. Two cases, first when the direction of propagation of the SH-type wave is taken along the direction normal to the layering of the composite structure, and second when the propagation direction is taken along the layering, are considered for the derivation of the phase velocity. The dispersion and the stop-pass band behavior of the Floquet wave is also discussed. Numerical results for phase velocity and stop band effect are presented for a periodic system of alternating PZT-5H and polythene layers. The influence of volume fraction on phase velocity and stop band effect is discussed.

Beschreibung: The traditional phase field method adopts periodic boundary conditions and thus can only be applied to a continuous medium. In this manuscript, an extended phase field model is developed to simulate the polarization switching in a finite ferroelectric body with free surfaces. The void region outside the ferroelectric body was modeled as an elastic body having the same elastic stiffness as the ferroelectrics as well as properly distributed eigenstrain which functions to satisfy the traction-free boundary condition. Based on this scheme, periodic boundary conditions can be applied to the discrete system including a finite ferroelectric body and the voids outside. The elastically inhomogeneous system can be solved easily. This model has high calculation efficiency and can be conveniently applied to finite ferroelectric bodies with arbitrary boundaries. Finally, the domain pattern formation in a ferroelectric nano-particle is simulated. The obtained polarization pattern and stress field are illustrated.

Beschreibung: Based on the Porous Media Theory presented by de Boer, the governing differential equations for a layered space-axisymmetrical fluid-saturated porous elastic body are firstly established, in which the suitable interface conditions between layers are presented. Then, a differential quadrature element method (DQEM) is developed, and the DQEM and the second-order backward difference scheme are applied to discretize the governing differential equations of the problem in the spatial and temporal domain, respectively. In order to show the validity of the present analysis, the dynamic response of a fluid-saturated porous medium is analyzed, and the obtained numerical results are directly compared with the existing analytical results. The effects of the numbers of the elements and grid points on the convergence of the numerical results are considered. Finally, the dynamic characteristics of a layered fluid-saturated elastic soil cylinder subjected to a water pressure or a dynamic loading are studied, and the effects of material parameters are considered in detail. From the above numerical results, it can be found that the DQEM has advantages, such as little amount in computation, good stability and convergence as well as high accuracy, so it is a very efficient method for solving the problems in soil mechanics, especially such problems with discontinuities.

Beschreibung: We present a Hamiltonian state space approach for problems of anisotropic elasticity and piezoelasticity. By means of Legendre’s transformation, the basic equations of piezoelasticity are formulated into a state equation and an output equation in terms of the state vector that comprises the generalized displacement vector and the conjugate generalized traction vector as the dual variables. The Hamiltonian features and symplectic orthogonality of the system, which are essential for the solution approach using eigenfunction expansion, are delineated at length. We show that the solution to 3D problems of a prismatic body hinges upon a 2D Hamiltonian eigensystem and the eigensolution associated with the zero eigenvalue leads to the solution to the generalized plane problem naturally. Based on the formalism, the solution to a problem of piezoelasticity is no more difficult than its elastic counterpart.

Beschreibung: Despite extensive studies of inclusions with simple shape, little effort has been devoted to inclusions of irregular shape. In this study, we consider an inclusion of irregular shape embedded within an infinite isotropic elastic matrix subject to antiplane shear deformations. The inclusion–matrix interface is assumed to be imperfect characterized by a single, non-negative, and constant interface parameter. Using complex variable techniques, the analytic function that is defined within the irregular-shaped inclusion is expanded into a Faber series, and in conjunction with the Fourier series, a set of linear algebraic equations for a finite number of unknown coefficients is determined. With this approach and without imposing any constraints on the stress distribution, a semi-analytical solution is derived for the elastic fields within the irregular-shaped inclusion and the surrounding matrix. The method is illustrated using three examples and verified, when possible, with existing solutions. The results from the calculations reveal that the stress distribution within the inclusion is highly non-uniform and depends on the inclusion shape and the weak mechanical contact at the inclusion/matrix boundary. In fact, the results illustrate that the imperfect interface parameter significantly influences the stress distribution.

Beschreibung: The transport problem in a three-layer channel consisting of a noticeable transition layer sandwiched by a free-fluid region and a homogeneous porous medium is investigated analytically. The heterogeneous transition layer is characterized by the continuous variation of porosity and permeability, which are specifically described by applying two sets of functions. The Brinkman model is employed in the transition layer, and the analytical velocity profile is obtained in terms of the Airy function. Consistency is found between the computation results and the PIV data measured by Goharzadeh et al. (Phys. Fluids 17:057102, 2005 ). After comparing the estimated permeability variations with the calculated variation, we find the former predicted permeability values are two orders of magnitude larger than the latter ones. The velocity discrepancy in the transition layer is ascribed to the effectiveness of the empirical permeability function: although the well-known Kozeny– Carman formula can precisely predict the permeability of the monodisperse spherical packing bed with constant porosity, it will overestimate the permeability in the transition layer. Then, the exact permeability variation is expressed by an exponential function, and a more general formula is needed to model the gradual change of permeability along the transition layer region.

Beschreibung: This paper investigates the buckling of a bi-layered material with functionally graded coating including a pre-existing interface crack. In order to investigate this phenomenon which is of particular interest to the tribological community, the stresses due to sliding cylindrical loading were determined. Solutions for stresses are obtained by use of Fourier transform technique. These stress fields under such loading are strongly affected by various parameters such as friction coefficient, indenter tip radius, film thickness, etc. Therefore, to assess the coating strength reliably, the mechanical stress field developed by mixed normal and tangential surface pressure was analyzed by considering the affected parameters. The mechanical properties of the FG coating are assumed to vary exponentially through the thickness. On the basis of stress analysis, a satisfactory framework was developed to study the buckling of FG coatings. An interface crack was assumed to model the actually occurring flaws in such coated systems, and the critical buckling stress was obtained.

Beschreibung: A finite-element formulation for geometrically exact multi-layer beams is proposed in the present work. The interlayer slip and uplift are not considered. The number of layers is arbitrary, and the basic unknown functions are the horizontal and vertical displacements of the composite beam’s reference axis and the cross-sectional rotation of each layer. Due to the geometrically exact definition of the problem, the governing equations are nonlinear in terms of basic unknown functions and the solution is obtained numerically. In general, each layer can have different geometrical and material properties, but since the layers are rigidly connected, the main application of this model is on homogeneous layered beams. Numerical examples compare the results of the present model with the existing geometrically nonlinear sandwich beam models and also with the 2D plane-stress elements and, where applicable, with the results from the theory of elasticity. The comparison with 2D plane-stress elements shows that the multi-layer beam model is very efficient for modelling thick beams where warping of the cross-section has to be considered.

Beschreibung: The dynamic deformation of a geometrically nonlinear rectangular simply supported plate under a moving lumped mass is evaluated using mode expansion method. The governing differential equations of motion for a largely deformable rectangular plate are derived using Lagrange method based on appropriate in and out-of-plane spatial functions which satisfy the proposed boundary conditions. Although the proposed procedure is applicable for any arbitrary edge boundary conditions, only the simply supported plates are addressed in the present work. On the other hand, all inertial components of the moving mass are included in the derivation of the equations of motion. A numerical example is used to study the dynamic behavior of the plate, considering large deformations. The obtained results indicate that ignoring the geometric nonlinearity in determining the vertical deformations of plates under the effect of moving masses, especially those of considerable weight and velocity, results in excessively large linear amplitudes leading to an unfavorable conservative structural design.

Beschreibung: A new approach to the derivation of the theory of thermoviscoelasticity is proposed. Neither the hypothesis of fading memory nor rheological models are used within the framework of this approach. The proposed approach is based on the mechanical model of a one-rotor gyrostat continuum. In special cases, the mathematical description of this model is proved to reduce to the equations of the coupled problem of thermoelasticity, the self-diffusion equation, and the equation describing the flow of a viscous incompressible fluid. In the context of this model, we consider the original treatment of the physical nature of the mechanism of thermal conduction and internal damping. The first part of the paper contains the aforesaid theoretical results. The second part of the paper is devoted to the determination of some parameters of the model. On the base of the proposed theory, we obtain the dependence of the acoustic wave attenuation factor on a signal frequency. This dependence is in close agreement with the classical dependence in the low-frequency range and agrees with the dependence obtained on the base of the phonon theory in the hypersonic frequency range. We discuss some ways of determining of the volume and shear viscosities and the heat flow relaxation timescale by using known values of the sound velocity and the acoustic wave attenuation factor. The obtained values of the heat flow relaxation timescale are compared with the values derived from the phonon theory.

