bluuebunny/crossref_metadata_2025 huggingface dataset:
Overview and comparison of different variants of the XFEM
Authors: Fries Thomas‐Peter
Published: December 2014

Different variants of the eXtended Finite Element Method (XFEM) have developed over the last years: The original, shifted, corrected, stable, and intrinsic XFEM. Herein, these variants are compared in terms of convergence rates and conditioning of the resulting systems of equations. Optimal convergence rates are achieved by the corrected, stable, and intrinsic XFEM for general enrichments. The original and shifted XFEM achieve optimal rates for selected enrichments only. In terms of the conditioning, it is found that the stable XFEM can be “optimal” in the sense that the same dependency on the mesh size as for the classical FEM is maintained. However, this finding only holds if one enrichment term is involved. In the presence of several enrichment terms, only the intrinsic XFEM yields well‐conditioned systems of equations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Topology Optimization of Flexible Multibody Systems Using Equivalent Static Loads and Displacement Fields
Authors: Moghadasi Ali , Held Alexander , Seifried Robert
Published: December 2014

Topology optimization techniques are applied in most cases for static applications. However, recently topology optimization procedures for structures under dynamic loads have been the focus of several studies. In this work, a topology optimization scheme for flexible multibody systems using equivalent static loads and displacement fields is investigated. The optimization problem is formulated using a homogenization method, more precisely, the solid isotropic material with penalization (SIMP) approach. The objective function in the optimization problem is the compliance and the method of moving asymptotes is used as optimizer. The objective function and the sensitivities are computed directly from the displacement field computed in the dynamic simulation. The examples of a 2‐arm manipulator and a slider‐crank mechanism are presented and the results are discussed to verify the improved dynamical behavior through this optimization method. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Model Reduction of Large Scale Finite Element Models
Authors: Volzer Thomas , Eberhard Peter
Published: December 2014

The usage of flexible bodies in Multibody simulations (MBS) has widely increased their industrial application. Finite Element (FE) models with up to 10 million degrees of freedom (DOF) and some hundred million nonzero matrix entries are used to describe the flexible bodies. Before such a model can be included into an MBS, the number of DOF must be reduced to an appropriate size. Using modal reduction often the critical issue arises which modes to choose while Component Mode Synthesis based methods often lead to a relatively big size of the resulting model. Alternative methods using Moment Matching and Balanced Truncation can result in a smaller size while still remaining accurate enough.

Sometimes these matrices are so huge that they can not even be stored in one computers main memory. The calculation of the necessary orthogonal Krylov subspaces needs an LU factorization which is also very memory intensive. To meet these requirements, distributed computation is used which also shortens the computational time of the reduced process.

In this work, an industrial relevant FE model is reduced to a much smaller size using alternative methods. Accuracy is verified by comparing the frequency response in a defined frequency range of the original and the reduced model. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Moon's perigee mass as a missing component of the Earth's precession‐nutation theory
Authors: Kiryan Dmitry , Kiryan George
Published: December 2014

In this work, the nutation momentum acting upon the Earth from the Moon's perigee mass that has not been taken into account in the Earth's precession‐nutation theory was revealed. This missing momentum exhibits itself in the so‐called “local latitude variation” with the Chandler's period. The results of our work raise the question of updating the Earth's precession‐nutation theory and revising some postulates of the time service, astronomy, geophysics, satellite navigation, etc. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Simulating underactuated multibody dynamics using servo constraints and variational integrators
Authors: Leitz Thomas , Leyendecker Sigrid
Published: December 2014

In underactuated dynamical systems, the number of control inputs nu is smaller than the number of degrees of freedom nq. Real world examples include e. g. flexible robot arms or cranes. In these two exmples the goal is to prescribe the trajectory of an end effector and find the necessary control variables. One approach to model these problems is to introduce servo constraints in the equations of motion that enforce a given trajectory for some part of the system [1]. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Usage of systematic multi‐body equations of motion for the design of a nonlinear vehicle dynamics controller
Authors: Nitzsche Gunter , Röbenack Klaus , Wagner Sebastian , Zipser Stephan
Published: December 2014

