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  • 1
    Publikationsdatum: 2013-02-09
    Beschreibung: Common structural optimisation problems consist of problem-specific objective functions which have to be minimised mathematically with respect to design and state variables taking into account particular constraints. In contrast to this, we adopt a conceptually different approach for the design of a structure which is not based on a topology-optimisation technique. Instead, we apply a one-dimensional energy-driven constitutive evolution equation for the referential density–originally proposed for the simulation of remodelling effects in bones–and embed this into the micro-sphere-concept to end up with a three-dimensional anisotropic growth formulation. The objective of this contribution is to investigate this approach with emphasis on its application to structural design problems by means of two three-dimensional benchmark-type boundary value problems. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 2
    Publikationsdatum: 2013-02-09
    Beschreibung: The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale. Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain representative numerical experiments are performed to investigate the resulting load-displacement-behaviour as well as the specific heat generation due to friction and plastic dissipation. A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Based on previous work, an adaptive remeshing scheme which uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence. In consequence, the formulation allows to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 3
    Publikationsdatum: 2013-11-30
    Beschreibung: Landfill gas is composed of methane (CH 4 ) and (CO 2 ) at a ratio of about (60% – 40%), whereby the impact of methane on the greenhouse effect is about 25 times higher than that of carbon dioxide. Bacterial methane oxidation, taking place in the landfill cover layer, helps to reduce the climate active emissions from landfill sites. This contribution presents a theoretical and numerical approach to model the coupled processes of bacterial methane oxidation. An isothermal biphasic model based on the Theory of Porous Media (TPM) and Mixture Theory is introduced as well as the coupled finite element (FE) calculation concept. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 4
    Publikationsdatum: 2013-11-30
    Beschreibung: The injection of supercritical CO 2 into deep saline aquifers is regarded as one possible alternative to lessen the impact of emitted CO 2 on the greenhouse effect. During injection, a great variety of thermodynamical and mechanical changes of both the fluid phases and the porous solid matrix can be expected. The prediction of these processes is crucial to prevent from critical incidents during CO 2 injection, such as leakage of CO 2 or contamination of drinking water. For simulation purpose, a macroscopic, fully coupled description of multi-phasic flow inside a deformable porous medium based on the Theory of Porous Media (TPM) is generated. Appropriate constitutive relations are applied to account for changes in the fluid properties of both the saline water and CO 2 during injection and leakage. Furthermore, an elasto-plastic description of solid deformations of the porous matrix is included. The model is tested based on a benchmark problem. Therein, the leakage of CO 2 through an abandoned well after injection is investigated. The fully coupled approach between fluid flow and solid deformation allows additional results to be gained from the simulation. Quantification of the leakage rate through the abandoned well and localisation of phase-change events are addressed to calibrate the presented model. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 5
    Publikationsdatum: 2013-11-30
    Beschreibung: The transitional and turbulent flow in the near wall sublayer is now mostly modeled based on the existing knowledge of simple 2D flows. To determine the effect of three dimensionality on the turbulent flow structures and turbulent heat transfer in the near wall areas the authors investigate numerically (SVV) turbulent flow in rotor/stator and rotor/rotor flows (with and without axial throughflow). These simple model flows contain most of the phenomena that are needed to understand more complex, 3D transitional and turbulent flows. Attention is focused on the turbulent characteristics which should have more universal character. To stabilize calculations for high Reynolds numbers (up to Re=800 000) the SVV operator is introduced into the Navier-Stokes and energy equations solver for cylindrical coordinate system without using complex numbers. Code optimization and parallelization have speeded up computations 20 times. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 6
    Publikationsdatum: 2013-11-30
    Beschreibung: In this essay a fully coupled, monolithic thermo-mechanical coupled simulation using high-order finite elements based on hierarchical shape-functions in combination with a high-order time-integration scheme using diagonally-implicit Runge-Kutta schemes is presented. The constitutive model is based on a finite strain thermo-viscoelasticity relation of overstress-type. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 7
    Publikationsdatum: 2013-11-30
    Beschreibung: In this work we present a novel approach to the modeling of magnetorheological elastomers (MREs) for finite deformations. Keeping in mind the composite nature at the microscale, we employ the microsphere model as an effective tool to capture the constitutive response of the material. The microsphere model has been successfully applied to the modelling of rubber-like materials. Here, we extend this approach by taking into account the effect of the magnetic dipole-dipole interactions on the orientation of the polymer chains. Thus, the presented microsphere model is directly motivated by considering the underlying phenomena at the microscale level. Finally the material model is embedded in a finite element framework and the results of a boundary value problems is presented. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 8
    Publikationsdatum: 2013-11-30
    Beschreibung: Finite element simulation of hot working of steel has gained significant importance in steel industries. The aim of describing such processes using the finite element method is to predict phenomena like shrinkage during solidification. Due to this thermo-mechanical behaviour residual stresses appear, which cause cracks and the final steel slab loses its required properties as a result. We propose a two-phase incompressible model based on the Theory of Porous Media (TPM) for a numerical description of steelmaking processes. A thermo-mechanical coupling is required to model a high temperature-dependency. In order to consider thermal expansion of solid, a multiplicative decomposition of the deformation gradient into a mechanical and a thermal part has been applied. The Von Mises J 2 plasticity with isotropic hardening criterion has been selected for the solid-phase of the model. Representative numerical examples, as well as the influence of single material parameters on the model will be shown. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 9
    Publikationsdatum: 2013-11-30
    Beschreibung: Within measurements of brake pads on the IDS high load Tribometer, the wear of pads was investigated by a new non-contact wear measurement under low normal pressures and low temperatures. The first results show that the wear of the pad in the sliding friction is nearly proportional to the friction work, and inversely proportional to the shear strength. The results are also interpreted by the adhesion theory of friction and Archard's equation. On the basis of further interpretations of shear strength and extension of adhesion theory of friction, the wear is derived as a piecewise linear function, which can evaluate explicitly the effect factors of wear and relative correlations at different pressures and different temperatures. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 10
    Publikationsdatum: 2013-11-30
    Beschreibung: The modeling of size effects in elastic-plastic solids, such as the width of shear bands or the grain size dependence in polycrystals, must be based on non-standard theories which incorporate length-scales. This is achieved by models of strain gradient plasticity , incorporating spatial gradients of selected micro-structural fields which describe the evolving dissipative mechanisms. The key aspect of this work is to provide a rigorous incremental variational formulation and mixed finite element design of additive finite gradient plasticity in the logarithmic strain space. We start from a mixed saddle point principle for metric-type plasticity, which is specified for the important model problem of isochoric plasticity with gradient-extended hardening/softening response. To this end, we propose a novel finite element design of the coupled problem incorporating a local-global solution strategy of short- and long-range fields. This includes several new aspects, such as extended Q1P0-type and MINI-type finite elements for gradient plasticity [4]. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 11
    Publikationsdatum: 2013-11-30
    Beschreibung: A one-dimensional strain gradient plasticity model is reviewed in the context of Finite Element Method (FEM) solvability. It is found that under certain conditions specified the resulting system of two coupled partial differential equations in space and time leads to a symmetric global stiffness matrix. This is achieved upon standard weak form approach and yields a favorable system for an efficient numerical solution. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 12
    Publikationsdatum: 2013-11-30
    Beschreibung: The deformation in polycrystals is often heterogenous, e.g. due to grain size dependent hardening. In a semi-analytical representative volume element (RVE), a log-normal distributed grain size is assumed together with a grain size dependent local plastic behavior. The numerical results are well approximated by a simple analytical expression. The effect of the homogenization comparison stiffness on the transient behaviour is explained using a simplified localization equation. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 13
    Publikationsdatum: 2013-11-30
    Beschreibung: In this paper, we present a constitutive model for granular materials exhibiting microstructures using the concept of energy relaxation. Within the framework of Cosserat continuum theory the free energy of the material is enriched with an interaction energy potential taking into account the counter rotations of the particles. The enhanced energy potential fails to be quasiconvex. Energy relaxation theory is employed to compute the relaxed energy which yields all possible displacement and micro-rotations field fluctuations as minimizers. Based on a two-field variational principle the constitutive response of the material is derived. The developed constitutive model is then implemented in a finite element analysis program using the finite element method. Numerical simulations are presented to observe the localized deformation phenomenon in a granular medium. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 14