Beschreibung: In this paper, the stability of delay differential equations (DDEs), describing self-excited vibrations in a micro-milling process, is investigated based on semi-discretization (SD) method. Due to the stubby geometry of micro-tools, the shear deformation and rotary inertia effects are considered for modeling the structure. The extended Hamilton’s principle is used to derive a detailed dynamical model of the spinning micro-tool with the support of misalignment in which the gyroscopic effects cause coupling of equations. Considering the actual geometry of the micro-end mill, exact dynamic stiffness (DS) formulations are developed to investigate the tool’s free vibration characteristics. The extracted mode shapes obtained from DS method are utilized as base functions in a Galerkin approach. Having considered regenerative cutting force, imposing the Galerkin method reduces the governing PDEs of the system to a set of DDEs. The resulting equations are discretized by means of SD procedure. Finally, numerical Floquet theory is utilized to investigate the stability of the system. Also, the effects of process damping on the stability diagrams are explored. The results show the efficiency of the proposed model and delineate the considerable influence of process damping on the stability borders of the system especially at low spindle speed.

Beschreibung: A multiscale strategy is developed for the thermo-elastic plastic stress analysis of heterogeneous multiphase materials. The strategy is based on the extended multiscale finite element method (EMsFEM) and the enriched partition of unity approach. In the formulation, the enriched numerical base functions are adapted into the EMsFEM, which show good applicability to the local deformation pattern. Thus, the microscopic variable fields can be reproduced precisely, which are crucial for the nonlinear analysis. Numerical examples of two-phase heterogeneous media with regular and irregular microstructures demonstrate the validity and efficiency of the proposed method.

Beschreibung: The smooth orthogonal decomposition (SOD) method is one of the output only modal analysis methods, which is originally suggested for the undamped/lightly damped systems. In this paper, the error sources of the SOD method for damped vibrating systems have been investigated. Then, in order to improve the accuracy of SOD for modal analysis of damped systems, some modifications have been made on the traditional SOD algorithm, and instead of the forward two-point differential operator D , the central eight-point differential operator D m is used. In order to compare the accuracy of improved SOD and traditional SOD, the two methods are applied for vibration analysis of a discrete system subjected to the random white noise with the same excitation arrangement. The estimated results are compared with the exact solution obtained by the structural eigenvalue problem. The comparison reveals that the improved SOD is more accurate than the traditional SOD method. In addition, the effects of the excitation arrangement and the measurement noise on the estimated modal parameters are investigated.

Beschreibung: Hybrid reliability analysis (HRA) with both aleatory and epistemic uncertainties is investigated in this paper. The aleatory uncertainties are described by random variables, and the epistemic uncertainties are described by a probability-box ( p -box) model. Although tremendous efforts have been devoted to propagating random or p -box uncertainties, much less attention has been paid to analyzing the hybrid reliability with both of them. For HRA, optimization-based Interval Monte Carlo Simulation (OIMCS) is available to estimate the bounds of failure probability, but it requires enormous computational performance. A new method combining the Kriging model with OIMCS is proposed in this paper. When constructing the Kriging model, we only locally approximate the performance function in the region where the sign is prone to be wrongly predicted. It is based on the idea that a surrogate model only exactly predicting the sign of performance function could satisfy the demand of accuracy for HRA. Then OIMCS can be effectively performed based on the Kriging model. Three numerical examples and an engineering application are investigated to demonstrate the performance of the proposed method.

Beschreibung: This paper deals with the combined effect of pressure and geometric imperfection on buckling of stressed thin films on a semi-infinite rigid substrate. Analytical approximate solutions are proposed by using the total potential energy of the system and the Rayleigh–Ritz’s method, and their stabilities are also determined. The present analytical approximate solutions agree very well with the numerical solutions obtained via the improved shooting method. The effect of pressure mismatch together with imperfection on the critical stress (above which the film buckles) and on the film-center deflection is characterized. It is found that, compared with the classical case of the Euler column buckling, the equilibrium solutions and critical stress of the film are strongly dependent on the linear combination of the pressure mismatch and imperfection amplitude.

Beschreibung: Because of the production process and constraint conditions, a circular graphene sheet may be opposed to structural defect and pin hole, respectively. Some of the defects and pin hole on a circular graphene sheet can be considered as an eccentric hole. So, analyzing the behavior of a circular graphene sheet with an eccentric hole is important. Free vibration of an eccentric annular graphene sheet, as the basis of any dynamical analysis, is analytically studied in this paper. Nonlocal thin plate theory is used to model the problem. The translational addition theorem for cylindrical vector wave functions is employed to solve the equation of motion for various boundary conditions. Results are compared with the literature, and their accuracy is approved. Effects of boundary conditions, geometrical properties and nonlocal parameter changes on symmetric and antisymmetric vibrational modes are investigated. It is approved that the eccentricity has a significant effect on the natural frequencies. Also, symmetric and antisymmetric modes of an annular graphene sheet have different behavior when geometrical and nonlocal parameters change.

