ALBERT

Description:    We analyze a classical problem of oscillations arising in an elastic base caused by rotor vibrations of an asynchronous driver near the critical angular velocity. The nonlinear coupling between oscillations of the elastic base and rotor takes place naturally due to unbalanced masses. This provides typical frequency–amplitude patterns, even let the elastic properties of the base be linear one. As the measure of energy dissipation increases, the effect of bifurcated oscillations can disappear. The latter circumstance indicates the efficiency of using vibration absorbers to stabilize the dynamics of the electromechanical system. The second section of this paper presents results of theoretical studies inspired by the problem of reducing the noise and vibrations by using hydraulic absorbers as dampers to dissipate the energy of oscillations in railway electric equipments. The results of experimental trials over this problem and some theoretical calculations, discussed in the text, are demonstrated the ability to customize the damping properties of hydraulic absorbers to save an electric power and to protect the equipment itself due to utilizing the synchronous modes of rotation of the rotors. Content Type Journal Article Pages 1-14 DOI 10.1007/s00419-011-0574-4 Authors Dmitry Anatolyevich Kovriguine, The Nizhny-Novgorod branch of the Institute of Mechanical Engineering A.A. Blagonravov, Russian Academy of Sciences, Belinsky st., 85, 603024 Nizhny Novgorod, Russia Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    The behavior of thermoelastic waves at the interface of layered medium and distributions of these waves through the domain are examined by applying the direct finite element method to obtain the field variables directly within the spatial and temporal domains. The analysis is performed in a one-dimensional domain with two different layers to provide a means to follow the behavior of the reflected thermoelastic waves at the interface. It appears that the distributions of thermoelastic waves in an isotropic slab with one layer are significantly different from those in multilayered slabs. For instance, the negative displacement waves, several stresses with positive or negative signs and temperature distributions produced in the multilayered domains, are quite different from those in a single layer. This method may be generalized to simulate the propagation of thermoelastic waves in various multilayered regions and analyze the behavior of the layered composite structures under the mechanical or thermal impact loads. Content Type Journal Article Pages 1-16 DOI 10.1007/s00419-011-0555-7 Authors S. K. Hosseini Zad, Mechanical Engineering Department, Amirkabir University of Technology, 15914 Tehran, Iran A. Komeili, Mechanical Engineering Department, Amirkabir University of Technology, 15914 Tehran, Iran M. R. Eslami, Mechanical Engineering Department, Amirkabir University of Technology, 15914 Tehran, Iran S. Fariborz, Mechanical Engineering Department, Amirkabir University of Technology, 15914 Tehran, Iran Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    In this study, the frictional contact problem for a layer bonded to a homogeneous substrate is considered according to the theory of elasticity. The layer is indented by a rigid cylindrical stamp which is subjected to concentrated normal and tangential forces. The friction between the layer and the stamp is taken into account. The problem is reduced to a singular integral equation of the second kind in which the contact pressure function and the contact area are the unknown by using integral transform technique and the boundary conditions of the problem. The singular integral equation is solved numerically using both the Jacobi polynomials and the Gauss–Jacobi integration formula, considering equilibrium and consistency conditions. Numerical results for the contact pressures, the contact areas, the normal stresses, and the shear stresses are given, for both the frictional and the frictionless contacts. Content Type Journal Article Category Original Pages 1-10 DOI 10.1007/s00419-012-0626-4 Authors İsa Çömez, Civil Engineering Department, Karadeniz Technical University, 61080 Trabzon, Turkey Ragıp Erdöl, Civil Engineering Department, Karadeniz Technical University, 61080 Trabzon, Turkey Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    In the present study, a coupled refined high-order global-local theory is developed for predicting fully coupled behavior of smart multilayered/sandwich beams under electromechanical conditions. The proposed theory considers effects of transverse normal stress and transverse flexibility which is important for beams including soft cores or beams with drastic material properties changes through depth. Effects of induced transverse normal strains through the piezoelectric layers are also included in this study. In the presence of non-zero in-plane electric field component, all the kinematic and stress continuity conditions are satisfied at layer interfaces. In addition, for the first time, conditions of non-zero