In this article the authors outline how systematic multi‐body equations can efficiently be used to derive a model for the design of a nonlinear vehicle dynamics controller for truck‐semitrailer combinations, steering the last trailer axle. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A Geometric Approach to Actuator Failure in Robotic Manipulators
Authors: From Pål Johan , Pham Cong Dung , Gravdahl Jan Tommy
Published: December 2014

The use of robotic manipulators in remote and sensitive areas calls for more robust solutions when handling joint failure, and the industry demands mathematically robust approaches to handle even the worst case scenarios. Thus, a systematic analysis of the effects of external forces on manipulators with passive joints is presented. In parallel manipulators passive joints can appear as a design choice or as a result of torque failure. In both cases a good understanding of the effects that passive joints have on the mobility and motion of the parallel manipulator is crucial. We first look at the effect that passive joints have on the mobility of the mechanism. Then, if the mobility, considering passive joints only, is not zero we find a condition for which the parallel manipulator is conditionally equilibrated with respect to a specific external force. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modular modelling of a multiple pendulum with a guided box attached to its end
Authors: Weyh Bernhardt , Zwiers Ulrike
Published: December 2014

A modular modelling strategy which combines motion equations in generalized coordinates with those formulated in terms of redundant coordinates is presented. The general idea is illustrated by the planar model of a multiple pendulum in the gravitational field whose upper end is spatially fixed, while its lower end is attached to an elastically guided box. It is shown how the governing differential‐algebraic system of equations can be reduced to a system of linear differential equations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Anisotropic viscohyperelastic behavior of intervertebral discs: Modeling and experimental validation
Authors: Azarnoosh Marzieh , Stoffel Marcus , Markert Bernd
Published: December 2014

Biomechanical investigations of human cartilage, especially intervertebral discs (IVDs), have greatly helped to improve people's health over the last several decades. The study of the underlying biomechanical characteristics of cartilage tissues is a key issue to understand its physiological function and degeneration or damage behavior. The aim of this investigation is to describe the biomechnical behavior of healthy sheep IVDs under various loading conditions. Experimental and cartilage histological data, including fiber orientation, are used to develop a viscohyperelastic material model, which allowed us to numerically study the mechanical behavior of IVDs, consisting of a cartilaginous, fiber‐reinforced ring surrounding a highly hydrated, gelatinous core. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Calculation of Optimal Bounds on the Probability of Failure of Soft Biological Tissues
Authors: Balzani Daniel , Schmidt Thomas , Ortiz Michael
Published: December 2014

In this contribution, a methodology for the calculation of optimal bounds on the probability of failure of soft biological tissues is presented. Two potential rupture criteria are considered and an uncertainty quantification method [1] is applied to a virtual experimental data set. The results for both criteria are compared in a finite element example. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Micro‐mechanical modeling of anisotropic inelastic response of soft tissues under supra‐physiological loading
Authors: Linka Kevin , Khiêm Vu Ngoc , Itskov Mikhail
Published: December 2014

Under supra‐physiological loading, soft tissues exhibit many inelastic phenomena, such as stress softening, hysteresis and permanent set [1]. Knowledge of the mechanical response of soft tissues under such a large range of deformation is vital for optimizations of vascular medical devices or improvement of injury prevention techniques. In this work, a micro‐mechanical model is proposed for soft collagenous tissues. Besides the anisotropy the model can also describe the aforementioned inelastic effects under extremal loadings. To this end, the dispersion of collagen fibers in the soft tissues is captured by a probability distribution of fiber orientations around preferred directions. The deformation induced damage inside the tissue is assumed to take place between collagen fibrils and is included within a statistical mechanical framework. Finally, the accuracy of the model is assessed by comparison with experimental data available in the literature. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Growing between barriers
Authors: Bolea Albero Antonio , Böl Markus
Published: December 2014

Growth in living materials is the result of the changes in volume and mass during their development. If volume expansion occurs in a constrained case, some living materials change its growth behaviour. For example, when growth takes place in an environment with restrictions of volume, living materials will stop their volume expansion under compression due to the high amount of water that makes these bodies nearly incompressible. In case boundary conditions limit the growth of the body, the growth direction changes and gives the body another shape as expected. We present a modelling approach that takes volume and shape restrictions during growth into account. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A mechanical approach to explain cortical folding phenomena in healthy and diseased brains
Authors: Budday Silvia , Steinmann Paul , Kuhl Ellen
Published: December 2014