Beschreibung:    Solutions for the generalized forms of Burgers, Burgers–KdV, and KdV equations with time-dependent variable coefficients and with initial and boundary conditions are constructed. The analysis rests mainly on the standard group method. Similarity solutions are found which reduce the nonlinear system of partial differential equations to systems of ordinary differential equations to obtain some exact solutions and others as numerical solutions. Content Type Journal Article Pages 1-16 DOI 10.1007/s00707-011-0503-1 Authors Mina B. Abd-el-Malek, Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, 21544 Egypt Medhat M. Helal, Department of Engineering Mathematics and Physics, Faculty of Engineering, Zagazig University, Zagazig, Egypt Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The dynamics of grain fragmentation is usually ignored in the study of rapid granular flows. This is realistic for experiments on small-scale chutes or in many industrial processes where the specific granular energy is too small for particles to break but is unrealistic for natural rock avalanches, where the extremely comminuted state is perhaps the most evident aspect of the deposit. Based on observations of natural landslide deposits, it has been suggested that the stress may increase along a sequence of force chains formed by the granular material. However, simple calculations show that rock avalanche deposits exhibit a much more advanced degree of fragmentation than explainable with the static chain model. It is thus deduced that fragmentation along force chains must be combined with the effect of a bumpy topography. A simple model of a force chain moving on a rugged incline is then introduced, which exhibits increased fragmentation rate in the presence of a bumpy topography. It is shown that both the wave number and amplitude of the topographic undulations are significant in the efficiency of fragmentation. Content Type Journal Article Pages 1-8 DOI 10.1007/s00707-011-0504-0 Authors F. V. De Blasio, Department of Geosciences, University of Oslo, Oslo, Norway Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In the present work, we investigate the problem of multiple cracks on the interface between a piezoelectric layer and an orthotropic substrate. The method of dislocation simulation and singular integral equation are used to solve the crack problem. The theoretical derivation is verified by the classical result in a special case. Numerical results of the stress intensity factor are obtained, and thereby the effects of geometrical parameters and material orthotropy are surveyed. The optimal stiffness ratio of the orthotropic substrate is suggested for the purpose of interfacial fracture prevention, which is significant for the design and assessment of such a kind of smart structures. Content Type Journal Article Pages 1-12 DOI 10.1007/s00707-011-0506-y Authors Fei-Xiang Feng, Academy of Armored Force Engineering, Beijing, 100072 China Kang Yong Lee, School of Mechanical Engineering, Yonsei University, Seoul, 120-749 Republic of Korea Yong-Dong Li, Academy of Armored Force Engineering, Beijing, 100072 China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The stresses developed in a body due to a moving load causing fracture are an interesting problem of mechanics having its application toward the stability of a medium. This paper is concerned with the stresses developed in an irregular isotropic half-space due to a normal moving load at a rough free surface. The irregularity has been taken in the form of a parabola and a rectangular irregularity has also been discussed as a special case of parabolic irregularity. Closed-form expressions for the normal and shear stresses have been obtained. The effect of friction, irregularity factor, and maximum amplitude of irregularity has been discussed for both stresses. Content Type Journal Article Pages 1-10 DOI 10.1007/s00707-011-0507-x Authors A. Chattopadhyay, Department of Applied Mathematics, Indian School of Mines Dhanbad, Dhanbad, 826004 India S. Gupta, Department of Applied Mathematics, Indian School of Mines Dhanbad, Dhanbad, 826004 India V. K. Sharma, Defence R & D Organisation, ISSA LAB, Metclafe House, Delhi, 110054 India Pato Kumari, Department of Mathematics, JIIT Noida, Noida, 201307 India Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In a recent paper of Weidman and Sprague (Acta Mech., 2011 ), the unsteady flows generated by an impermeable infinite flat plate advancing with constant velocity V toward, or receding from an orthogonal (plane or axisymmetric) stagnation-point flow, have been investigated by an exact similarity reduction of the Navier–Stokes equations. It has been shown that in the co-moving reference frame of the plate, the induced flow appears as a steady flow, with an additional term R f ′′ in the governing equation of the similar stream function f ( η ). The Reynolds number R involved in this additional term is proportional to the plate velocity V . The present paper shows, however, that with the aid of a simple transformation, the additional term R f ′′ can be removed from the governing equation, its effect being transferred in the boundary condition for f ( η ). As a consequence, the unsteady flow problems of Weidman and Sprague reduce to the classical steady stagnation-point flow problems for permeable surfaces with a uniform lateral suction or injection of the fluid, so that the transpiration parameter f (0) coincides with R for the plane and with R /2 for the axisymmetric flow, respectively. The main benefit of this approach is that all the results of the latter well-investigated problems can simply be transcribed for the problems formulated by Weidman and Sprague (Acta Mech, 2011 ). Content Type Journal Article Pages 1-5 DOI 10.1007/s00707-011-0502-2 Authors Eugen Magyari, Departement Physik, Universität Basel, Klingelbergstr. 82, CH 4056 Basel, Switzerland Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper, free vibrations of symmetric angle-ply laminated cylindrical shells are presented under different thickness variations. The thickness variations of the shells are linear, exponential, and sinusoidal. Spline function techniques are adopted to approximate the displacement functions, and the point collocation method is used to obtain the generalized eigenvalue problem with appropriate boundary conditions. The effects of the geometric parameters, thickness parameters, and material parameters on the frequencies of symmetric angle-ply laminated cylindrical shells with two kinds of material properties under different boundary conditions are analyzed. Content Type Journal Article Pages 1-11 DOI 10.1007/s00707-011-0505-z Authors K. K. Viswanathan, Department of Naval Architecture and Ocean Engineering, Inha University, #253, Yonghyun dong, Nam ku, Inchon, 402-751 South Korea Jang Hyun Lee, Department of Naval Architecture and Ocean Engineering, Inha University, #253, Yonghyun dong, Nam ku, Inchon, 402-751 South Korea Zainal Abdul Aziz, Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia I. Hossain, Department of Physics, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In the proposed paper, a new problem on the steady-state oscillations of an elastic infinite cone is solved for the point oscillating force enclosed to a cone’s vertex. On a cone’s conic surface, the stresses are given. The auxiliary problem for a cone truncated by a spherical surface is formulated with the aim to obtain the solution of the initial problem. The solution is constructed with the help of the integral transformation method and the method of Green’s function. The limiting transition in the solution’s formulas is carried out to obtain the exact solution of the initial problem. The calculation of the displacements and the stress wave field of the cone is performed. Content Type Journal Article Pages 1-10 DOI 10.1007/s00707-011-0501-3 Authors G. Popov, Institute of Mathematics, Economics and Mechanics, Odessa Mechnikov University, str. Dvoryanskaya, 2, 65082 Odessa, Ukraine N. Vaysfel’d, Institute of Mathematics, Economics and Mechanics, Odessa Mechnikov University, str. Dvoryanskaya, 2, 65082 Odessa, Ukraine Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    Buoyancy-driven bubbles and drops are deformable and exhibit different boundaries from mobile to immobile. Owing to the complexity of these flows, the literature knows various scaling parameters for their description. This paper determines a set of parameters on the basis of the force balance equations. It identifies the Archimedes number as the leading parameter while the Reynolds number is considered a flow variable. This ordering scheme of parameters is applied to a set of new data on bubbles rising in five different silicon oils. Data representation and limiting cases come out consistently. The use of the Archimedes number leads even to a successful simple model for the normalized rise velocity. Content Type Journal Article Pages 1-14 DOI 10.1007/s00707-010-0431-5 Authors Franz Peters, Department of Mechanical Engineering, Chair of Fluid Mechanics, University of Bochum, Bochum, Germany Björn Gaertner, Department of Mechanical Engineering, Chair of Fluid Mechanics, University of Bochum, Bochum, Germany Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    Targeted energy transfer (TET) in a compound nonlinear 2 degrees-of-freedom system during free and forced excitations is studied analytically and numerically. The nonlinearity of the system is represented intentionally by a non-smooth piece-wise linear function for the sake of practical investigations. Further stability analysis of the system is demonstrated and commented upon and the behavior of the system during relaxation and its strongly modulated response is studied and pinpointed. Content Type Journal Article Pages 1-26 DOI 10.1007/s00707-011-0492-0 Authors Claude-Henri Lamarque, Université de Lyon, École Nationale des Travaux Publics de l’État, DGCB, FRE CNRS 3237, 3 rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, France Oleg V. Gendelman, Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, 32000 Technion City, Haifa, Israel Alireza Ture Savadkoohi, Université de Lyon, École Nationale des Travaux Publics de l’État, DGCB, FRE CNRS 3237, 3 rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, France Emilie Etcheverria, Université de Lyon, École Nationale des Travaux Publics de l’État, DGCB, FRE CNRS 3237, 3 rue Maurice Audin, 69518 Vaulx-en-Velin Cedex, France Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    Functionally graded materials are the materials whose material properties are smoothly varying along one axis, and they are used as buffer layers to connect two dissimilar materials. By choosing proper functionally graded parameters, the material properties at the interface can be identical to prevent the interfacial fracture problem. This study analyzes the heat conduction problem of nonhomogeneous functionally graded materials for a layer sandwiched between two half-planes. From the Fourier transform method, the full-field solutions of temperature and heat flux are obtained in explicit forms. Numerical calculations based on the analytical solutions are performed and are discussed in detail. The continuous characteristics of the temperature and heat flux along the interface are emphasized, and some interesting phenomena are presented in this study. It is noted that the temperature and heat flux fields along the interface for nonhomogeneous functionally graded materials are continuous if the conductivities are identical at the interface. Furthermore, the temperature and heat flux q y have the identical contour slopes across the interface. Content Type Journal Article Pages 1-15 DOI 10.1007/s00707-011-0498-7 Authors Chien-Ching Ma, Department of Mechanical Engineering, National Taiwan University, Taipei, 10617 Taiwan, ROC Yi-Tzu Chen, Department of Mechanical Engineering, National Taiwan University, Taipei, 10617 Taiwan, ROC Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung: Solutions are offered for a cylindrically orthotropic circular tube of finite length with radial inhomogeneity and subjected to torsional shear loads, and the end effects are emphasized in this study. By explicit expressions of the shear stresses, the actual stress distributions all over the body can be thoroughly examined. The concept of end effect coordinates is introduced to estimate the extent of an end effect when the trends and features are explored. According to the examples, when considering end surfaces subjected to a power-distributed shear load or a tangential ring shear load, the extent of an end effect is strongly dependent on material anisotropy. In general, for a given material anisotropy, variations of the longitudinal shear stress and transverse shear stress reveal different trends along the radial coordinate. The end effect extent of the longitudinal shear stress is larger on the cylindrical surfaces than inside the body, and it is larger on the inner surface than on the outer surface. Furthermore, while no end effects in the transverse shear stress are detected on both the inner and outer cylindrical surfaces, we cannot ignore them inside the tube body.