    Publikationsdatum: 2013-11-30
    Beschreibung: In nowadays polymer materials are used in a multitude of different applications. A promising class of smart materials are biodegradable polymers. The present work proposes a micromechanical motivated description of degradation. Since degradation leads finally to an eroding material both cases of erosion, namely bulk and surface erosion, are considered. Degradation is modelled in a strong coupled chemo mechanical framework for an arbitrary spatial motion problem. Deformations arising due to surface erosion are described as material motion. Finally, the modelling concept is embedded in a finite element method. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 15
    Publikationsdatum: 2013-11-30
    Beschreibung: For the simulation of the interaction of elastic waves in CFRP plates with inhomogeneities and defects the spectral finite element method (SEM) is under investigation. The SEM uses high-order shape functions which are composed of Lagrange polynomials with nodes at the Gauss-Lobatto quadrature (GLq) points. In this way we obtain a diagonal mass matrix which makes an explicit time scheme more efficient. The goal of this work is to investigate the effect of SEM on the CFL-Condition. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 16
    Publikationsdatum: 2013-11-30
    Beschreibung: In this paper, composite structures are considered which consist of several layers of carbon fiber reinforced plastics (CFRP). For such layered composite structures, delamination constitutes one of the major failure modes and hence predicting its initiation is essential for their design. Evaluating stress-strength relation based onset criteria requires an accurate representation of the through-the-thickness stress distribution, which can be particularly delicate in the case of shell-like structures. Thus, in this paper, a solid-shell finite element is utilized, which allows for incorporating a fully three-dimensional material model, still being suited for application to thin structures. Moreover, locking phenomena are cured by using both the EAS and the ANS concept, and numerical efficiency is ensured through reduced integration. The proposed anisotropic material model accounts for the material's micro-structure by using the concept of structural tensors. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 17
    Publikationsdatum: 2013-11-30
    Beschreibung: In this contribution, a micromechanical modeling approach in the framework of poromechanics is adopted to study structure-stiffness relations of two quite different species, namely spruce and yew, in detail. In particular, microstructural specialties of yew and spruce are assessed. A dominant influence of the cellulose content and its orientation on the stiffness of the cell wall is revealed, while on the macroscopic scale, density is found to be the governing microstructural characteristic for elastic properties. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 18
    Publikationsdatum: 2011-12-10
    Beschreibung: We consider the use of the Restricted-Denominator (RD) rational Arnoldi method for the computation of the core functions of exponential integrators for parabolic problems. Reliable and easy-to-use a-posteriori error bounds are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 19
    Publikationsdatum: 2011-12-10
    Beschreibung: The concept of head loss coefficients K for the determination of losses in conduit components is discussed in detail. While so far it has mainly been applied to fully turbulent flows it is extended here to also cover the laminar flow regime which is relevant for micro systems due to the low Reynolds numbers of these flows. Specific numbers of K can be determined by integration of the entropy generation field (second law analysis) obtained from a numerical simulation. It will be shown that a definition of K based on entropy generation is superior to a widely used definition that refers to a pressure drop caused by the conduit component. With the second law analysis details of the physics become available. For example it can be shown that often the main part of the entropy generation occurs downstream of the component. This aspect becomes important when several conduit components are combined in close proximity, like two 90 degree bends that are close to each other. Often in such situations the combination as a whole has to be looked upon as one new complex component. The general approach is discussed and illustrated for various conduit components and combinations of them. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 20
    Publikationsdatum: 2011-12-10
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 21
    Publikationsdatum: 2011-12-10
    Beschreibung: A biological tissue in general is formed by cells, extracellular matrix (ECM) and fluids. Consequently, its overall material behaviour results from its components and their interaction among each other. Furthermore, in case of living tissues, the material properties do not remain constant but naturally change due to adaptation processes or diseases. In the context of the Theory of Porous Media (TPM), a continuum-mechanical model is introduced to describe the complex fluid-structure interaction in biological tissue on a macroscopic scale. The tissue is treated as an aggregate of two immiscible constituents, where the cells and the ECM are summarised to a solid phase, whereas the fluid phase represents the extracellular and interstitial liquids as well as necrotic debris and cell or matrix precursors in solution. The growth and remodelling processes are described by a distinct mass exchange between the fluid and solid phase, which also results in a change of the constituent material behaviour. To furthermore guarantee the compliance with the entropy principle, the growth energy is introduced as an additional quantity. It measures the average of chemical energy available for cell metabolism, and thus, controls the growth and remodelling processes. To set an example, the presented model is applied for the simulation of the early stages of avascular tumour growth in the framework of the finite element method (FEM). (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 22
    Publikationsdatum: 2011-12-10
    Beschreibung: This contribution is concerned with mixed finite element formulations for modeling piezoelectric beam and shell structures. Due to the electromechanical coupling, specific deformation modes are joined with electric field components. In bending dominated problems incompatible approximation functions of these fields cause incorrect results. These effects occur in standard finite element formulations, where interpolation functions of lowest order are used. A mixed variational approach is introduced to overcome these problems. The mixed formulation allows for a consistent approximation of the electromechanical coupled problem. It utilizes six independent fields and could be derived from a Hu-Washizu variational principle. Displacements, rotations and the electric potential are employed as nodal degrees of freedom. According to the Timoshenko theory (beam) and the Reissner-Mindlin theory (shell), the formulations account for constant transversal shear strains. To incorporate three dimensional constitutive relations all transversal components of the electric field and the strain field are enriched by mixed finite element interpolations. Thus the complete piezoelectric coupling is appropriately captured. The common assumption of vanishing transversal stress and dielectric displacement components is enforced in an integral sense. Some numerical examples will demonstrate the capability of the presented finite element formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 23
    Publikationsdatum: 2011-12-10
    Beschreibung: Time-optimal motion planning along specified paths is a well-understood problem in robotics for which well-established methods exist for some standard effects, such as actuator force limits, maximal path velocity, or sliding friction. This paper describes an extension of the classical method that allows for considering, on the one hand side, additional non linear constraints such as sticking friction, acceleration limits at the end-effector, as well power limits for the overall system, and on the other, general paths featuring smooth interpolation of angular acceleration as well as arbitrary multibody systems comprising multiple loops. The methods are illustrated with two applications from robotics and the mining industry. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 24
    Publikationsdatum: 2011-12-10
    Beschreibung: This work discusses two different structure preserving integrators in the framework of optimal control simulations with contact. The first one is a variational integrator, based on the constrained version of the Lagrange-D'Alembert. The resulting scheme preserves the symplecticity and the momentum maps of the simulated multibody dynamics. The second integrator is an energy momentum scheme and it is based on the augmented Hamiltonian equations, which are discretised using the discrete derivative in [2]. Both integrators are applied to simulate the optimal control of compass gait, for which the contact between the foot and the ground is modelled as perfectly plastic contact. The second example represents a monopedal jumper and it is used to examine the dynamical behaviour of the perfectly elastic and perfectly plastic contact formulation. The resulting differential algebraic equations (DAEs) are solved by the aforementioned symplectic momentum method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 25
    Publikationsdatum: 2011-12-10
    Beschreibung: Passively compliant drive concepts are often used in bio-inspired robot designs. Especially fluidic artificial muscles share many characteristics with their natural counterparts. Industrial manipulators can benefit from the increased robustness and safety (in contrast to rigid drives) especially in cooperative human/robot environments. We compare different model-based control concepts for a single rotational joint actuated by two fluidic muscles in combination with proportional valves. While the complete valve and muscle models are already included in this setup, the mechanical model becomes more complex when we extend the control to a full seven axes articulated robot arm with both, electrically and pneumatically actuated joints. In this case the Projection Equation in subsystem description is used for the multibody model, allowing a straight-forward realtime application to different robot kinematics. Remaining model errors and disturbances are handled by observer algorithms. We present measurement results and compare them to simulation outputs. Besides the position control, possible approaches for sensorless external force estimation are discussed. They take advantage of the compliance of the robot and are again based on the actuator and multibody models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 26
    Publikationsdatum: 2011-12-10