The development of the human brain with its characteristically folded surface morphology remains an intensively discussed topic. Impressive advancements in different fields of research have enhanced the understanding of the brain. However, the mechanism that underlies the folding process in healthy and diseased brains remains undetermined. Here, we hypothesize that growth induced mechanical instabilities drive folding. Using the nonlinear field theories of continuum mechanics supplemented by the theory of finite growth [1], we model the human brain as a bi‐material with the cerebral cortex, a morphogenetically growing outer layer of gray matter, and the subcortex, a strain‐driven growing inner core of white matter [2]. This approach integrates the two popular but competing hypotheses that cortical folding is either driven by differential growth or by axon elongation. Through systematic sensitivity analyses, we identify the critical process parameters of cortical folding and quantify their impact on brain morphology. We further simulate phenomena causing malformations like lissencephaly and polymicrogyria [3], which are associated with neurological disorders, including severe retardation, epilepsy, schizophrenia, and autism. Understanding the mechanisms of cortical folding during brain development might facilitate the diagnostics and treatment of malformed brains. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multi‐dimensional, mechanical stimulation of cartilage implants
Authors: Fuhrmann‐Nelles Nadine , Rath Björn , Stoffel Marcus , Markert Bernd
Published: December 2014

In biomedical engineering, it is a common practice to replace injured cartilage by implants, which are seeded with human cartilage cells. Before implanting, the implants are cultivated and usually stimulated electrically or mechanically in a bioreactor to initiate cell multiplication and oriented cell growth.

A new experimental set‐up is developed leading to the possibility of stimulating such implants in a multi‐dimensional, physiologically consistent way. In cooperation with the University Medical Centre Aachen, a human knee simulator is developed. Cell‐seeded implants are placed in a recreated human environment and stimulated with several load cycles of reproduced walking. After the cultivation period, the implanted material is removed and biologically and mechanically evaluated. The quality of the implanted material as well as the influence of the body‐conformable load on the material is studied.

To understand the correlation between tissue remodelling and mechanical load history, the load and movement scenario is also numerically investigated. For this reason, the experiment is transferred to a geometrically realistic FE model of a human knee. As a first approach, an elastic material model is used. The aim is to have a predictive FE model with an optimal trade‐off between accuracy and efficiency using an appropriate material formulation. The results will be compared to experimental data. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiphasic Modelling of the Vertebral Bone for Cement‐Injection Studies
Authors: Bleiler Christian , Wagner Arndt , Stadelmann Vincent , Windolf Markus , Gueorguiev‐Rüegg Boyko , Köstler Harald , Boger Andreas , Ehlers Wolfgang , Röhrle Oliver
Published: December 2014

The stability of the human spine is highly dependent on the cancellous bone structure of the vertebra. In the case of osteoporosis and accompanied weaking of the vertebral structure, compression fractures and other lesions of the affected patient may occur. The reinforcement of the porous cancellous bone by the injection of bone‐cement is a common procedure in order to overcome this issues. The modelling and computational simulation of vertebroplasty, i.e., bone‐cement‐injection into the vertebra, is of major interest to obtain valid and reliable predicitions for this surgery. A detailed micromechanical (and locally single‐phasic) model exhibits the drawback that all geometrical and physical transition conditions of the individual parts and their complex microstructure have to be known. Therefore, this study considers a macro‐scopic (and multi‐constituent) continuum‐mechanical model based on the Theory of Porous Media, where the homogenisation of the underlying micro‐structure results in a model of three constituents. In particular, these are the solid bone skeleton, which is saturated by bone marrow, where the latter may be displaced by the injected liquid bone cement. The micro‐architecture is regarded by heterogeneous and anisotropic permeability tensors and the preferred directions of the trabecular bone structure. The presented strongly coupled macroscopic model offers the opportunity to not only simulate the flow of the pore fluids but also predicts the arising stresses and strains of the solid bone skeleton due to the numerical investigation of the injection process. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling and computation of acrylic bone cement injection and curing within the framework of vertebroplasty
Authors: Landgraf Ralf , Ihlemann Jörn , Kolmeder Sebastian , Lion Alexander , Lebsack Helena , Kober Cornelia , Schmölz Werner , Blattert Thomas R.
Published: December 2014