Beschreibung:    A general model is presented to unify the explanation of different meta-heuristic algorithms. This model is based on the concept of fields of forces from physics and covers many meta-heuristic algorithms consisting of Genetic Algorithms, Ant Colony Optimization, Particle Swarm Optimization, Big Bang–Big Crunch algorithm and Harmony Search. The properties of these algorithms can be explained using the presented general model that is called the fields of forces (FOF) model. This extension provides efficient means to improve, expand, modify and hybridize the meta-heuristic algorithms. An improved and hybridized algorithm is then developed using the FOF model. Content Type Journal Article Pages 1-20 DOI 10.1007/s00707-011-0494-y Authors A. Kaveh, Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran S. Talatahari, Department of Civil Engineering, University of Tabriz, Tabriz, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    An analytical approach for evaluating the forced vibration response of uniform beams with an arbitrary number of open edge cracks excited by a concentrated moving load is developed in this research. For this purpose, the cracked beam is modeled using beam segments connected by rotational massless linear elastic springs with sectional flexibility, and each segment of the continuous beam is assumed to satisfy Timoshenko beam theory. In this method, the equivalent spring stiffness does not depend on the frequency of vibration and is obtained from fracture mechanics. Considering suitable compatibility requirements at cracked sections and corresponding boundary conditions, characteristic equations of free vibration response are derived. Then, forced vibration response is treated under a moving load with a constant velocity. Using the determined eigenfunctions, the forced vibration response may be obtained by the modal superposition method. Finally, some parametric studies are presented to show the effects of crack parameters and moving load velocity. Content Type Journal Article Pages 1-19 DOI 10.1007/s00707-011-0495-x Authors M. Shafiei, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, P.O. Box 14115–397, Tehran, Iran N. Khaji, Faculty of Civil and Environmental Engineering, Tarbiat Modares University, P.O. Box 14115–397, Tehran, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    A 3-D, dynamic, non-linear Finite Element Model (FEM) involving contact is used to determine apparent coefficients of friction,  μ , for the interaction between the bristles of a flicking brush for street sweeping and concrete. Also, brush contact arcs, as well as suitable brush penetrations as functions of the debris height, are determined for cutting and F128 brushes. Available experimental results are used to determine the coefficients of friction. The bristles are modelled through beam elements, which are subjected to inertia forces. The results suggest that the model is valid and that the coefficient of friction affects the brush vertical force in the flicking brush, but it does not significantly affect its counterpart in the cutting brush. The results also indicate that the coefficient of friction for the flicking brush depends on the sliding velocity, v , and these were fitted to an exponential  μ − v curve. Content Type Journal Article Pages 1-14 DOI 10.1007/s00707-011-0490-2 Authors L. V. Vanegas-Useche, Facultad de Ingeniería Mecánica, Universidad Tecnológica de Pereira, La Julita, Pereira, Colombia M. M. Abdel-Wahab, Department of Mechanical Construction and Production, Faculty of Engineering, Ghent University, 9000 Ghent, Belgium G. A. Parker, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, Surrey, GU2 7XH UK Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this article, we use the small strain micromorphic plasticity (MP) to study the wedge indentation of a thin film on a substrate and find qualitative agreement with experiments. A two-dimensional plane strain finite element formulation of the entire MP theory framework is outlined. The generalization of the radial return method for modeling the elasto-plastic deformation is presented. The numerical results show that the MP theory is capable of describing the initial fall in hardness at small depth of indentation and then the rise at larger depth for a soft film on a hard substrate. The indentation force and hardness increase with decreasing film thickness for a given depth. It is also shown that the hardness falls monotonically as the indentation depth increases and never approaches a constant for a hard film on a soft substrate. Contrary to the soft film/hard substrate system, the force and hardness diminish with decreasing film thickness for a given depth. Besides, the influences of internal length scale and hardening modulus of the film on hardness predictions are investigated. Content Type Journal Article Pages 1-13 DOI 10.1007/s00707-011-0483-1 Authors Z. H. Zhang, Applied Mechanics Lab., School of Aerospace, Tsinghua University, Beijing, 100084 China Z. L. Liu, Applied Mechanics Lab., School of Aerospace, Tsinghua University, Beijing, 100084 China X. M. Liu, Applied Mechanics Lab., School of Aerospace, Tsinghua University, Beijing, 100084 China Y. Gao, Applied Mechanics Lab., School of Aerospace, Tsinghua University, Beijing, 100084 China Z. Zhuang, Applied Mechanics Lab., School of Aerospace, Tsinghua University, Beijing, 100084 China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    We study the initiation and propagation of a vertical crack in an elastic semi-infinite plate, reinforced on its boundary by an infinite discontinuous stringer within the limits of the theory of brittle failure. The plate is subjected to uniform distributed tensile forces at infinity, as well as to contact stresses due to application of forces to the stringer. We find the appropriate loading of the coherent stringer, and consequently we consider a problem where the stringer is cracked and a vertical crack has developed within the plate. We deduce the exact analytical solution for the principal singular integral equation for this case; hence the stringer is perfectly rigid and we calculate characteristic parameters of the problem. The results show that the crack tip has a logarithmic singularity, and the tangential contact stresses under the stringer at that end point are finite and generally differ from zero. Content Type Journal Article Pages 1-28 DOI 10.1007/s00707-011-0473-3 Authors Dimosthenis I. Bardzokas, National Technical University of Athens, Athens, Greece S. M. Mkhitaryan, Institute of Mechanics, National Academy of Sciences of Republic of Armenia, 24b Marshal Baghramianave., Erevan, 0019 Republic of Armenia Georgios I. Sfyris, National Technical University of Athens, Athens, Greece Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    This paper discusses the effect of shear deformation of the cross-section on the contact behavior of a buckled Timoshenko beam in frictionless contact with a rigid plane wall. The deformation is assumed to be small, and only planar deformation is considered. The results are compared with those from the Euler beam model. In the case when a buckled Euler beam is in line contact with a plane wall, the plane wall exerts concentrated forces at the boundary points of the line-contact segment but no distributed force. In the case of a Timoshenko beam, on the other hand, the concentrated forces are replaced by a distributed contact force. The distribution of the contact force approaches the two concentrated forces at the boundary points when the shear effect is negligible. The line-contact deformation may become unstable when the edge thrust reaches a secondary buckling load. It is found that the normalized critical length of the contact segment is always smaller when the shear effect is more significant. On the other hand, the normalized secondary buckling load reaches a maximum when the slenderness ratio (beam length over thickness) is in the order of 45. Content Type Journal Article Pages 1-8 DOI 10.1007/s00707-011-0529-4 Authors Jen-San Chen, Department of Mechanical Engineering, National Taiwan University, Taipei, 10617 Taiwan Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The first passage failure of multi-degree-of-freedom (MDOF) quasi-integrable Hamiltonian systems with damping described by a fractional derivative is studied. The stochastic averaging procedure is applied to derive the averaged equations for first integrals. The conditional reliability function and the conditional mean of first passage failure time are obtained by solving the associated backward Kolmogorv equation and Pontryagin equation together with suitable boundary conditions and initial condition, respectively. One example of two coupled nonlinear oscillators with fractional derivative damping is given to illustrate the proposed procedure. The accuracy of the method is substantiated by comparing the analytical results with those from Monte Carlo simulation. Effects of some parameters of fractional order, damping coefficients and nonlinear strength on the system’s reliability are examined. Content Type Journal Article Pages 1-16 DOI 10.1007/s00707-011-0533-8 Authors Lincong Chen, College of Civil Engineering, Huaqiao University, Xiamen, 361021 China Qingqu Zhuang, College of Mathematical Science, Huaqiao University, Quanzhou, 362021 China Weiqiu Zhu, Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, 310027 China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    This paper presents the stochastic elastic modulus reduction method for system reliability analysis of spatial variance frames based on the perturbation stochastic finite element method (PSFEM) and the local average of a random field. The stochastic responses and reliability index of each element of a structural frame are characterized by the PSFEM and the first-order second-moment method, to properly handle the correlation structures and scale of fluctuation of random fields. A strategy of elastic modulus adjustment for the estimation of system reliability is developed to determine the range and magnitude of elastic modulus reduction, by taking the element reliability index as a governing parameter. The collapse mechanism and system reliability index of a stochastic framed structure are determined through iterative computations of the PSFEM. Compared with the failure mode approaches in traditional system reliability analysis, the proposed method avoids two major difficulties, namely the identification of significant failure modes and estimation of the joint probability of failure modes. The influences of the correlation structure and scale of fluctuation of the random field upon system reliability are investigated to demonstrate the accuracy and computational efficiency of the proposed methodology in system reliability analysis of spatial variance frames. Content Type Journal Article Pages 1-16 DOI 10.1007/s00707-011-0546-3 Authors Lu Feng Yang, Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil Engineering and Architecture, Guangxi University, Nanning, 530004 China Bo Yu, Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, School of Civil Engineering and Architecture, Guangxi University, Nanning, 530004 China J. Woody Ju, Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095, USA Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The large amplitude free vibration of a laminated composite parabolic plate with parabolically orthotropic plies is investigated for the first time. The effects of out-of-plane shear deformations, rotary inertia, and geometrical nonlinearity are taken into account. The geometry of the plate is described, and the analysis performed in the parabolic coordinate system. The problem is solved numerically using a new parabolic hierarchical finite element. The nonlinear equations of free motion are mapped from the time domain into the frequency domain using the harmonic balance method. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. Results for the fundamental linear and nonlinear frequencies are obtained for symmetric and antisymmetric laminates with clamped and simply supported edges. Comparisons are made with the finite element method for clamped and free isotropic parabolic plates and show excellent agreement. The aspect ratio, thickness ratio, moduli ratio, number of plies, layup sequence, and boundary conditions are shown to affect the hardening behavior. Content Type Journal Article Pages 1-16 DOI 10.1007/s00707-011-0550-7 Authors Abderrahim Houmat, Faculty of Engineering, Department of Mechanical Engineering, University of Tlemcen, B.P. 230, 13000 Tlemcen, Algeria Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    This paper deals with the formulation of an analytical model for the dynamic behavior of anisotropic plates, with an arbitrarily located internal line hinge with elastic supports and piecewise smooth boundaries elastically restrained against rotation and translation among other complicating effects. The equations of motion and its associated boundary and transition conditions are derived using Hamilton’s principle. By introducing an adequate change of variables, the energies that correspond to the different elastic restraints are handled in a general framework. The concept of transition conditions and the determination of the analytical expressions are presented. Analytical examples are worked out to illustrate the range of applications of the developed analytical model. One of the essential features of this work is to demonstrate how the commonly formal derivations used in the applications of the calculus of variations can be made rigorous. Content Type Journal Article Pages 1-20 DOI 10.1007/s00707-011-0552-5 Authors Ricardo Oscar Grossi, INIQUI-CONICET, Facultad de Ingeniería, Universidad Nacional de Salta, Avenida Bolivia 5150, Salta, República Argentina Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    We solve the linear resisted projectile motion problem using the Lambert W function. In the problem, the launching point is higher than the landing point. The explicit solutions for the range and optimal angle of elevation are expressed in terms of the Lambert W function. The two conclusions can be made for the same projectile: (i) The higher the launching point, the larger the range is. (ii) The higher the launching point, the smaller the optimal angle is. Content Type Journal Article Category Note Pages 1-7 DOI 10.1007/s00707-011-0571-2 Authors H. Hu, School of Civil Engineering, Hunan University of Science and Technology, Xiangtan, Hunan 411201, People’s Republic of China Y. P. Zhao, School of Civil Engineering, Hunan University of Science and Technology, Xiangtan, Hunan 