    Beschreibung: Mechanical systems with dynamics on varying time scales, in particular those including highly oscillatory motion, impose challenging questions for numerical integration schemes. Tiny step sizes are required to guarantee a stable integration of the fast frequencies. However, for the simulation of the slow dynamics, integration with a larger time step is accurate enough. Small time steps increase integration times unnecessarily, especially for costly function evaluations. For systems comprising fast and slow dynamics, multirate methods integrate the slow part of the system with a relatively large step size while the fast part is integrated with a small time step. Main challenges are the identification of fast and slow parts (e.g. by separating the energy or by distinguishing sets of variables), the synchronisation of their dynamics and in particular the treatment of mixed parts that often appear when fast and slow dynamics are coupled by constraints. In this contribution, a multirate integrator is derived in closed form via a discrete variational principle on a time grid consisting of macro and micro time nodes. Variational integrators (based on a discrete version of Hamilton's principle) lead to symplectic and momentum preserving integration schemes that also exhibit good energy behavior. The resulting multirate variational integrator has the same preservation properties. An example demonstrates the performance of the multirate integrator for constrained multibody dynamics. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 27
    Publikationsdatum: 2011-12-10
    Beschreibung: Detailed dynamical modeling is the basis for simulation and model based control. In this contribution the Projection Equation is used for the modeling of a biped walking machine, resulting in the equations of motion which are needed for gait generation and verification of its stability. For biped robots one main issue is the generation of stable trajectories for the center of mass (CoM). Several different approaches based on the Zero Moment Point (ZMP) scheme have been presented in the past. Due to the complex dynamic structure of bipedal robots most of the considered algorithms use a linear inverted pendulum as a simplified model. This results in a decoupling of the ZMP equations in lateral and forward direction, but limits the trajectories to a constant height of the CoM. An extension of the well known LQR theory by future reference values has been proposed. This model based approach seems to perform quite well, but does not allow the consideration of constraints on the position of the ZMP. This limitation is removed by the use of Model Predictive Control (MPC) with inequality constraints. By extending this approach to a time invariant one the restriction to a constant height of the CoM is no longer necessary. Both methods as well as the time invariant approach for variable CoM heights have been evaluated in simulations and will be experimentally verified on a real robot soon. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 28
    Publikationsdatum: 2011-12-10
    Beschreibung: The articulated robot ElRob, consisting of flexible links and joints, is considered in several publications. Recent developments are presented in this work. The overall goal of the research is to decrease the effects of structural elasticities in lightweight robots. For this purpose model-based control concepts are investigated and very accurate and efficient kinematic and dynamic models are necessary. The robot is split into groups of bodies, the so called subsystems, with separated describing velocities and coordinate systems. To obtain structured equations of motion the Projection Equation is used. The beams are modelled using the floating frame of reference formulation and a Ritz-approach. Because of its flexibility, the examined robot is an underactuated system leading to special difficulties. As an example is it not possible to compute the desired joint angles with respect to a reference path in task space for the flexible system (inverse kinematic problem). Different methods to solve this drawback and other problems resulting from flexibility are discussed with special focus on feed forward control and different feedback control concepts. The resulting end point error, the necessary control input and other interesting results for the laboratory experiment are presented and compared. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 29
    Publikationsdatum: 2011-12-10
    Beschreibung: This paper reviews the singular perturbation control theory in the context of flexible multibody systems. The theory is motivated and explained by a simple, but sufficiently complex model. It is explained that based on the singular perturbed model an end-effector trajectory tracking can be achieved by an integral manifold controller. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 30
    Publikationsdatum: 2011-12-10
    Beschreibung: The coupling of multibody system dynamics and optical simulations by using ray tracing through moving lens systems will be summarized for both rigid and flexible lens systems. Furthermore, a method will be introduced for efficient simulations in the time domain. This method provides a direct integration of the optical simulation into the equations of motion of a multibody system. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 31
    Publikationsdatum: 2011-12-10
    Beschreibung: In many fields of the multi-body world friction must be taken into account. Friction is usually reduced to a ratio: the coefficient of friction. Newer theories also consider dynamic friction laws. For the use in multi-body models, a stepped complexity and measurably hedged description of the friction is necessary. Therefore, different experimental designs that allow dynamic measurements are discussed. An example friction pair is investigated by measurements and the quality of the results is pointed out. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 32
    Publikationsdatum: 2011-12-10
    Beschreibung: Mechanical stimuli play a crucial role in the differentiation process of mesenchymal stem cells (MSC). The resulting mechanical signals are important in the regulation of various cell functions and maintenance of many tissues. The underlying molecular and biophysical mechanisms of the differentiation process are poorly understood. Present remodelling and growth models are purely phenomenological without linkage to cell mechanisms. The presented macroscopic model of MSC mechanics is based on a multiphasic-multicomponent formulation within the framework of Theory of Porous Media (TPM), where a single cell is considered as a mixture of interacting constituents. In particular, the constituents are the solid cytoskeleton saturated by a fluid phase (cytoplasm), which itself consists of a liquid solvent and mobile components, e. g., chemical messengers, proteins, etc. To demonstrate the capabilities of the developed model, first qualitative numerical simulations of the impact of external forces on MSC are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 33
    Publikationsdatum: 2011-12-10
    Beschreibung: Underactuation occurs, when only some generalized coordinates have a control input. For end-effector trajectory tracking a combined feed-forward and feedback control is often a suitable approach. Feed-forward control design based on an inverse model for underactuated multibody systems is presented. The starting point is the transformation of the multibody system into a nonlinear input-output normal-form. The inverse model follows from this and consists of chains of differentiators, driven internal dynamics and an algebraic part. Especially when using the end-effector as system output the internal dynamics is often unbounded. In order to obtain a viable feed-forward control, a bounded solution must be determined. For this task the internal dynamics is solved as a nonlinear optimization problem. Thereby, the coordinates of the internal dynamics define the objective function which is minimized. The equation of the internal dynamics must be fulfilled at each point of a discrete time grid. In addition continuity of the solution is achieved by adding as equality constraint an integration formula, e.g. trapezoidal rule. The optimization problem is then solved by a SQP-method. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 34
    Publikationsdatum: 2011-12-10
    Beschreibung: In this contribution, a constitutive model adopted from the computational plasticity-models of Drucker-Prager and von Mises is presented. This model captures the material behavior of osseointegration and the curing-process of bone cement. With this basic model, both simulations of bone-ingrowth of uncemented implants and simulations of the curing process of bone cement for cemented implants are carried out in a bone-implant interface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 35
    Publikationsdatum: 2011-12-10
    Beschreibung: In fibre reinforced materials, the interface toughness has a significant influence on strength and damage resistance. Especially in discontinuous fibre reinforced composites, where high densities of fibre ends are apparent, it has been shown that additives which improve the interfacial toughness can increase the effective strength of the materials [1]. Due to the fact that interface properties are strongly dependent on the manufacturing process, only experimental techniques providing the possibility to take these influences into account, are promising for an integrated material characterization. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
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  • 36
    Publikationsdatum: 2011-12-10
    Beschreibung: The material behaviour of skeletal muscles can be decomposed into two parts: an active part, describing the contractile mechanisms, and a passive one, characterising the passive components such as the connective tissue. Computational models are used to support the understanding of complex mechanism inside a muscle. In the present work, we focus on the three-dimensional passive tissue behaviour from the experimental as well as modelling point of view. Therefore, quasi-static experiments have been performed on specimens with regular geometry. By using a three-dimensional optical measurement system the shape of the specimens has been reconstructed at different deformation states. On the modelling side a hyperelastic model with transversal isotropic fibre orientation has been used to describe non-linear stress responses. The model has been validated by performing analyses for different fibre orientations. In summary, it figures out that the proposed modelling approach is able to reflect the experimental results in a satisfying manner. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 37
    Publikationsdatum: 2011-12-10
    Beschreibung: The aim of the presented work is to characterize the mechanical properties of different types of articular cartilage replacement materials. For this propose an elastic-diffusion model is developed to identify the elastic and diffusion properties of the replacement materials. A set of unconfined compression tests were performed with several kinds of implants. By means of finite element simulation integrated with an user-defined material model, the material parameters were identified. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 38