This contribution deals with the simulation based investigation of processes related to the surgical treatment of vertebroplasty. In this regard, a simulation framework has been developed, which includes the generation of microstructural computer models of cancellous bone structures, the simulation of bone cement injection by computational fluid dynamics (CFD) methods and finite element (FE) simulations of bone cement curing processes. The modelling and computation strategy is illustrated and different material modelling approaches for the representation of acrylic bone cements as a non‐linear fluid and a non‐linear viscoelastic solid with curing dependent properties are outlined. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mathematically modelling surface EMG signals
Authors: Mordhorst Mylena , Heidlauf Thomas , Röhrle Oliver
Published: December 2014

Comprehension and correct interpretation of EMG signals and their generation could still be well improved. Computational models that can predict the EMG signal resulting from realistic motor unit recruitment as well as the underlying biophysical processes of single skeletal muscle fibres are therefore highly desirable. Having such a model available, one can test, verify and improve algorithms determining motor unit recruitment. Here, we present a three‐dimensional, continuum‐based, forward model that is able to produce a virtual EMG signal based on the underlying biophysical principles of skeletal muscle fibre activation. The result is a virtual EMG signal for complex and realistic geometries that may even undergo deformations as in the case of dynamic contractions. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Variational Phase Field Modeling of Fracture Caused by Fluid Transport in Poroelastic Solids
Authors: Ulmer Heike , Mauthe Steffen , Miehe Christian
Published: December 2014

The numerical modeling of failure mechanisms due to fracture based on sharp crack discontinuities is extremely demanding and suffers in situations with complex crack topologies. This drawback can be overcome by recently developed diffusive crack modeling concepts, which are based on the introduction of a crack phase field. Such an approach is conceptually in line with gradient‐extended continuum damage models which include internal length scales. In this paper, we extend our recently outlined mechanical framework [1–3] towards the phase field modeling of fracture in the coupled problem of fluid transport in deforming porous media. Here, extremely complex crack patterns may occur due to drying or hydraulic induced fracture, the so called fracking. We develop new variational potentials for Biot‐type fluid transport in porous media at finite deformations coupled with phase field fracture. It is shown, that this complex coupled multi‐field problem is related to an intrinsic mixed variational principle for the evolution problem. This principle determines the rates of deformation, fracture phase field and fluid content along with the fluid potential. We develop a robust computational implementation of the coupled problem based on the potentials mentioned above and demonstrate its performance by the numerical simulation of complex fracture patterns. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A gradient‐enhanced continuum damage model for fibre‐reinforced materials at finite strains
Authors: Waffenschmidt Tobias , Polindara César , Menzel Andreas
Published: December 2014

The assumption of purely local continuum damage formulations may imply a loss of well‐posedness of the underlying boundary value problem. With regard to numerical methods such as the finite element method, this may lead to mesh‐dependent solutions, a vanishing localised damage zone upon mesh refinement, and hence physically questionable results. In order to circumvent these deficiencies, i.e. to regularise the problem, we, in this contribution, apply a non‐local gradient‐based damage formulation within a geometrically non‐linear setting allowing for large deformations. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the gradient enhancement of microplane damage models
Authors: Zreid Imadeddin , Kaliske Michael
Published: December 2014

The microplane model allows for the description of damage induced anisotropy in a natural manner by introducing constitutive laws for quantities on individual microplanes at each material point. However, if damage or other strain softening constitutive laws are used within the microplane approach, the well‐known problem of localization arises leading to pathological mesh dependency. This contribution focuses on the implicit gradient enhancement and its efficient application to regularize microplane damage models. Previous works enhanced the strain tensor, thus resulting in large number of additional degrees of freedom. A new method which enhances the equivalent strain driving the damage on each microplane is introduced. The new method limits the number of additional degrees of freedom to one, while preserving the regularizing effect. The capabilities of the proposed formulation are demonstrated by a numerical example. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of fiber‐reinforced PMMA at different scales
Authors: Díaz Guillermo , Mosler Jörn
Published: December 2014