411201, People’s Republic of China Y. J. Guo, School of Civil Engineering, Hunan University of Science and Technology, Xiangtan, Hunan 411201, People’s Republic of China M. Y. Zheng, School of Civil Engineering, Hunan University of Science and Technology, Xiangtan, Hunan 411201, People’s Republic of China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    This paper deals with the study of mechanical behavior of a circular functionally graded material (FGM) micro-plate subjected to a nonlinear electrostatic pressure and mechanical shock. It is assumed that the FGM micro-plate is made of metal and ceramic and that material properties are changed continuously along the plate thickness according to a typical function. The nonlinear equation of static deflection and dynamic motion is solved using a step-by-step linearization method and Galerkin-based reduced order model, respectively. In order to find the response of the FGM micro-plate to the electrostatic load and analyze stability of fixed points, static deflection, time history and phase portrait for different applied voltages and initial conditions are illustrated and the effects of different percentages of metal and ceramic constituent on the response of the system are investigated. In addition, effects of mechanical shocks characteristics (amplitudes and durations) on the stability of FGM micro-plate are studied. Content Type Journal Article Pages 1-13 DOI 10.1007/s00707-011-0576-x Authors Naser Sharafkhani, Mechanical Engineering Department, Urmia University, Urmia, Iran Ghader Rezazadeh, Mechanical Engineering Department, Urmia University, Urmia, Iran Rasool Shabani, Mechanical Engineering Department, Urmia University, Urmia, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The paper presents exact non-reflecting boundary conditions for transient plane waves in an anisotropic elastic solid for oblique incidence. The boundary conditions are expressed through the eigenvectors of the acoustic tensor and are written in impedance form as a relation between the velocity vector and the traction vector. The approach is extended to anisotropic fluid-saturated porous solids. Exact plane-wave non-reflecting boundary conditions are derived for transient non-dissipative waves in a medium with infinite or zero permeability, and for steady-state dissipative waves. Content Type Journal Article Pages 1-15 DOI 10.1007/s00707-011-0583-y Authors V. A. Osinov, Institute of Soil Mechanics and Rock Mechanics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    A contact model between a homogeneous half-space with a linearly graded layer and a rigid punch is proposed and studied in the present paper. The governing equation, which describes the relation of the displacements and the normal tractions at the contact interface, is obtained by means of Fourier transform and a transfer matrix method. Appropriate collocation methods are used in order to solve the equation numerically. Singular behaviors at the edge of a flat punch are revealed. Compared to the case with a graded surface varying according to an exponential law, stress concentration is relatively weaker in the case with the graded surface varying according to a linear law. Furthermore, stress distributions in cases of a flat or cylindrical punch are given for different varying graded laws, thickness of graded layer, ratios of stiffness, and frictional coefficients. All the results are helpful for the design of strong and wear resistance coating surfaces. Content Type Journal Article Pages 1-15 DOI 10.1007/s00707-011-0581-0 Authors Peijian Chen, LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190 China Shaohua Chen, LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190 China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The propagation of transient SH-waves in a plate is discussed. An SH-wave source is placed on a fixed edge of the plate and the other edge moves outward with uniform velocity. Two Laplace transforms in fixed and moving coordinate systems are employed. Developing an exchange formula between two Laplace transforms, a coupled functional equation for two unknown coefficients is derived and solved by iteration. The solution obtained here is exact up to three reflection times of an incident (source) wave, and the time-development of the wave front shape is also discussed. Content Type Journal Article Pages 1-14 DOI 10.1007/s00707-012-0631-2 Authors Kazumi Watanabe, Department of Mechanical Engineering, Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510, Japan Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The first part of the article presents a motion analysis of a vibro-impact system based on an oscillator moving along a rough circle line in a vertical plane, under the action of an external single-frequency force. Non-ideality of the bond originates of sliding Coulomb’s type friction force with coefficient  μ  =  tg α 0 . The oscillator consists of one heavy mass particle whose forced motion is limited by one stabile angular elongation limiter. The differential equation of motion of the analyzed vibro-impact system cannot be solved explicitly (in closed form). For its approximately solving, the software package WOLFRAM Mathematica 7 is used. The results are checked by using the software package MATLAB R2008a. The combination of the analytical–numerical results for the defined parameters of the analyzed vibro-impact system, is base for the motion analysis visualization, as a first part of this analytic research. In the second part, the influence of parameters (amplitude and circle frequency) of the external single-frequency force to the system motion, based on real geometry and kinetic parameters of the analyzed vibro-impact system, is investigated. As a result of this study in the second part of this article, there is a conclusion that the motion of the analyzed vibro-impact system in or out of the resonant area can be influenced, and this is significant for engineering practice. Content Type Journal Article Pages 1-16 DOI 10.1007/s00707-012-0623-2 Authors Srđan Jović, Faculty of Technical Sciences, Kralja Petra I br. 149/12, Kosovska Mitrovica, 38 220 Serbia Vladimir Raičević, Faculty of Technical Sciences, Kralja Petra I br. 149/12, Kosovska Mitrovica, 38 220 Serbia Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper, a symmetric Galerkin boundary element formulation for 3D linear poroelasticity is presented. By means of the convolution quadrature method, the time domain problem is decoupled into a set of Laplace domain problems. Regularizing their kernel functions via integration by parts, it is possible to compute all operators for rather general discretizations, only requiring the evaluation of weakly singular integrals. At the end, some numerical results are presented and compared with a collocation BEM. Throughout these studies, the symmetric Galerkin BEM performs better than the collocation method, especially for not optimal discretizations parameters, i.e. a bad relation of mesh to time-step size. The most obvious advantages can be observed in the fluid flux results. However, these advantages are obtained at a higher numerical cost. Content Type Journal Article Pages 1-18 DOI 10.1007/s00707-012-0637-9 Authors Michael Messner, Institute of Applied Mechanics, Graz University of Technology, Technikerstraße 4, 8010 Graz, Austria Martin Schanz, Institute of Applied Mechanics, Graz University of Technology, Technikerstraße 4, 8010 Graz, Austria Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper, a parametrically resonated MEMS gyroscope is considered, and the effect of its parameters on the system stability is studied. Unlike the general case of MEMS gyroscopes with harmonic excitation, in this new class of gyroscopes with parametric excitation, the origin is one stationary point of the system. The study starts with the stability analysis of the origin, and then it goes on to analyze the effect of each parameter on the stability of periodic orbits. Stabilities are studied by means of Floquet theory. As the results indicate, presence of a non-trivial response for the system is closely interconnected to the stabilities (and instabilities) of the system. It is demonstrated that the stability of the origin always contributes to a zero response for the sensor, and hence the instability of origin is required for the occurrence of parametric resonance. In contrast, stability of a periodic orbit does not necessarily guarantee a resonant response for the gyroscope, and again it is the instability of the origin which is required for this purpose. Because in the case of linear stiffness—linear parametric excitation the instability of the origin results in instability of the system, it is concluded that nonlinearities are required for a parametrically actuated gyroscope. Content Type Journal Article Pages 1-17 DOI 10.1007/s00707-011-0609-5 Authors Ali Pakniyat, Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, PO Box 11155-9567, Tehran, Iran Hassan Salarieh, Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, PO Box 11155-9567, Tehran, Iran Aria Alasty, Center of Excellence in Design, Robotics and Automation (CEDRA), School of Mechanical Engineering, Sharif University of Technology, PO Box 11155-9567, Tehran, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper the dynamic response of compound bridges under moving loads is analyzed. The main structure is modeled as a two-layer beam consisting of a steel girder connected elastically to the concrete deck. The governing sixth-order partial differential equation of motion of the homogenized beam is extended to include uncertainty in the mechanical property of the interface. The slip modulus is considered to be a random variable, whose probability density function is considered to be zero outside of a given interval, that is, it is a member of a fuzzy set with bounded uncertainty. The analysis of the illustrative problem is based on the interval representation with a triangular membership function of the slip modulus assigned. Membership functions of the random natural frequencies are determined. Both, fuzzy peak deflection and acceleration are derived for a single-span compound bridge subjected to a single moving load as well as to a series of repetitive moving loads traveling with constant speed. Content Type Journal Article Pages 1-15 DOI 10.1007/s00707-012-0641-0 Authors C. Adam, Unit of Applied Mechanics, University of Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria R. Heuer, Center of Mechanics and Structural Dynamics, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria F. Ziegler, Center of Mechanics and Structural Dynamics, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    Transverse vibration of the shear beams containing rotary inertia and with a two-parameter elastic foundation is studied. Using asymptotic analysis of Timoshenko beam theory, we derive explicit characteristic equations of the nonclassical shear beams with Winkler-Pasternak elastic restraint and with both ends linked to translational and rotational springs. The condition of the nonclassical shear beams reducing to the classical ones is found. Natural frequencies of the nonclassical modes are evaluated for free- and pinned-elastically restrained shear beams with or without bracing. The influences of elastic restraint stiffness and rotary inertia on the natural frequencies are discussed. Some extreme cases can be recovered from the present. The obtained results are helpful in the design of a tall frame building. Content Type Journal Article Pages 1-14 DOI 10.1007/s00707-011-0604-x Authors X.-F. Li, School of Civil Engineering, Central South University, Changsha, 410075 Hunan, China G.-J. Tang, College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha, 410073 Huan, China Z.-B. Shen, College of Aerospace and Materials Engineering, National University of Defense Technology, Changsha, 410073 Huan, China K. Y. Lee, School of Mechanical Engineering, Yonsei University, Seoul, 120-749 Korea Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    Suspensions of two-dimensional buoyant drops in Poiseuille flow are studied at nonzero Reynolds numbers by numerical simulations. The flow is studied as a function of the Froude number, the Reynolds number, the Capillary number and the density ratio. First, the lateral migration of a drop is studied. Results agree with two-dimensional simulations of solid circular cylinders by Feng et al. (J Fluid Mech 261:95–134, 1994 ; J Fluid Mech 277:271–301, 1994 ) qualitatively. At a relatively large Reynolds number (120) and a moderate Froude number (43), a drop shows oscillations across the channel and does not obtain a stable equilibrium position. Simulations are also performed at low and moderate area fractions (0.22, 0.44). It is found that the effective viscosity strongly depends on the Froude number for heavy drops ( α 〉 1). The effective viscosity changes with the Froude number for light drops as well ( α 〈 1), but to a lower extent. The distribution and the fluctuation energy of drops across the channel are non-uniform for buoyant drops that depend on the Froude number. The density ratio also affects the distribution and fluctuation energy of drops across the channel. The effect of the Reynolds number on the effective viscosity of the suspension is also investigated. Content Type Journal Article Pages 1-18 DOI 10.1007/s00707-012-0765-2 Authors H. Khalili, Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran S. Mortazavi, Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper a new graph-based evolutionary algorithm, gM-PAES, is proposed in order to solve the complex problem of truss layout multi-objective optimization. In this algorithm a graph-based genotype is employed as a modified version of Memetic Pareto Archive Evolution Strategy (M-PAES), a well-known hybrid multi-objective optimization algorithm, and consequently, new graph-based crossover and mutation operators perform as the solution generation tools in this algorithm. The genetic operators are designed in a way that helps the multi-objective optimizer to cover all parts of the true Pareto front in this specific problem. In the optimization process of the proposed algorithm, the local search part of gM-PAES is controlled adaptively in order to reduce the required computational effort and enhance its performance. In the last part of the paper, four numeric examples are presented to demonstrate the performance of the proposed algorithm. Results show that the proposed algorithm has great ability in producing a set of solutions which cover all parts of the true Pareto front. Content Type Journal Article Pages 1-22 DOI 