    Publikationsdatum: 2011-12-10
    Beschreibung: Unfortunately, the human brain is compromised by an amount of brain diseases, such as strokes or cerebral tumours. In this contribution, special attention is paid to the constitutive modelling procedure and the numerical simulation of the so-called convection-enhanced delivery process, where an effective treatment of malignant brain tumours is achieved by bypassing the blood-brain barrier via a direct infusion of therapeutic agents into the extra-vascular space of the brain tissue using implanted catheters. The modelling approach of the complex brain-tissue aggregate proceeds from the Theory of Porous Media including an elastically deformable solid skeleton, provided by the tissue cells and the vascular walls. The tissue is permeated by two liquid phases, the blood and the interstitial fluid. In order to describe a distribution process of the inserted drugs, the interstitial fluid phase is treated as a chemical solution of two components, the liquid solvent and the dissolved therapeutic solute. The inhomogeneous anisotropic nature of the white-matter tracts is considered by spatially varying permeability tensors, obtained by diffusion-weighted magnetic resonance imaging. The strongly coupled solid-liquid transport problem is simultaneously approximated in all primary unknowns using mixed finite elements and solved in a monolithic manner with an implicit time-integration scheme. The numerical investigation is applied to un-bloody numerical studies. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 39
    Publikationsdatum: 2011-12-10
    Beschreibung: This work outlines an approach that combines the advantages of explicit and implicit descriptions of the crack geometry in the context of the extended finite element method (XFEM). The XFEM is typically combined with an implicit description of the crack which is realized by the level-set method. This facilitates the definition of the enrichments in the XFEM. However, the update of the crack geometry during the propagation of a crack is simpler by means of explicit crack descriptions where the crack surface is meshed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 40
    Publikationsdatum: 2011-12-10
    Beschreibung: Refractory materials, for example ceramic materials, initially contain a multitude of defects such as voids, microcracks, grain boundaries etc. The deformation process and failure mechanisms due to thermal shock at high temperatures above 1000°C are going along with the creation of new micro defects as well as the growth and coalescence of cracks. A material damage model based on the theoretical concept of damage mechanics and the mechanics of microcracks is presented in this paper. Cell models are developed as representative volume elements (RVE) including crack initiation and growth as well as microstructural shielding effects. For simple configurations of the microstructure, the relation between stress, strain and temperature is derived from analytical considerations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 41
    Publikationsdatum: 2011-12-10
    Beschreibung: Numerical simulations of the formation and the characteristic shape of plastic zones at crack tips in rubber-toughened polymers are performed in order to get a better understanding of the underlying micromechanisms. Complementing previous work, the present study focuses on the contribution of distributed crazing. A macroscopic constitutive model therefore has been developed that describes the overall effect of distributed crazing as an anisotropic flow process. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 42
    Publikationsdatum: 2011-12-10
    Beschreibung: A boundary element method for the transient thermoelastic fracture analysis in isotropic, continuously non-homogeneous and linear elastic functionally graded materials subjected to a thermal shock is presented. The material parameters are assumed to be continuous functions of the Cartesian coordinates. Laplace-domain fundamental solutions of linear coupled thermoelasticity for infinite, isotropic, homogeneous and linear elastic solids are applied to derive the boundary-domain integral equation formulation. The numerical implementation is performed by using a collocation method for the spatial discretization. Numerical results for the dynamic stress intensity factors are presented and discussed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 43
    Publikationsdatum: 2011-12-10
    Beschreibung: The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 44
    Publikationsdatum: 2011-12-10
    Beschreibung: Nondestructive test methods are important for examination of elastic devices regarding existence, position and size of cracks. In the case of hidden cracks (which do not touch the boundary), a simple visual control is not sufficient. The basic idea of this paper is to examine appropriate boundary measurements under certain loads. We focus on a method presented by ANDRIEUX, BEN ABDA and BUI [1] for isotropic linear elasticity, and generalize the crack plane detection to anisotropic linear elastic material. The main idea is the use of the reciprocity principle in order to connect data from the outer boundary with the unknown crack properties. Some 2D numerical examples demonstrate, that the method is working with simulated data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 45
    Publikationsdatum: 2011-12-10
    Beschreibung: Delamination models are derived as the limits of models for partial isotropic volume damage via dimension reduction. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 46
    Publikationsdatum: 2011-12-10
    Beschreibung: Piezoelectric materials offer many possibilities in advanced engineering structures due to their inherent coupling effects between mechanical and electrical fields and are widely applied in smart devices and structures like transducers, actuators and sensors [2]. An important application of piezoelectric materials is related to layered or laminated composites because they can be optimized to satisfy the high-performance requirements according to different in-service conditions. Beside cracks inside homogeneous domains, one of the most dominant failure mechanisms in layered or laminated composites is the interface failure. Interface cracks and interface debonding may be induced by the mismatch of the mechanical, electrical and thermal properties of the material constituents during the manufacturing process and the in-service loading conditions. This paper presents a hypersingular symmetric Galerkin boundary element method (SGBEM) for crack analysis in two-dimensional (2D), layered and linear piezoelectric solids. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 47
    Publikationsdatum: 2011-12-10
    Beschreibung: In this work we present methods for the detection of cracks in plate and shell structures. In contrast to most of the common monitoring methods taking advantage of the reflection of surface waves at crack faces, the presented approach is based on the strain measured at different locations on the surface of the structure. This allows both the identification of crack position parameters, such as length, location and angles with respect to a reference coordinate system and the calculation of stress intensity factors (SIF). The solution of the direct problem is performed on the basis of the BFM (body force method) and the method of assembled point dislocations. The inverse problem is solved applying the PSO (particle swarm optimization) algorithm. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 48
    Publikationsdatum: 2011-12-10
    Beschreibung: The breathing mechanism of a transversely cracked rotor and its influence on a rotor system that appears due to the shaft weight is studied. This breathing mechanism is based on experimental and simulation result for the crack shape reported in the literature. If the crack depth is small, the crack closure line is a straight line while for larger crack depths the crack closure becomes more curved. For both cases, a method is proposed for the evaluation of the stiffness losses in the cross section that contains the crack. This method is based on a cohesive zone model (CZM) instead of linear elastic fracture mechanics (LEFM) approach, because LEFM is valid only for the fully open crack and cannot be extended to other intermediate situations. As the crack is closed, the stress intensity factor (SIF) will not appear at the boundary between the closed cracked areas and the open cracked areas. The CZM is developed for mode-I plane strain conditions and accounts explicitly for triaxiality of the stress state by using constitutive relations. The proposed model gives more realistic results than models based on LEFM for the stiffness losses of the crack rotor system for a wide range of the crack depth. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 49
    Publikationsdatum: 2011-12-10
    Beschreibung: Rational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present a heuristic for the automated pole selection when the function to be approximated is of Markov type, such as the matrix square root. The performance of this approach is demonstrated at several numerical examples. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 50
    Publikationsdatum: 2011-12-10
    Beschreibung: This paper deals with the dynamical modeling and control of modular redundant robots. The robots under consideration consist of modular actuators (brushless DC motors with Harmonic Drive gears) connected by rigid links. Different configurations can be designed by rearranging these subsystems. In order to fulfill the requirement for an efficient dynamical modeling, the Projection Equation in subsystem representation is used. The subsystems are connected via the kinematical chain. The Projection Equation offers the possibility to calculate the minimal accelerations recursively, leading to an O(n) computational effectiveness. To validate the proposed method, the model of an articulated robot arm with seven joints is considered. Simulation results are compared to measurements. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 51
    Publikationsdatum: 2011-12-10
    Beschreibung: In the present paper a three-dimensional beam finite element undergoing large deformations is proposed. Since the definition of the proposed finite element is based on the absolute nodal coordinate formulation (ANCF), no rotational coordinates occur in the formulation. In the current approach, the orientation of the cross section is parameterized by means of slope vectors. Since those are no unit vectors, the cross-section can deform, similar to existing thick beam and shell elements. The nodal displacements and the directional derivatives of the displacements are chosen as nodal coordinates, but in contrast to standard ANCF elements, the proposed formulation is based on the two transversal slope vectors per node only. Different approaches for the virtual work of elastic forces are presented: a continuum mechanics based formulation, as well as a structural mechanics based formulation, which is in accordance with classical nonlinear beam finite elements. Since different interpolation functions as in standard ANCF elements are used, a much better convergence rate (up to order four) can be obtained. Therefore, the present element has high potential for application in geometrically nonlinear problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 52