This paper deals with the modeling of fiber‐reinforced PMMA. Focus is on the macroscopic mechanical response with emphasis on the fracture properties such as the ultimate strength and the fracture energy. In order to capture the macroscopic mechanical response of PMMA, a finite element formulation is presented. While the elastic response of the fibres and that of the surrounding matrix are modelled in standard manner, i.e., by standard bulk material models, the relevant failure modes such as cracking of the fibres are accounted for by means of the so‐called Strong Discontinuity Approach (SDA). Since the fibres are relatively small, their fracture mechanical properties crucially depend on their geometry, i.e., they show a pronounced size effect. Based on numerical analyses of fibres with different geometries, the aforementioned size effect is naturally incorporated into the formulation [1]. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Three‐dimensional cell model analysis of ductile damage under dynamic loading condition
Authors: Gerke Steffen , Kuhnt Kevin , Brünig Michael
Published: December 2014

The paper deals with the damage and fracture behavior of ductile metals under dynamic loading conditions. The in [1–3] presented phenomenological continuum damage and fracture model, which takes into account the rate‐ and temperature‐dependence of the material, provides reasonable results of experiments with high strain rates while the identification of the corresponding material parameters results difficult from the available experimental data. This lack of information can be resolved by micro‐mechanical numerical simulations of void containing unit‐cells. In this context results of dynamic micro‐mechanical simulations are presented which can be used to study the damage effects on the micro‐scale and to validate the rate‐dependent continuum damage model. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
PROCRACK‐A Software Tool for Finite Element Simulation of Three‐Dimensional Fatigue Crack Growth
Authors: Ludwig Christian , Rabold Frank , Kuna Meinhard
Published: December 2014

The lifetime of structural components is limited by fatigue cracks. After initiation from an existing defect the crack grows subcritically until it reaches a critical size. At this point it becomes unstable and the structural component fails. PROCRACK is a powerful tool that enables the commercial finite element software Abaqus to calculate the crack propagation in pre‐cracked components. The complete capability of Abaqus can be used to simulate nearly arbitrary geometries. Abaqus/CAE is used for the three‐dimensional modeling of the initial crack at a geometrical level by means of points, lines and triangles. The numerical analysis is performed by Abaqus/Standard. PROCRACK automatically generates a tube‐shaped submodel around the crack front to calculate the stress intensity factors with high accuracy. The Paris law or the NASGRO equation can be used to calculate the incremental crack growth. The shape of the crack and the finite element mesh are updated in every crack growth step. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Structural damage detection strategy using correlation functions under inconsistent excitation
Authors: Zhang Muyu , Schmidt Rüdiger
Published: December 2014

Structural damage detection using vibration response signals is appealing in recent years since it does not require the identification of the modal parameters or building the structures' finite element model, among which the correlation‐function‐based damage detection methodologies is a novel topic [1]. Beginning with the introduction of the correlation function theory, this paper proposes a new damage detection strategy using the auto correlation function values of vibration response signals of the structure. The maximum value of the auto correlation functions of the vibration responses from different measurement points are used to form the damage index to locate the damage. Differences of the damage index are used to make the damage location more clearly. As in real world applications, structures may undergo different external excitations [2]. Different external excitations are input into the intact and damaged structure. The results from numerical simulation of stiffness reduction detection of a 12‐story frame structure show that the proposed strategy can locate the damage correctly and has a very good anti‐noise ability under inconsistent external excitations. As only the vibration responses before and after damage are used in this damage detection strategy, it can be a useful tool for structural health monitoring. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Optimization of Slender Reinforced Concrete Columns
Authors: Bekdas Gebrail , Nigdeli Sinan Melih
Published: December 2014