10.1007/s00707-012-0754-5 Authors A. Kaveh, Centre of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran K. Laknejadi, Centre of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    For a dynamical system in phase space, a new Lie symmetrical method to find a conserved quantity is presented in a general infinitesimal transformation of Lie groups. Based on the invariance of the differential equations of motion for the system under a general infinitesimal transformation of Lie groups, the Lie symmetrical determining equations are obtained. Then, an important relationship that reveals the interior properties of a dynamical system in phase space is given. By using the relationship, a Lie symmetrical basic integral variable relation and a new Lie symmetrical conservation law for the dynamical system in phase space are given. The new conserved quantity is constructed in terms of the infinitesimal generators of Lie symmetry and the system itself without solving the structural equation. Furthermore, the method is applied in the Hamiltonian system, the nonconservative Hamiltonian system and the nonholonomic Hamiltonian system. Finally, one example is given to illustrate the method and results of the application. Content Type Journal Article Pages 1-12 DOI 10.1007/s00707-012-0729-6 Authors Shao-Kai Luo, Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018 People’s Republic of China Zhuang-Jun Li, Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018 People’s Republic of China Lin Li, Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018 People’s Republic of China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper, a new type of hybrid fundamental solution-based finite element method (HFS-FEM) is developed for analyzing plane piezoelectric problems with defects by employing fundamental solutions (or Green’s functions) as internal interpolation functions. The hybrid method is formulated based on two independent assumptions: an intra-element field covering the element domain and an inter-element frame field along the element boundary. Both general elements and a special element with a central elliptical hole or crack are developed in this work. The fundamental solutions of piezoelectricity derived from the elegant Stroh formalism are employed to approximate the intra-element displacement field of the elements, while the polynomial shape functions used in traditional FEM are utilized to interpolate the frame field. By using Stroh formalism, the computation and implementation of the method are considerably simplified in comparison with methods using Lekhnitskii’s formalism. The special-purpose hole element developed in this work can be used efficiently to model defects such as voids or cracks embedded in piezoelectric materials. Numerical examples are presented to assess the performance of the new method by comparing it with analytical or numerical results from the literature. Content Type Journal Article Pages 1-21 DOI 10.1007/s00707-012-0741-x Authors Changyong Cao, Research School of Engineering, Australian National University, Canberra, ACT 0200, Australia Aibing Yu, School of Materials Science and Engineering, University of New South Wales, Sydney, NSW 2052, Australia Qing-Hua Qin, Research School of Engineering, Australian National University, Canberra, ACT 0200, Australia Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper, a bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping is proposed. First, the partially averaged Itô equations for the energy processes of individual degree of freedom are derived by using the stochastic averaging method. Second, the dynamical programming equations for the control problems of maximizing the reliability function and maximizing the mean first passage time are established from the partially averaged Itô equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equation and control constraints. Third, the conditional reliability function and mean first passage time of the optimally controlled system are obtained by solving the backward Kolmogorov equation and Pontryagin equation associated with the fully averaged Itô equation, respectively. The application of the proposed procedure and effectiveness of the control strategy are illustrated by using two examples. Besides, the effect of fractional derivative order on the reliability of the optimally controlled system is examined. Content Type Journal Article Pages 1-19 DOI 10.1007/s00707-012-0722-0 Authors Lincong Chen, College of Civil Engineering, Huaqiao University, Xiamen, 361021 China Qun Lou, College of Civil Engineering, Huaqiao University, Xiamen, 361021 China Qingqu Zhuang, College of Mathematical Science, Huaqiao University, Quanzhou, 361021 China Weiqiu Zhu, State Key Laboratory of Fluid Power Transmission and Control, Department of Mechanics, Zhejiang University, Hangzhou, 310027 China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper, a dual criterion of stochastic linearization method is developed for multi-degree-of-freedom systems subjected to random excitation. A closed system is obtained for determining coefficient matrices of the linearized system. Two examples of two-degree-of-freedom systems subjected to random excitation are presented. The mean-square responses obtained by the dual approach are compared with those obtained by two other methods, namely, conventional linearization technique and energy method. The results show that the dual criterion gives a good prediction on mean-square responses of the original nonlinear system when the nonlinearity is increasing. Content Type Journal Article Pages 1-18 DOI 10.1007/s00707-012-0738-5 Authors N. D. Anh, Institute of Mechanics, 264, Doi Can, Ba Dinh, Hanoi, Vietnam V. L. Zakovorotny, Don State Technical University, 1 Gagarin Sq., Rostov-on-Don, Russia N. N. Hieu, Institute of Mechanics, 264, Doi Can, Ba Dinh, Hanoi, Vietnam D. V. Diep, Institute of Military Vehicle, Hanoi, Vietnam Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    A new multi-layered model is developed for the fracture analysis of a functionally graded interfacial zone with arbitrary material properties. It is assumed that the interfacial zone is divided into sub-layers with the material properties of each sub-layer varying in a power-law function. The model is used to study the crack problem in the functionally graded interfacial zone between two homogeneous half-planes under a dynamic anti-plane load. Using Fourier–Laplace transforms and the transfer matrix method, the mixed boundary value problem is reduced to a Cauchy singular integral equation, which is solved numerically in the Laplace transform domain. Laplace numerical inversion transform is employed to obtain the stress intensity factors. The results show that the new model is general and effective for the crack problem of the functionally graded interfacial zone with arbitrary properties. Content Type Journal Article Pages 1-12 DOI 10.1007/s00707-012-0734-9 Authors Ke Di, Xi’an Hi-Tech Institute, 601 staff room, Xi’an, 710025 Shanxi, China Yue-Cheng Yang, Xi’an Hi-Tech Institute, 601 staff room, Xi’an, 710025 Shanxi, China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    High-temperature oxidation of metals induces residual stresses both in the metals and in the growing oxide scales. In this work, considering the case of asymmetric oxidation, a new analysis model to elucidate the residual stress evolutions in an oxide scale/metal substrate system during an isothermal oxidation process is developed. Elastic and creep deformations in both oxide and metal phases are considered in this work. The oxidation growth strain generated in oxide scale is also taken into account and is described by the Clarke model, that is, the growth strain rate increases linearly with the oxide thickening rate during isothermal oxidation. A comprehensive numerical study is carried out by the present approach. Results reveal that the proposed model can lead to an excellent agreement with the published experimental results and thus well validate the present model. Effects of the growth parameter, creep constants, Young’s modulus, and substrate thickness on the residual stress evolutions in the oxide scale/metal substrate system have also been discussed. Content Type Journal Article Pages 1-11 DOI 10.1007/s00707-012-0739-4 Authors J. L. Ruan, AML, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084 China Yongmao Pei, LTCS, College of Engineering, Peking University, Beijing, 100871 China Daining Fang, LTCS, College of Engineering, Peking University, Beijing, 100871 China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    A modified Michens iteration procedure and a direct Michens iteration procedure are applied to determine approximate periods and analytical approximate periodic solutions of a class of nonlinear jerk equations. When we use the modified Michens iteration procedure to deal with the nonlinear jerk equations, we need to solve the nonlinear algebra equation for determining the approximate angular frequency. The higher the number of iterations, the more difficult it is to deal with the nonlinear algebra equation. This is because the k th-order approximate solution obtained by the modified Michens iteration procedure is a function of the angular frequency. However, since the k th-order approximate solution obtained by the direct Michens iteration procedure is independent on the k th-order approximate angular frequency, the form of nonlinear algebra equation that determines the k th-order approximate angular frequency of nonlinear jerk equation is similar. The second-order approximate period obtained by the direct Michens iteration procedure provides very accurate results for the large initial velocity amplitudes. But the second-order approximate period obtained by the modified Michens iteration procedure is invalid for all amplitudes B of the initial velocity. A comparison of the first- and second-order approximate periodic solutions obtained by the direct Michens iteration procedure with the numerically exact solutions shows that the second-order approximate periodic solution is much more accurate than the first one. Thus, the direct Michens iteration procedure is very effective for the class of nonlinear jerk equations. Content Type Journal Article Category Note Pages 1-9 DOI 10.1007/s00707-012-0723-z Authors M. Y. Zheng, State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082 Hunan, People’s Republic of China B. J. Zhang, State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082 Hunan, People’s Republic of China N. Zhang, State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082 Hunan, People’s Republic of China X. X. Shao, State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082 Hunan, People’s Republic of China G. Y. Sun, State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082 Hunan, People’s Republic of China Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    A micromechanics-based analytical model is developed to evaluate the performance of 1–3–2 piezoelectric composite where both matrix and fiber materials are piezoelectrically active. A parametric study is conducted to investigate the effects of variations in the poling characteristics of the fiber phase on the overall thermo-electro-mechanical behavior of a 1–3–2 piezocomposite. The performance of the 1–3–2 composite as a transducer for underwater and biomedical imaging applications is analyzed. The proposed model is capable of predicting the effective properties of the composite subjected to thermo-electro-mechanical loading conditions. The predicted variations in the effective elastic, piezoelectric and dielectric material constants with fiber volume fraction are nonlinear in nature. It is observed that the influence of thermal effects on effective properties of the composite also induces polarization in the composite. The analytical results show that an appropriate selection of the poling characteristics of the individual fiber and matrix phases could lead to the development of a piezocomposite with significant effective properties. Content Type Journal Article Pages 1-17 DOI 10.1007/s00707-012-0652-x Authors M. Sakthivel, Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600 036 India A. Arockiarajan, Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600 036 India Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this study, a stress analysis of a substrate coated by nanomaterials with a vacancy under uniform extension load is investigated. The behavior of the coated substrate is modeled with the behavior of a two-layered beam, in which one of the layers is elastic and described by the continuous medium and the second layer consists of a nanomaterial with damage of a vacancy. The extension of the coating is carried out by stretching of the first layer, which lies on the substrate and by the cohesive forces between the layers. It is assumed that vacancies do not vary along the width of the substrate. The constitutive equations of the first layer (i.e., an elastic substrate) are given in the framework of Hooke’s law and the constitutive equations of the second layer; that is, the coating is carried out by taking into account discreteness of the nanomaterial with a vacancy. The expressions for the determination of the contact pressure and stresses of the substrate with a nanocoating that have vacancies are obtained. In addition, damage conditions for the substrate and nanocoating are determined. Finally, carrying out some computations, effects of the characteristics of a nanocoating with and without vacancies on the values of contact pressure and stresses of the coated substrate have been studied. Content Type Journal Article Pages 1-13 DOI 10.1007/s00707-012-0649-5 Authors A. N. Alizada, Department of Applied Mechanics, Azerbaijan State Marine Academy, Baku, Azerbaijan A. H. Sofiyev, Department of Civil Engineering, Suleyman Demirel University, 32260 Isparta, Turkey N. Kuruoglu, Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Bahcesehir University, Istanbul, Turkey Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this paper, a laminated composite plate is analyzed using a multiscale method. At first, material properties of a lamina are obtained using an analytical micromechanical approach called simplified unit cell method (SUCM), and then in structural level, the generalized differential quadrature method (GDQM) is used to analyze a laminated composite plate. By means of the Boltzmann superposition principle, the viscoelastic behavior of the matrix is obtained. The Prony series is considered to define the compliance of matrix. To verify the results, graphiteT300/epoxy5208 composite material is analyzed