    Publikationsdatum: 2011-12-10
    Beschreibung: This paper concerns with the finite element simulation of textile reinforced concrete (TRC) behavior under tension loading by using discrete cracking concept and fracture mechanics approaches. 3D Finite-Element models are formulated on the meso-scale by simulating all the heterogeneous structural components, the matrix, the fibers, and the fracture mechanisms in both fiber-matrix interface, and the discrete cracks of the matrix. The presented numerical simulation in this study allows for better understanding of the stress distribution and the interaction between all damage mechanisms and the corresponding energy dissipations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 53
    Publikationsdatum: 2011-12-10
    Beschreibung: Today, the local approach to fracture is widely applied to simulate the failure of specimens. For ductile damage processes the Gurson-Tvergaard-Needleman model is the quasi-standard. In the last time non-local extensions allowed a mesh-size independent simulation of crack growth. However, most publications dealing with this subject focus upon the convergence regarding global quantities such as the load-displacement relation. Minor attention is paid to the fields directly at the crack tip. Correspondingly, the interrelationship between the intrinsic length of the model and relevant microscopic damage processes at the crack tip is only partly established until now. In the present study the crack propagation is simulated for an implicitly gradient enriched GTN-model within a boundary layer in order to overcome influences of the specimen geometry. The different stages of damage evolution are resolved by a fine mesh. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 54
    Publikationsdatum: 2011-12-10
    Beschreibung: In this article we develop the a priori error analysis of so-called two-grid hp -version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V (𝒯 H , P ). The resulting ‘coarse’ numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V (𝒯 h , p ); thereby, only a linear system of equations is solved on the richer space V (𝒯 h , p ). Numerical experiments confirming the theoretical results are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 55
    Publikationsdatum: 2011-12-10
    Beschreibung: This paper presents mixed finite element methods of higher-order for an idealized frictional contact problem in linear elasticity. The approach relies on a saddle point formulation where the frictional contact condition is captured by a Lagrange multiplier. The convergence of the mixed scheme is proven and some a priori estimates for the h - and p -method are derived. Furthermore, a posteriori error estimates are presented which rely on the estimation of the discretization error of an auxiliary problem and some further terms capturing the error in the friction and complementary conditions. Numerical results confirm the applicability of the a posteriori error estimates within h - and hp -adaptive schemes. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 56
    Publikationsdatum: 2011-12-10
    Beschreibung: This paper presents a hybrid model to describe drill string dynamics for deep hole drilling. Generally, a typical rotary drill string has a length of several kilometers, but the diameter is less than half a meter. Due to the large ratio of length to diameter, a drill string is a very flexible system. Consequently, an operating drill string is always affected by axial, torsional and lateral vibrations, which potentially induce serious failures. In order to avoid fatal defects, simulations to forecast vibrations are necessary. The simulation should be capable to exhibit the complex dynamical phenomena, e.g. sick-slip, forward whirl and backward whirl, and interactions between drill string and borehole. Usually, these simulations are very time-consuming. In this work, a hybrid model consisting of lumped masses connected with weightless beam elements representing the drill string is developed. The interaction between the drill string and the borehole is implemented by unilateral constraints to describe the nonlinear contact behavior. It was shown that accuracy and simulating time were improved by this model with respect to classical finite-element models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 57
    Publikationsdatum: 2011-12-10
    Beschreibung: Especially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method. In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state-of-the-art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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  • 58
    Publikationsdatum: 2011-12-10
    Beschreibung: The choice of coordinates for the description of multibody dynamics has a strong impact on the form of the equations of motion. In the talk two alternative formulations are compared: (i) joint coordinates along with Euler angles for the orientation of rigid bodies, and (ii) redundant coordinates where the orientation of rigid bodies is described in terms of direction cosines. In the case of multibody systems with tree structure the use of generalized coordinates yields equations of motion in the form of ordinary differential equations. In contrast to that, the choice of redundant coordinates yields differential-algebraic equations. The two alternative formulations are compared and their influence on the numerical time integration is highlighted. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 59
    Publikationsdatum: 2011-12-10
    Beschreibung: Active control of flexible vibrations by distributed piezoelectric actuators and sensors plays an increasing role in engineering, especially in light-weight structures. Exemplarily, in this contribution a rotating beam is studied which can be found in many practical applications, e.g. as robot arms or flexible manipulators in production processes. It has been intensively shown in the literature that it is possible to completely suppress the flexible vibrations by an appropriate distribution of piezoelectric actuation strains. In order to compensate the inertial forces in the considered rotating beam, a complex distribution is obtained, such that a practical realisation would be very extensive. To overcome the problem, a discrete approximation by piezoelectric patches is applied. In order to find an optimal configuration for an experimental setup, and to investigate several control strategies, a numerical simulation model has been implemented based on Bernoulli-Euler beam theory. The numerical results are verified by an experimental set-up, in which 48 piezoelectric patches have been attached on a beam with rectangular hollow cross-section. Each patch can be used either as an actuator or a sensor. Additionally, strain gauges can be used as sensors. For monitoring, acceleration sensors are used. The control system is implemented within a dSpace environment. The results show a significant reduction of the flexible vibrations. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 60
    Publikationsdatum: 2011-12-10
    Beschreibung: The paper contains the identification and the taking into account the vibrations produced by the machines, the lathe with different number of rotation, and them action over the human bodies inside the working space. For the identification of vibrations is applied a new method, the Moiré projection method, that did not used until this moment regarding the vibrations action over the human body. Our research was to apply the Moiré projection method to the human hand. They were compared with the measured vibrations using a classic vibrometer with three-axial accelerometer. The results in the booth situation were in the same order of the unit scale, and the optical method named Moiré projection method can be considered a valid method for the human vibrations measurements without touch of the surface. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 61
    Publikationsdatum: 2011-12-10
    Beschreibung: Synthesis of adequate mathematical description of the main mechanical line of rolling mill are considered. The four-mass model with weightless elastic connections is chosen as mathematical model of dynamic system of the main mechanical line of the rolling mill. The problem was reduced to solution of integral equation of the first kind (to unsteady problem). The methods of obtaining of the steady solutions are suggested. Synthesis of the adequate mathematical descriptions with unitary model of external load are suggested. The metal rolling was executed with using of real experimental measurements as an example. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 62
    Publikationsdatum: 2011-12-10
    Beschreibung: This paper aims at creating a mathematical model of a bending oscillation rotor system which enables to execute a dynamical analysis of its vibration including the influence of nonlinear bearing characteristics. More specifically, using the finite element method the model of rotating system supported by four hydrodynamic bearings was created. The basic dynamical analysis of the rotor system was performed and the eigenvalues, eigenvectors and stability conditions were evaluated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 63
    Publikationsdatum: 2011-12-10
    Beschreibung: The present work deals with the incorporation of residual stresses existing in circumferential direction of arterial walls. For the consideration of the residual stresses a novel model will be presented. This model is based on the assumption that residual stresses decrease the stress gradients through the thickness of the arterial wall. Since arterial walls exhibit a pronounced material behavior in fiber direction, the radial gradients of the fiber stresses are considered for the definition of the residual stresses. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 64
    Publikationsdatum: 2011-12-10
    Beschreibung: In this contribution a finite element model for the three dimensional investigation of hip joint contact is described. A shell-like interface element with variable thickness is developed for modelling fluid flow in the synovial gap. For this purpose the Taylor-Hood element is extended in order to take a spatial thickness distribution and local thickness changes into account. The interaction between the synovial fluid and the cartilage layers is solved by a staggered iteration using an artificial compressibility method. Cartilage is modelled using the theory of porous media and three dimensional geometries are reconstructed from medical imaging data. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 65
    Publikationsdatum: 2011-12-10