Slenderness is an important issue in design of reinforced concrete (RC) columns. Especially for long columns, second order effects may be not so small to neglect, but the calculation of second order effects may take too much time. For that reason, ACI 318 design code includes a simple approach in order to increase the flexural moment of columns according to their slenderness. Thus, second order effects are considered. In optimization, the effect of slenderness can be considered by using the factored design flexural moments. In this paper, harmony search (HS) algorithm is employed to find the optimum design variables of slender RC columns. These design variables are web width, height, diameter and number of reinforcements. The optimization objective is total cost of materials including concrete and steel. The developed method is effective to find the optimal design for axial force, flexural moment and shear force values. As numerical examples, optimum design of columns with different lengths, but with the same loadings and material properties were investigated. Thus, the effect of slenderness was seen on the optimum costs. By the increase of column length, increase of total material cost is more than a linear increase. This situation shows us the effect of slenderness on optimum RC columns (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On Some Analytic Methods for Calculating of Cusped Prismatic Shells
Authors: Chinchaladze Natalia
Published: December 2014

Cusped plates, on the one hand, are very important details from the practical point of view, such plates and beams are often encountered in spatial structures with partly fixed edges, e.g., stadium ceilings, aircraft wings, submarine wings etc., in machine‐tool design, as in cutting‐machines, planning‐machines, in astronautics, turbines, and in many other areas of engineering (e.g., dams); on the other hand, their theoretical analysis and calculation are mathematically connected with the study of the problems for degenerate partial differential equations which are not covered by the general theory for degenerate partial differential equations (see, e.g., [3]). Some satisfactory results are achieved in this direction in the case of Lipschitz domains but in the case of non‐Lipschitz domains there are a lot of open problems. To investigate such problems are the main part of the the present paper. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Determination of the Transverse Shear Stress in an Euler‐Bernoulli Beam Using Non‐Admissible Virtual Displacements
Authors: Eugster Simon , Glocker Christoph
Published: December 2014

The point of view that a beam can be considered as a three‐dimensional continuum with a constrained position field (cf. [1]) together with the virtual work principle and the concept of perfect constraint stresses, leads to a systematic way to reduce the equilibrium equations of the continuous body to an ordinary differential equation describing the constrained displacement field of the beam. Using virtual displacements, being non‐admissible with respect to the constrained beam kinematics, together with the solution of the boundary value problem, allows us to analytically determine the constraint stresses and consequently the total stresses of a beam up to a certain indeterminacy. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Kinematic modeling of flexure hinges and compliant mechanisms
Authors: Roesner Malte , Lammering Rolf
Published: December 2014

In this paper, the kinematic performance of flexure hinges and compliant mechanisms calculated by conventional modeling techniques are compared. As these exhibit certain drawbacks with regard to control strategies, mainly large number of degrees of freedom or unacceptable errors, a novel modeling approach for flexure hinges is presented. Instead of the entire flexure hinge only its significant regions are modeled by 3‐D structural solids. These master patterns are positioned appropriately and connected by rigid constraint conditions to build a compliant mechanism. The resulting model is characterized by considerably fewer degrees of freedom than a full solid model as well as a marginal deviation of the deflection compared to that of pseudo‐rigid‐body models, 3‐D tapered finite beam elements and analytical Timoshenko beam theory. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Bending behavior of a bi‐morph piezoelectric curved beam
Authors: Usta Raif , Arslan Eray
Published: December 2014

A simple and concise mathematical model describing the deformation and the electrical behavior of a bi‐morph piezoelectric curved sensor subjected to pure bending is developed. In particular, the influence of the couple moment on the electrical potential generated in the sensor is investigated and the results are presented in graphical form. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Comparison of measured and calculated eigenmodes for squirrel cage rotors using methods of design of experiments
Authors: Großhauser Johannes
Published: December 2014

To compare measured and calculated mode shapes, the natural frequencies and the mode shapes must be checked. For sensitivity analysis, which is the first step when optimizing parameters, the results must be automatically evaluated. When evaluating mode shapes and dependent natural frequencies, numerical values have to be determined. In this paper, a method is shown, how mode shapes and natural frequencies can be considered within one value for each mode shape. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Displacement‐based finite difference approximations of derivatives of the tangent stiffness matrix with respect to the load parameter
Authors: Jia Xin , Mang Herbert A.
Published: December 2014