and the results are compared with existing experimental data. The multiscale algorithm includes obtaining overall properties of the composite by SUCM; then, these properties are used to define the bending stiffness. Governing equations of motion of laminated composite plate are solved via GDQM and Newton–Raphson method. Variations of stresses and displacements versus time and volume fraction of the fibers are shown for laminated composite plates with different boundary conditions. Content Type Journal Article Pages 1-18 DOI 10.1007/s00707-012-0710-4 Authors Saeed Masoumi, Amirkabir University of Technology, Tehran, Islamic Republic of Iran Manouchehr Salehi, Amirkabir University of Technology, Tehran, Islamic Republic of Iran Mehdi Akhlaghi, Amirkabir University of Technology, Tehran, Islamic Republic of Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    We recover an unknown space–time-dependent force in an Euler–Bernoulli beam vibration equation by an effective combination of the Lie-group adaptive method (LGAM) and the differential quadrature method (DQM). The layer-stripping technique is used to simplify this identification problem. The DQM is a feasible tool to semi-discretize the Euler–Bernoulli beam equation into a system of ordinary differential equations (ODEs) in time. Then, we can develop a two-point Lie-group equation to recover the unknown force through a few iterations. The success of the present method hinges on a rationale that the local in time ODEs and the global in time algebraic Lie-group equation have to be self-adapted during the iteration processes . The feasibility, accuracy and efficiency of the present method are assessed by comparing the estimated results with some exact solutions. Content Type Journal Article Pages 1-17 DOI 10.1007/s00707-012-0707-z Authors Chein-Shan Liu, Department of Civil Engineering, National Taiwan University, Taipei, Taiwan Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this article, a set of equivalent variational formulations for computing the driving forces for domain switching in ferroelectric materials is presented. It is proven that these formulations allow the free adoption of any couple of mechanical and electric fields as independent variables while obtaining consistent results. In addition, explicit expressions are provided for each formulation which allows for the study of the phase transformation process under different constraints. Content Type Journal Article Pages 1-14 DOI 10.1007/s00707-012-0702-4 Authors S. F. Zheng, Google Inc., 76 9th Avenue, New York, NY 10011, USA E. A. Tuncer, Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA A. M. Cuitiño, Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    Structures may fail due to a myriad of different causes. Often, distinction is made between structural and material failure, that means a structure can fail, while the material is still intact (this is the case in so-called stability loss), or the material fails, which, as consequence, may lead to structural failure. The material behavior may turn out difficult to be mathematically guessed at the macro-level. On the other hand, a lot may be known about the chemistry or the microstructure of the material of interest. Herein, we aim at categorizing different scenarios which in the end provoke structural failure, discussing various cases investigated during the last five years, at the Institute for Mechanics of Materials and Structures of Vienna University of Technology: A well-chosen eigenvalue problem shows considerable potential for categorizing stability loss. We then turn to complex composite materials with a hierarchical organization, where a single constituent dominates the overall quasi-brittle failure of the material, such as lignin in wood and wood products, or the cement–water reaction products (shortly called hydrates) in cement-based materials. The picture changes if the first inelastically behaving constituent is related to ductile load carrying, then the loads within the microstructure are re-distributed before the overall material fails: this turns out to be the case in bone. Finally, due to highly confined multiaxial stress states, the elastic portion of the overall energy invested into the material may become negligible—and then yield design analysis employed on material volumes gives an idea of the highly ductile behavior of complex confined materials, such as asphalt. What integrates all the reported cases is the high capacity of mature mathematical and mechanical formulations to reveal the intricate, yet decipherable nature of the (continuum) mechanics of materials and structures. Content Type Journal Article Pages 1-21 DOI 10.1007/s00707-012-0685-1 Authors H. A. Mang, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria B. Pichler, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria T. Bader, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria J. Füssl, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria X. Jia, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria A. Fritsch, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria J. Eberhardsteiner, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria Ch. Hellmich, Institute for Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The paper is focused on the elastic buckling behavior of piezocomposite elliptical cylindrical shell finite element formulation. The formulation is based on the shear deformation theory, and the serendipity quadrilateral eight-node element is used to study the elastic behavior of elliptical cylindrical shells. The strain-displacement relations are accurately accounted for in the formulation. The contributions of work done by the applied load are also incorporated. A constant gain displacement control algorithm coupling the direct and inverse piezoelectric effect is applied to provide active control of composite non-circular shells in a self-monitoring and self-controlling system. The governing equations obtained using the principle of minimum potential energy are solved through an eigenvalue approach. The influences of elliptical cross-sectional parameter and displacement feedback gain ( G d ) values on the critical buckling loads of elliptical cylindrical shells are examined. Content Type Journal Article Pages 1-18 DOI 10.1007/s00707-012-0705-1 Authors Elham Kazemi, Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran Mansour Darvizeh, Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran Abolfazl Darvizeh, Department of Mechanical Engineering, Islamic Azad University of Bandar Anzali, Anzali, Iran Reza Ansari, Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The charged system search as a recently developed meta-heuristic algorithm has been successfully utilized for optimum design of different examples. In addition, the fields of forces model provides a means to enhance the algorithm, and this results in the enhanced charged system search (ECSS). This paper utilizes positive features of the chaos in the ECSS algorithm to optimize engineering design problems. Simulation results and comparisons based on various well-known mechanical and engineering design problems show the efficiency of the present algorithm. Content Type Journal Article Pages 1-17 DOI 10.1007/s00707-012-0704-2 Authors S. Talatahari, Marand Faculty of Engineering, University of Tabriz, Tabriz, Iran A. Kaveh, Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran R. Sheikholeslami, Department of Civil Engineering, University of Tabriz, Tabriz, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In the present paper, the mixed-mode Dugdale model is applied to investigate the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers. In the analysis, both normal and shear stresses are assumed to exist in the plastic zones and satisfy the Von Mises yield criterion. The plastic zone sizes can be determined on condition that the stress intensity factors caused by the stresses in the plastic zones and applied loading are zero. Then, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, the plane stress condition is considered. The plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers under a uniform load are examined. The effects of Dundurs’ parameters and the thickness of materials on the plastic zone size and the crack tip opening displacement are investigated in detail. Numerical results show that in the case of small thickness, the values of the normalized plastic zone size and the normalized crack tip opening displacement decrease with increasing Dundurs’ parameters, α and β , while, in the case of infinite thickness, the value of the normalized plastic zone size is independent of α , and the value is symmetric about the axis on which β = 0. Content Type Journal Article Pages 1-15 DOI 10.1007/s00707-012-0698-9 Authors D. K. Yi, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore J. Zhuang, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore Z. M. Xiao, School of Mechanical and Aerospace Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore S. K. Tan, School of Civil and Environmental Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, Singapore Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    The introduction of a format for thermoplasticity is given based on the quantities that are measurable, at least principally. The important assumption is that of equal thermoelastic behaviour within all elastic ranges. For simplicity, the theory is restricted to small deformations. A simple example is given to demonstrate the results. The question of uniqueness of the thermodynamical variables is discussed. Content Type Journal Article Pages 1-12 DOI 10.1007/s00707-012-0700-6 Authors Albrecht Bertram, IFME, University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany Arnold Krawietz, Hildburghauser Str. 241b, 12209 Berlin, Germany Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles. Content Type Journal Article Pages 1-13 DOI 10.1007/s00707-012-0728-7 Authors X. Yuan, Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, M3J 1P3 Toronto, Canada Z. H. Zhu, Department of Earth and Space Science and Engineering, York University, 4700 Keele Street, M3J 1P3 Toronto, Canada Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In normal circumstances, numerous practical engineering problems are multi-degree-of-freedom (MDOF) nonlinear non-autonomous dynamical systems. Generally, exact solutions for MDOF dynamical systems are hardly obtained; thus, the development of analytical approximations becomes a robust and appealing avenue for an analysis of these systems. The homotopy analysis method (HAM) is one of the analytical methods, which can overcome the foregoing barriers of conventional asymptotic techniques. It has been widely used for solving various nonlinear problems in physical science and engineering. In this paper, the extended homotopy analysis method (EHAM) is presented to establish the analytical approximate solutions for MDOF weakly damped non-autonomous dynamical systems. In terms of its flexibility and applicability, the EHAM is also applied to derive the approximate solutions of parametrically and externally excited thin plate systems. Besides, comparisons are performed between the results obtained by the EHAM and the numerical integration (i.e. Runge–Kutta) method. The present findings show that the analytical approximate solutions of the EHAM agree well with the numerical integration solutions. Content Type Journal Article Pages 1-12 DOI 10.1007/s00707-012-0725-x Authors W. Zhang, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124 People’s Republic of China Y. H. Qian, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124 People’s Republic of China S. K. Lai, Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Pokfulam, Hong Kong Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    In this study, a spectral finite element formulation for free and transient vibration analysis of a rectangular un-symmetric cross-ply laminated composite plate of Levy-type is developed. Plate kinematics obeys classical lamination plate theory. The formulation is based on dynamic shape functions in frequency-domain derived from the exact solution of the governing wave equations. Based on Levy-type solution and finite strip method, 2/D space-time partial differential equations (PDEs) of motion are transformed to 1/D space-time PDEs. Spectral elements are used to transform 1/D space-time PDEs to temporal ordinary differential equations. For investigating validity and accuracy of the model presented, numerical solutions are established for both free and transient vibrations. Comparison of spectral finite element method (SFEM) time responses with an exact analytical method demonstrates the superiority of SFEM in both reducing computational cost and increasing numerical accuracy. It is correct especially for excitations of high-frequency contents. A comparison of SFEM and FEM shows the same result. Content Type Journal Article Pages 1-16 DOI 10.1007/s00707-012-0719-8 Authors Hesam Hajheidari, Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran Hamid Reza Mirdamadi, Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111 Isfahan, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    Multivectorial algebra is of both academic and technological interest. Its application, however, is not always easy. A distinction must be made between polar and axial vectors and between scalars and pseudo-scalars. Eight element types are often considered even if they are not always identified as multivectors. In some cases, for simplicity’s sake, only vectorial algebra or quaternion algebra is explicitly used for physical and mechanical applications. It would, however, be more convenient to use more complex algebra directly in order to have a wider range of mechanical applications. The aim of this paper is to examine one particular type of Clifford algebra that could solve this problem. The present study focusses on showing how these quantities can be used to model mechanical and engineering problems. First, continuum mechanics in a Cauchy medium is investigated for elastic transformations. Second, a specific type of shot-peening application is studied. Applications are then used to illustrate the scope and efficiency of this type of modeling based on geometric algebra. Content Type Journal Article Pages 1-15 DOI 10.1007/s00707-012-0727-8 Authors Benoit Panicaud, Laboratoire des Systèmes Mécaniques et d’Ingénierie Simultanée (LASMIS), Institut Charles Delaunay (ICD), CNRS UMR 6279,Université de Technologie de Troyes (UTT), 12, rue Marie Curie, P.O. Box 2060, 10010 Troyes cedex, France Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970