    Beschreibung: The present work deals with optimal control problems governed by differential-algebraic equations (DAEs). In particular, the control effort, which is necessary for moving a multibody system from one configuration to another, will be minimized. The orientation of the rigid bodies will be described using directors, which facilitates the integration of the equations of motion with an energy-momentum consistent time-stepping scheme [1]. This type of structure-preserving integrators offer outstanding numerical stability and robustness properties in comparison to the often applied generalized coordinates formulation. In the context of optimal control, other kinds of consistent integrators have been applied previously in [2] and [3]. We will test the different formulations with two numerical examples, a 3-link manipulator and a satellite. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 66
    Publikationsdatum: 2011-12-10
    Beschreibung: Modeling cardiac function is an important task to increase the understanding of the physiological response of the heart and to determine how complex structural heart components influence the biomechanical behavior of the heart. In this communication a coupled model of orthotropic ventricular myocardium is presented using fiber and sheet orientations that is matching regionally measured experimental data. This approach generates a more realistic and homogenized stress distribution when compared to a model with a generic fiber and sheet orientation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 67
    Publikationsdatum: 2011-12-10
    Beschreibung: This article presents the vibration action on the human body found in a tram travel, where made the vibration measurements. Also presented a mathematical model with two degrees of freedom. Finally a comparison was made between the results obtained from measurements and the results of integration. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 68
    Publikationsdatum: 2011-12-10
    Beschreibung: Bone tissues are formed by cells, bone matrix and fluids. The bone matrix is a porous structure, which is remodelled by bone-cells. To describe this process, a coupled systems-biological and biomechanical model is presented. The macroscopic mechanical behaviour of bone is specified by a biphasic model embedded in the Theory of Porous Media, where the solid phase represents cells and bone matrix, and the fluid phase summarises the extracellular fluids and its components. In this context, the bone remodelling process is described on the macro-scale by a distinct mass exchange that also results in a change of the constituents'material properties. On the micro-scale, the description of the bone remodelling process stems from a systems-biological cell interaction model. Therein, the bone matrix formation and resorption are a result of the stress-regulated activity of cells. Here, a staggered solutions strategy is presented. Therein, snapshots of the mechanical stress distribution are calculated on the macro-scale by use of the finite element method. The snapshots are locally evaluated on the micro-scale by use of a cell interaction model, which calculates the long term remodelling process. The evaluation results of the micro-scale are then used to update the reference configuration of the mechanical simulation. As an integrative modelling platform scientific workflows and web-service technologies are employed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 69
    Publikationsdatum: 2011-12-10
    Beschreibung: The paper presents a study regarding the linear mechanical models corresponding to hand-arm system. These models was simplified unused the joint in wrist, elbow and shoulder. Also, for these mechanical models effectuated the equations system that would integrate, it obtained the solutions (displacements and velocities) finally. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 70
    Publikationsdatum: 2011-12-10
    Beschreibung: The aim of the paper is to investigate the remodeling phenomenon of a cell-seeded material (collagen type-I) due to collagen type-II newly synthesized by the cells. For the experiments, a cell-seeded condensed collagen gel is mechanically stimulated in a bioreactor for four weeks. The remodeled stiffness of the cell-seeded gel is measured by a compression test and is explained with an evolution law. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 71
    Publikationsdatum: 2011-12-10
    Beschreibung: For surgery training and on-line support during surgeries a method is required which is able to reduce simulation time possibly even to realtime. This contribution compares the effectiveness of three model reduction methods, all of which are widely used for linear problems, in the context of nonlinear structural mechanics. Three reduction methods will be extended to nonlinear elasticity including large deformations. The performance of the extended concepts is investigated for a simplified model of a human inferior turbinate in the context of the functional endoscopic sinus surgery. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 72
    Publikationsdatum: 2011-12-10
    Beschreibung: Propulsion at human dolphin swimming is gained by performing an undulatory motion through the hole body. This movement is similar to undulatory fish motion. Special physical properties like stiffness of upper and lower extremity parts are creating significant unsteady vortex structures around the hole swimmer when performing dolphin kick. The characteristic of these structures and their influence at propulsion are not very well investigated yet. The present paper discribes the creation of a realistic model using data scans of a female swimmer. It is updated with her unique dolphin motion to simulated complete swim motion. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 73
    Publikationsdatum: 2011-12-10
    Beschreibung: Biomechanical simulation of human locomotion is commonly done via dynamical simulations of multibody systems. The actuation of the system is thereby often represented via muscle models that create a force depending on muscle length and activation level. We show a comparison of such a simulation using a structure preserving integration framework to MATLAB/Simulink results. The conclusion is that structure preservation is important to represent such systems correctly, in particular concerning energy and angular momentum evolutions. We introduce a method for structure preserving simulation of muscle actuated movements. Additionally we show examples of a simple arm movement including only one muscle as well as a finger movement including up to six muscles as an example for more complex biomechanical systems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 74
    Publikationsdatum: 2011-12-10
    Beschreibung: The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to optimize mechanical efficiency creating a naturally optimum structure. The current study utilized an advanced structural optimization algorithm, called design space toptimization (DSO), to perform a three-dimensional computational bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The large-scale simulation utilized a 175 µm mesh resolution with over 23.3 million elements. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using radiography. The results qualitatively showed several anisotropic trabecular regions that were comparable to the natural human femur. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as Wolff hypothesized. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 75
    Publikationsdatum: 2011-12-10
    Beschreibung: The present contribution is motivated by the desire to compute physiological loads on the intervertebral discs (IVD) of a human lumbar spine during activities like standing, bending and falling. Following this, a mechanical multi-body system (MBS) is utilised to capture the overall mechanical behaviour of a human, whereas an inhomogeneous, anisotropic, multi-phasic finite-element model (FEM) is applied to resolve the resulting field quantities inside an IVD. In order to couple the FEM of the IVD with the numerically diverse MBS, a homogenisation procedure has to be applied such that field quantities can be converted into discrete quantities. In particular, the MBS captures the mechanical behaviour of an IVD using a bushing element, which provides discrete force-displacement and moment-rotation relations. The goal of this contribution is to present a homogenisation method for the IVD as well as a possibility to include the homogenised results in the MBS without the need for embedded FE computations in the MBS. Instead, certain deformation modes of the IVD are pre-computed and represented using a non-linear constitutive equations. This task becomes even more challenging, as the resulting discrete DOF of a motion segment appear in a coupled fashion due to the structure of the IVD, i. e., a rotation in the sagittal plane triggers a resulting moment and a resulting force. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 76
    Publikationsdatum: 2011-12-10
    Beschreibung: The interpretation of human knee joint kinematics in terms of displacements is an outcome of the underlying model of the joint and the measurement technique. Measurement errors and noise challenge the development of optimization procedures which, based on a reduction in degrees of freedom, aim for the reproducibility of joint displacements by computational techniques. So far, optimization algorithms have been applied which are based on a kinematic model of the healthy human tibio-femoral joint (TFJ) as a compound hinge with two fixed orthogonal axes. On the other hand, empirical studies find non-orthogonal rotational axes. Therefore, it was the aim of the present study to investigate the implications of a refined kinematic model on the accuracy of computed joint rotation angles. For the purpose of quantitative comparison, kinematic data of a TFJ with two axes intersecting at an arbitrary angle were simulated. The joint rotations were optimized for the assumption of (a) two orthogonal and intersecting axes (model A), and (b) two axes intersecting at an arbitrary angle (model B). Model B recovers the original input data closer in case of low noise level as encountered in invasive measurement techniques. Skin mounted markers tracking involves non-normally distributed noise which is typically larger by on order of magnitude. In this case, model A exhibits a more favorable performance. These observations motivate the search for alternative kinematic descriptions of the TFJ. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 77
    Publikationsdatum: 2011-12-10
    Beschreibung: In a seated posture into an autovehicle, humans are most sensitive to whole-body vibrations under low-frequency excitation. This research is focused only on the effect of the backrest angle on the biodynamic response functions. In this paper there are present the results of investigations for 10 participants, whose mean body mass was 61.4 kg. For the biodynamic responses of a seated human body subjected to vertical vibrations, three automotive postures was study: without backrest support, with backrest inclined 7° and respectively 15°, by measurement of transmitted vibration in two different situations: with belt and respectively without this. Knowledge of human responses to vibration provides information about the position of backrest support to mitigate vibration transmitted through the body ensuring the health, comfort and performance. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 78