The vehicle to investigate to which extent energy‐based categorization of buckling can be linked up with spherical geometry is the so‐called consistently linearized eigenproblem. This investigation requires computation of the first and the second derivative of the tangent stiffness matrix
$\tilde{\bf{K}}_T$
with respect to a dimensionless load parameter λ in the frame of the Finite Element Method (FEM). A finite‐difference approximation of the first derivative of
$\tilde{\bf{K}}_T$
, redefined as a directional derivative, has proved to meet the requirements of computational efficiency and sufficient accuracy. It represents a displacement‐based finite‐difference approximation, abbreviated as DBFDA. The present work is devoted to the computation of a DBFDA of the second derivative of ˜ KT with respect to λ. For the special case of a two‐dimensional co‐rotational beam element, an analytical solution of this derivative is presented. A circular arch, subjected to a vertical point load on its apex, serves as an example for numerically assessing the usefulness of the computed DBFDAs of the first and the second derivative of
$\tilde{\bf{K}}_T$
with respect to λ. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On the non‐ideal vibrating structures
Authors: Chiroiu Veturia , Donescu Stefania , Dumitriu Dan
Published: December 2014

In this work, analysis of the response to vibrations of a small building equipped with an electromechanical vibration absorber is investigated. The case of harmonic excitation with constant or time dependent frequencies is considered. The interaction between the structure and the energy source is analyzed via the Sommerfeld effect inside the resonance region. The resonance capture and the vibration reduction are displayed by the time history displacement of the last story. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimum Tuned Mass Dampers for Structures at Rock and Soil Sites
Authors: Nigdeli Sinan Melih , Bekdas Gebrail
Published: December 2014

In optimum design of tuned mass dampers (TMD), several factors are effective. One of the most important factors is the characteristics of the excitation. Earthquake excitations recorded at soil and rock sites show different characteristics in period and damping. In this paper, optimum TMD properties are separately searched for seismic structures at soil sites and rock sites. For each optimization, six different earthquake records were used. A design methodology was used by employing harmony search (HS). The approach was applied to a ten story structure with one second critical period. Although more damping ratio for TMD is needed for soil sites than rock sites, TMD is more effective for rock sites than soil sites. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An energy‐entropy‐consistent time stepping scheme for finite thermo‐viscoelasticity
Authors: Krüger Melanie , Groß Michael , Betsch Peter
Published: December 2014

This paper presents a time integrator, which is based on a time discrete spatially weak finite element formulation, but fulfills the same balance laws as the underlying (five) differential equations. Namely, in addition to the balances of linear and angular momentum as well as entropy, also the balances of total energy and LYAPUNOV function are fulfilled. The spatially weak formulation is obtained by integration by parts. Where the resulting virtual stress power term is well‐known, the virtual entropy production by conduction of heat is less known. The time discretisation is based on the midpoint rule and non‐standard time discrete differential operators. This time integrator is a further development of the TC integrator of I. ROMERO. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Enhanced low‐order displacement finite elements using incompatible mass scaling and static condensation in explicit time integration
Authors: Schmied Christoph , Mattern Steffen , Schweizerhof Karl
Published: December 2014

For nonlinear transient problems as well as rather slow quasi‐static processes explicit time integration has proven to be a suitable and robust time integration algorithm. As a consequence of the Courant‐Friedrichs‐Lewy (CFL) criterion small time step sizes are necessary and the overall computation time is dominated by the operations on element level. Privileged use of low order finite elements is common in explicit time integration due to their efficiency and robustness. In order to suppress artificial locking effects the work of Bischoff and Romero [1] is followed where a generalization of the method of incompatible modes (IM) is derived being equivalent to the class of enhanced assumed strain (EAS) elements originally proposed by Simo and Rifai [2]. These concepts are bound to a static elimination procedure of internal parameters which may result in a considerable expansion of the computational costs in the case of an explicit time integration scheme. In order to avoid the static elimination procedure inertia is considered for the incompatible parameters as suggested by Mattern et al. [3, 4]. This step allows integrating the incompatible parameters directly in time, but since rather large stiffnesses are related to the incompatible parameters – particularly for the volumetric mode enhancements – the highest eigenfrequency may be increased which would lead to a decrease of the time step size. This motivates scaling the masses associated to these incompatible parameters to control their effect on the time step size. It is possible to derive analytically based estimates for the scaling of the IM‐masses in order to achieve results agreeing very good with the classical EAS approach including large deflections and nonlinear material behaviour with elasto‐plasticity. The numerical implementation is performed using AceGen [5]. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Assessment of the static and fatigue strength of a precession driven dynamo under thermomechanical loads
Authors: Beisitzer Stephan , Scheffler Michael , Beitelschmidt Michael
Published: December 2014