Beschreibung:    This paper investigates the large-amplitude free vibration of a double-walled carbon nanotube (DWCNT) surrounded by an elastic medium in the presence of temperature change. Based on continuum mechanics, a nonlocal elastic beam model is employed in which nanotubes are coupled together via the van der Waals (vdW) interlayer interactions. The Pasternak foundation model and a nonlinear vdW model are utilized to describe the surrounding elastic medium effect and the vdW interlayer interactions, respectively. DWCNTs with different boundary conditions are analyzed utilizing the Timoshenko beam theory that considers the shear deformation and rotary inertia effects. The governing equations are derived from Hamilton’s principle; the Galerkin method is utilized to discretize the governing equations. The influences of the nonlocal parameter, spring constant, carbon nanotube aspect ratio, and temperature change on the nonlinear free vibration characteristics of a double-walled carbon nanotube with different boundary conditions are thoroughly investigated. It is deduced that the nonlocal parameter, spring constant, and the aspect ratio play significant roles for the value of the nonlinear frequency. Also, the temperature change and the type of boundary conditions have an effect on the nonlinear frequency. Content Type Journal Article Pages 1-14 DOI 10.1007/s00707-012-0718-9 Authors R. Ansari, Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran R. Gholami, Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran M. A. Darabi, Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran Journal Acta Mechanica Online ISSN 1619-6937 Print ISSN 0001-5970