    Publikationsdatum: 2011-12-10
    Beschreibung: The interaction between capillary fluid films and micro-structural rough surfaces is one of the main challenges in studying self-cleaning mechanisms. The surface behavior of the deformable fluid film is governed by the Young-Laplace equation, which is highly non-linear. Therefore, a numerical solution is introduced using the finite element method, based on a continuum mechanical formulation. Surface and line contact at the fluid-structure interface are modeled by enforcing a contact constraint, and a contact angle, respectively. The numerical solution is validated against the analytical solution of a test case. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 79
    Publikationsdatum: 2011-12-10
    Beschreibung: This paper introduces, for the first time, a methodology to achieve a forward dynamics simulation of the musculoskeletal system using three-dimensional continuum-mechanical skeletal muscle models. This is achieved by coupling one- and three-dimensional skeletal muscle models. The feasibility of this methodology is demonstrated through a forward dynamics simulation of the upper limb involving the biceps and triceps muscle. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 80
    Publikationsdatum: 2011-12-10
    Beschreibung: Applanation tonometry estimates intraocular pressure (IOP) by quantifying the force needed to create a defined amount of deformation of the cornea (Goldmann tonometer) or by estimating the diameter of the circular contact area of the cornea and flat tonometer of defined load (Maklakov tonometer). The first simplest models of the applanation method for measurement of the IOP were based on approach, in which an eyeball is modelled as a thin-walled spherical liquid-filled soft shell with corneal biomechanical properties. It was usually supposed that these properties were the same for all patients. In this work numerical simulation have been carried out using finite element code ANSYS. The eye shell is modeled as two joint shells (cornea and sclera) with different mechanical properties. The results are obtained for numerous sets of parameters and were compared to clinical data. For statistics the measurements of IOP for both eyes of 120 patients before and one month after refractive surgery are used. All parameter of refractive surgery (depth, the width and the place of ablation - refractive surgery for myopia or hypermetropia) have effect on IOP reading obtained with both Goldmann and Maklakov tonometry. The results obtained by Goldmann tonometer are significantly more sensitive to all parameters of refractive surgery than those found with Maklakov tonometer with load 10 g. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 81
    Publikationsdatum: 2011-12-10
    Beschreibung: Standard methods for predicting the mechanical response of a human femur bone from quantitative computer-tomography (qCT) scans are classically based on the h -version of the finite element method. These methods are often limited in accuracy and efficiency due to the need for segmentation and the slow convergence rate. With the Finite Cell Method (FCM) a high-order fictitious domain method has been developed that overcomes the aforementioned problems and provides accurate results when compared to high-order finite element methods and experimental results. Herein the FCM applied to the analysis of a patient-specific femur is presented. The femur model is determined based on qCT-scans and the elastic response under compression is presented in terms of strains and displacements. The results are compared with a p -FE analysis and validated by results from an in-vitro test of the modeled femur. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 82
    Publikationsdatum: 2011-12-10
    Beschreibung: The aim of this research is to represent, within one modelling framework, selected parts of the musculoskeletal system using principles of continuum mechanics, while other parts are modelled using lumped-parameter models and principles of Multi-Body Dynamics. The most challenging part within such a framework will be to properly model the transition from 3D to 1D models for skeletal muscles as many of the skeletal muscles extend beyond the selected part. Hence, this paper focuses on an interface condition for the 3D-1D transition within a skeletal muscle. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 83
    Publikationsdatum: 2011-12-10
    Beschreibung: On daily activity a human operator is exposed to vibration in working environment. So, the human body will react in different way. The problem is how much from the initial signal will be sent to the other parts of the body and how much that motion will be damped along the studied parts. The vibrations in horizontal plane are some unexpected, so the human operator will not take any position to prevent them. In this condition the horizontal vibrations will have the higher effect possible. In this paper, the shoulder, neck and the head are modeled together like a mechanical system with four degree of freedom. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 84
    Publikationsdatum: 2011-12-10
    Beschreibung: 2-D fracture dynamics' problems for elastic bimaterials with cracks located at the bonding interface under the oblique time harmonic wave are considered in the study. The system of boundary integral equations for displacements and tractions is derived from Somigliana identity taking the contact interaction of the opposite crack faces into account. For the numerical solution the collocation method with piecewise constant approximation is used. The numerical results are obtained for various values of the angle of the wave incidence and the wave frequency taking the friction effects into account. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 85
    Publikationsdatum: 2011-12-10
    Beschreibung: The thermodynamical and variational consistency of cohesive zone models is analyzed in the present contribution. Based on a naive application of the classical Coleman & Noll procedure, it is shown that the second law of thermodynamics is not fulfilled in general. This can even be seen, in case of hyperelastic interfaces. For guaranteeing thermomechanical consistency, additional surface stresses acting at the interface have to be introduced. Based on such findings, a thermomechanically consistent model including dissipative effects is proposed. This model possesses a natural variational structure. More precisely, all state variables can naturally and jointly be computed by minimizing an incrementally defined potential. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 86
    Publikationsdatum: 2011-12-10
    Beschreibung: Ice shelves are important elements of the climate system and sensitive to climate changes. The disintegration of large Antarctic ice shelves is the focus of this fracture mechanical analysis. Ice is a complex material which, depending on the context, can be seen as a viscous fluid or as an elastic solid. A fracture event usually occurs on a rather short time scale, thus the elastic response is important and linear elastic fracture mechanics can be used. The investigation of the stress intensity factor as a measure of crack tip loading is based on a 2-dimensional analysis of a single crack with a mode-I type load and additional body loads. This investigation is performed using configurational forces. Depth dependent density and temperature profiles are considered. The relevant parameters are obtained by literature, remote sensing data analysis and modeling of the ice dynamics. The criticality of wet surface cracks is investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 87
    Publikationsdatum: 2011-12-10
    Beschreibung: In the current work, the physical phenomena of dynamic fracture of brittle materials involving crack growth, acceleration and consequent branching is simulated. The numerical modeling is based on the approach where the failure in the form of cracks or shear bands is modeled by a jump in the displacement field, the so called ‘strong discontinuity’. The finite element method is employed with this strong discontinuity approach where each finite element is capable of developing a strong discontinuity locally embedded into it. The focus in this work is on branching phenomena which is modeled by an adaptive refinement method by solving a new sub-boundary value problem represented by a finite element at the growing crack tip. The sub-boundary value problem is subjected to a certain kinematic constraint on the boundary in the form of a linear deformation constraint. An accurate resolution of the state of material at the branching crack tip is achieved which results in realistic dynamic fracture simulations. A comparison of resulting numerical simulations is provided with the experiment of dynamic fracture from the literature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 88
    Publikationsdatum: 2011-12-10
    Beschreibung: To characterise the randomly distributed strength and fracture toughness of brittle steels, many specimens have to be destroyed. Since the Small Punch Test (SPT) needs only little material, it is a well suited experiment, when only a small volume of material is available. In this study the cleavage fracture of a ferritic steel at low temperature was investigated using the Beremin model. The failure probability is described with a 2-parameter Weibull distribution in terms of the so-called Weibull stress, which is calculated using an elastic-plastic finite element stress analysis. While the transfer of Weibull parameters works well between similar geometries and loading conditions, it works bad in more general cases. Modifications of the Beremin model are necessary to overcome this problem. Recent publications consider a lower threshold value of the Weibull stress, which leads to a lower Weibull modulus and therefore to a stronger volume size effect of strength. The suitability of this approach to transfer cleavage fracture results from SPT to fracture mechanics specimens was investigated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 89
    Publikationsdatum: 2011-12-10
    Beschreibung: Delamination of thermally sprayed corrosion protection coatings as a consequence of thermo-mechanical fatigue is investigated. This study focusses on the modelling of interfacial damage initiation and evolution under cyclic loading with the help of a cohesive zone model. The presented model features a slight non-linearity at unloading from the exponential “damage locus” as well as cyclic damage accumulation restricted to (re)loading conditions. Additionally, an endurance limit is introduced indicating the maximum sustainable traction for an infinite number of load cycles. The capability of the model is demonstrated. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 90
    Publikationsdatum: 2011-12-10