shear and normal tractions are satisfied even while the bottom or the top layer of the beam is piezoelectric. A combination of polynomial and exponential expressions with a layerwise term containing first order differentiation of electrical unknowns is used to introduce the in-plane displacement field. Also, the transverse displacement field is formulated utilizing a combination of continuous piecewise fourth-order polynomial with a layerwise representation of electrical unknowns. Finally, a quadratic electric potential is used across the thickness of each piezoelectric layer. It is worthy to note that in the proposed shear locking-free finite element formulation, the number of mechanical unknowns is independent of the number of layers. Excellent correlation has been found between the results obtained from the proposed formulation for thin and thick piezoelectric beams with those resulted from the three-dimensional theory of piezoelasticity. Moreover, the proposed finite element model is computationally economic. Content Type Journal Article Category Original Pages 1-44 DOI 10.1007/s00419-012-0621-9 Authors S. B. Beheshti-Aval, Civil Engineering Faculty, K.N. Toosi University of Technology, Tehran, Iran M. Lezgy-Nazargah, Civil Engineering Faculty, K.N. Toosi University of Technology, Tehran, Iran Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    The method of vertical lines in the case of quasi-static solid mechanics applying constitutive models of evolutionary-type yields after the spatial discretization by means of finite elements a system of differential-algebraic equations. It is of substantial interest how fast, accurate, and stable such computations can be carried out. Moreover, the questions are how simple the implementation can be done and how susceptible a procedure is to programming errors. In this article, this is investigated for half-explicit Runge–Kutta methods that are applied to small and finite strain viscoelasticity. The advantage of the method is given by a non-iterative scheme on element level. Additionally, it turns out that for models where linear elasticity is one ingredient in the constitutive model, the method leads to only one required LU-decomposition at the beginning of the entire computation, and in each time step, only one back-substitution step has to be carried out. This outperforms current finite element computations. Order investigations of various integration schemes and the automatic step-size behavior are studied. This new proposal is compared to a classical Backward-Euler implementation, high-order stiffly accurate diagonally implicit Runge–Kutta, and recently proposed Rosenbrock-type methods. Advantages and disadvantages of the applied schemes are discussed. Content Type Journal Article Category Special Issue Pages 1-18 DOI 10.1007/s00419-012-0617-5 Authors Steffen Rothe, Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Str. 2A, 38678 Clausthal-Zellerfeld, Germany Ahmad-Wahadj Hamkar, Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Str. 2A, 38678 Clausthal-Zellerfeld, Germany Karsten J. Quint, Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Str. 2A, 38678 Clausthal-Zellerfeld, Germany Stefan Hartmann, Institute of Applied Mechanics, Clausthal University of Technology, Adolph-Roemer-Str. 2A, 38678 Clausthal-Zellerfeld, Germany Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    This paper proposes an extension of the SHB8PS solid–shell finite element to large strain anisotropic elasto-plasticity, with application to several non-linear benchmark tests including sheet metal forming simulations. This hexahedral linear element has an arbitrary number of integration points distributed along a single line, defining the “thickness” direction; and to control the hourglass modes inherent to this reduced integration, a physical stabilization technique is used. In addition, the assumed strain method is adopted for the elimination of locking. The implementation of the element in Abaqus/Standard via the UEL user subroutine has been assessed through a variety of benchmark problems involving geometric non-linearities, anisotropic plasticity, large deformation and contact. Initially designed for the efficient simulation of elastic–plastic thin structures, the SHB8PS exhibits interesting potentialities for sheet metal forming applications—both in terms of efficiency and accuracy. The element shows good performance on the selected tests, including springback and earing predictions for Numisheet benchmark problems. Content Type Journal Article Category Original Pages 1-22 DOI 10.1007/s00419-012-0620-x Authors A. Salahouelhadj, Laboratoire d’Étude des Microstructures et de Mécanique des Matériaux, LEM3, CNRS, Arts et Métiers ParisTech-Metz, 4 rue A. Fresnel, 57078 Metz Cedex 03, France F. Abed-Meraim, Laboratoire d’Étude des Microstructures et de Mécanique des Matériaux, LEM3, CNRS, Arts et Métiers ParisTech-Metz, 4 rue A. Fresnel, 57078 Metz Cedex 03, France H. Chalal, Laboratoire d’Étude des Microstructures et de Mécanique des Matériaux, LEM3, CNRS, Arts et Métiers ParisTech-Metz, 4 