    Beschreibung: The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. We focus on the extension of a recently developed phase field model for fracture from the quasi-static setting towards the dynamic setting. It is obtained by taking into account inertial terms and associated dynamic integrators. The introduction of a history field, containing a maximum fracture-driving energy, provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of an extremely robust operator split technique. In a subsequent step, the proposed model is extended to three dimensional problems. The dynamic treatment opens the door to the analysis of complex fracture phenomena like multiple crack branching and crack arrest. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
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    Thema: Mathematik , Physik , Technik allgemein
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  • 91
    Publikationsdatum: 2011-12-10
    Beschreibung: A new soft computing approach is described, which can be applied for the identification of uncertain time-dependent material behaviour. Artificial neural networks are utilized for model-free material formulations. Uncertain stress-strain-time dependencies obtained from uncertain results of experimental investigations are described by recurrent neural networks for fuzzy data. An incremental finite element formulation is presented using neural networks instead of material models. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
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  • 92
    Publikationsdatum: 2011-12-10
    Beschreibung: In this paper, new solid-shell and solid-beam finite element formulations for finite deformation problems are introduced. One application of interest, concerning these types of elements, can be found in the simulation of stent implementation in the treatment of stenosis. The beam-like structure of the stent and the shell-like structure of the blood vessel can be modelled easily by using these types of elements. Moreover, the modelling of the interaction of the different structural types between each other and with the surounding tissue becomes more simple. A high rate of convergence, by using only one element in thickness direction that is comparable to classical structural elements, can be named as a major requirement for the element formulations. In this regard, different locking effects are cured by a special combination of the assumed natural strain method (ANS) and the enhanced assumed strain method (EAS). In addition a variable number of quadrature points can be used in thickness direction in order to capture nonlinearites. This is combined with the concept of reduced integration for the sake of computational efficiency. An adaptive hourglass stabilization that also accounts for material nonlinearities is a crucial issue in this regard. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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  • 93
    Publikationsdatum: 2011-12-10
    Beschreibung: In this paper a new approach for designing mechatronic vibrating branched structures has been presented. Mechatronic structures have been built from mechanical discrete systems connected to piezoelectric actuator and external L x R x C x network, with different configurations. Modeling simplification has been performed by use of non dimensional transformations and retransformations. In each case reverse task has been solved by distribution into partial fraction method in respect to required dynamic properties in form of frequency spectrum: resonant and anti resonant frequencies. Furthermore, different configurations of final L x R x C x network have been presented. These considerations have been supported by calculation examples, and all results have been presented in the graphical form. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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  • 94
    Publikationsdatum: 2011-12-10
    Beschreibung: We will present a comparison between two formulations of the normal vector field for contact algorithms based on the mortar method. First the non steady normal field is discussed. The non steadiness is a result of the C 0 continuity of the boundary discretization. This is the common result if one discretize the domain with classical finite element methods. Second we will present results for a special normal field distribution. We average the nodal normal vector of two ascending edges and interpolate this nodal normal throughout the edges. We have implemented both methods and present comparisons based on numerical experiments. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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  • 95
    Publikationsdatum: 2011-12-10
    Beschreibung: Due to the roughness of technical surfaces only the surface peaks are in contact for moderate contact pressures. Thus, the real contact area is smaller than the apparent contact area. Contact forces can only occur in the real contact area. Consequently it is necessary to determine the deformation of surface asperities in order to analyse the tribological properties of surfaces. The real contact area is usually small in initial contact. This leads to large contact pressures which in turn lead to the plastic deformation of surface roughness peaks. Therefore an elastic-plastic model is necessary. The halfspace model seems to be beneficial because there is only a system of equations on a surface mesh to be solved and not on a volume mesh like in the Finite-Element-Method. This leads to a much smaller system of equations which should allow reasonable calculation times even for large contact surfaces. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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  • 96
    Publikationsdatum: 2011-12-10
    Beschreibung: In this work, a molecular mechanics model embedded in the finite element framework is applied to analyze the buckling behaviour of carbon nanotubes. Within this model a specific finite element is set up for the underlaying interatomic potential describing the behaviour of the multi particle system. The model relies on the fully nonlinear description of the interatomic potential and the atomic kinematics. Stability points of the system are located by an accompanying eigenvalue analysis and the bifurcation point is detected using a bisection algorithm. To follow the nonlinear load-deformation path in the area of postbuckling a branch switch is performed. With the help of this molecular mechanics model, the response of carbon nanotubes on different loading conditions with respect to buckling is studied. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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  • 97
    Publikationsdatum: 2011-12-10
    Beschreibung: Simply supported rectangular Kirchhoff-plates with two-parametric Pasternak-type foundation are studied under the action of a transient temperature moment, which is span-wise constant. In extension to a previous study it can be shown, that an excellent convergence of the series solutions of the static problem can be achieved by means of Kummer's transformation and Cesaro's generalized C 1 -Summation. The convergence improvement of the other types of the solutions can be performed analogously. The dynamic solution for the deflection and shear forces is computed using the derived efficient solution for the quasi-static case with fast convergent Fourier series. Modal expansion is applied for the computation of the vibrations about this quasi-static part. The results of he analytical solution for defined parameters of the foundation are shown for some characteristic points of the plate and compared to the FE computation results . (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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  • 98
    Publikationsdatum: 2011-12-10
    Beschreibung: Suitable continuous Sobolev embeddings are applied in order to derive smoothness estimators for adaptive hp -refinements in the context of hp -finite element methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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  • 99
    Publikationsdatum: 2011-12-10
    Beschreibung: Thin-film flows are involved in many coating processes, where it is desirable to achieve thin and homogeneous fluid layers. In the present investigations, we treat droplets, spreading on rotating solid substrates. Micro-scale effects appear, firstly, at the wetting front, where the film height tends to zero. Secondly, micro-scale effects may appear at other locations, where the free liquid/gas-interface approaches the solid substrate, as e.g. at film rupture. For such situations, molecular effects need to be considered, e.g. in form of the disjoining pressure (DJP), to get physically-correct solutions. Otherwise, the spreading can be modeled within the frame of continuum mechanics, augmented by the (empirical) law of Tanner to capture the contact-line dynamics. We present, on the one hand, an overview of several interesting issues, as (i) spreading with and without considering the DJP, (ii) spreading after central rupture, including hysteresis effects, and (iii) non-isothermal spreading, including temperature-dependent surface tension (Marangoni effect) and temperature-dependent density (Rayleigh-Bénard effect). On the other hand, we present results for the instability of the contact line, for which the contact line gets corrugated (under isothermal conditions). This instability goes along with a transition from (rotationally-symmetric) two-dimensional to three-dimensional behavior. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
    Standort Signatur Erwartet Verfügbarkeit
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  • 100
    Publikationsdatum: 2011-12-10
    Beschreibung: The importance of lightweight constructions are steady increasing since they promise a low energy consumption together with higher movement speeds. However these demand modern, model-based feed-forward control designs. Especially the undesired vibrations due to the reduced overall stiffness of such manipulators have to be taken into account. A convenient way to model the dynamical behavior of systems that perform large, nonlinear motions superposed with small, elastic deformations is the floating frame of reference approach in a flexible multibody system. The application of the Newton-Euler-Formalism together with D'Alembert's principle to parallel manipulators results in a set of differential-algebraic equations. Therefore, the consideration of the trajectory tracking problem with so-called servo constraints appears to be promising. In case of a non-flat system, the arising set of differential-algebraic equations, which consists of the system dynamics, the holonomic loop closing constraint equations and the servo constraints embodies nontrivial dynamics. With an oblique projection, the embedded set of ordinary differential equations describing the internal dynamics can be obtained. The stability properties of these dynamics determines the complexity of the feed-forward control design, as two-point boundary value problems might have to be solved. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
    Digitale ISSN: 1617-7061
    Thema: Mathematik , Physik , Technik allgemein
    Publiziert von Wiley
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