rue A. Fresnel, 57078 Metz Cedex 03, France T. Balan, Laboratoire d’Étude des Microstructures et de Mécanique des Matériaux, LEM3, CNRS, Arts et Métiers ParisTech-Metz, 4 rue A. Fresnel, 57078 Metz Cedex 03, France Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    The soil depth is generally considered to be constant for the analysis of plates resting on elastic foundation in the literature. However, it is most reasonable to have a variable subsoil depth as the plate dimensions get larger. In present study, linearly varying subsoil depth is considered as well as constant, linear and quadratic variation of modulus of elasticity with subsoil depth. Also, a parametric study is performed to demonstrate the behavior of thick plates on elastic foundations with variable soil depth. Modified Vlasov Model is used for the analysis of the plate foundation system, and 8-noded Mindlin plate element incorporating shear strain throughout plate thickness is used for the finite element model. Numerical examples are obtained from the literature to compare results and to show the influence of variable soil stratum depth on the behavior of plates. Displacements, bending moments, and shear forces are presented in tabular and graphical formats. As far as results are compared, it can be concluded that variable soil depth significantly affects the variation of the displacements and therefore the internal forces of the plate while keeping it constant ends up with unrealistic results. Content Type Journal Article Category Original Pages 1-10 DOI 10.1007/s00419-012-0703-8 Authors Korhan Ozgan, Department of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey Ayse T. Daloglu, Department of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey A. İhsan Karakaş, Department of Civil Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    The incremental sensitivity analysis associated with variation of structure material parameters, shape or topology variation is generally discussed by analyzing the evolution of potential and complementary energies, or arbitrary functionals of state fields. The concept of configuration and sensitivity generalized forces is used in presenting the sensitivity derivatives. The general reciprocity relations are derived for the case of potential or complementary energy variations. The topology variations in bar structures related to introduction of elements and introduction of inclusions and voids in plates are discussed, and the sensitivity forces are derived. Content Type Journal Article Category Special Issue Pages 1-15 DOI 10.1007/s00419-012-0672-y Authors Z. Mróz, Institute of Fundamental Technological Research, Warsaw, Poland D. Bojczuk, Faculty of Management and Computer Modelling, Kielce University of Technology, Kielce, Poland Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    We propose a new approach for the construction of the closed-form solutions of standing waves of the cubic nonlinear Schrödinger equation (NLS). Through appropriate functional transformations, we reduce the radially symmetric NLS into an Emden–Fowler equation whose solution results to the derivation of the closed forms of the standing waves. We also derive the necessary restrictions under which the derived solutions are admissible. Content Type Journal Article Category Special Issue Pages 1-12 DOI 10.1007/s00419-012-0658-9 Authors D. E. Panayotounakos, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 9, Heroon Polytechniou str., Zografou Campus, 15773 Athens, Greece T. I. Zarmpoutis, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 9, Heroon Polytechniou str., Zografou Campus, 15773 Athens, Greece C. I. Siettos, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 9, Heroon Polytechniou str., Zografou Campus, 15773 Athens, Greece Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533

Description:    Making use of a mixed variational formulation based on the Green function of the substrate, which assumes as independent fields the structure displacements and the contact pressure, a simple and efficient finite element-boundary integral equation coupling method is derived and applied to the stability analysis of beams and frames resting on an elastic half-plane. Slender Euler–Bernoulli beams with different combinations of end constraints are considered. The examples illustrate the convergence to the existing exact solutions and provide new estimates of the buckling loads for different boundary conditions. Finally, nonlinear incremental analyses of rectangular pipes with compressed columns and free or pinned foundation ends are performed, showing that pipes stiffer than the soil may exhibit snap-through instability. Content Type Journal Article Category Original Pages 1-16 DOI 10.1007/s00419-012-0694-5 Authors Nerio Tullini, Department of Engineering, University of Ferrara, Ferrara, Italy Antonio Tralli, Department of Engineering, University of Ferrara, Ferrara, Italy Daniele Baraldi, Department of Engineering, University of Ferrara, Ferrara, Italy Journal Archive of Applied Mechanics Online ISSN 1432-0681 Print ISSN 0939-1533