At the Helmholtz‐Zentrum Dresden‐Rossendorf an experimental plant is developed to investigate the formation of magnetic fields in flows of liquid metals. Because of the enormous hazard potential of the used liquid sodium it is essential to avoid any damages during operation and so a detailed analysis using the finite element method is necessary considering the various mechanical and thermal loads. Therefore several tens of thousands load cases have to be taken into account. Hence an algorithm is developed to identify the relevant stresses referring to FKM guideline which are used for the static and fatigue strength assessment. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A two‐scale simulation method accounting for thermal effects during turning
Authors: Schindler Stefan , Zimmermann Marco , Aurich Jan C. , Steinmann Paul
Published: December 2014

During chip formation in turning processes, mechanical work is dissipated into thermal energy by plastic deformations and frictional processes. In case of dry cutting, the generated heat is in part removed with the chips while the rest flows into the tool and the workpiece. Within the latter, the temperature increases due to this heat flow, which in turn causes thermal expansions that increase the cutting depth and thus induce deviations from the nominal workpiece geometry. These effects are treated separately by a local model for the chip formation and a global model for the whole workpiece in order to determine the temperature distribution inside the workpiece and the dependent thermal expansion. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modeling of packaging behavior in closed‐cell aluminum foam
Authors: Ievdokymov Mykola , Eremeyev Victor A. , Altenbach Holm
Published: December 2014

The aim of this paper is to present the available modeling strategy available for description of the packaging behavior, which often takes place in the foams. The packaging process is modeled by means of approaches, which are used in the phase transformation theory. The constitutive model is based on the double‐well elastic potential, which is defined for small strains. Two principal approaches are used for the research: discrete method based on the Voronoi tessellation and phase‐field method. Discrete modeling approach is required for the estimations of the critical stresses in foams, which leads to the initiation of the packaging process. The phase‐field approach is the continual approach, which is required for description of the packaging propagation in the foam. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
On a least‐squares formulation for hyperelastic, transversely isotropic problems
Authors: Steeger Karl , Schwarz Alexander , Schröder Jörg , Starke Gerhard , Müller Benjamin
Published: December 2014

In the present work a mixed finite element based on a least‐squares formulation is proposed. In detail, the provided constitutive relation is based on a hyperelastic free energy including terms describing a transversely isotropic material behavior. Basis for the element formulation is a weak form resulting from a least‐squares method, see e.g. [1]. The L2‐norm minimization of the residuals of the given first‐order system of differential equations leads to a functional depending on displacements and stresses. The interpolation of the unknowns is executed using different approximation spaces for the stresses (Wq (div, Ω)) and the displacements (W1,p(Ω)), under consideration of suitable p and q. For the approximation of the stresses vector‐valued shape functions of Raviart‐Thomas type, related to the edges of the respective triangular element, are applied. Standard interpolation polynomials are used for the continuous approximation of the displacements. The performance of the proposed formulation will be investigated considering a numerical example. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Modelling and Simulation of Asphalt
Authors: Wimmer Johannes , Schnepp Johannes , Reese Stefanie
Published: December 2014

Increasing requirements on the durability of road pavements demand the conception of innovative asphalt types. Particularly the stability under load needs improvement in order to prevent rutting. Since the load bearing capabilities of asphalt are mainly governed by the granular lattice and the binder that glues the rocks together, simulation based approaches that aim on supporting R&D in road engineering must capture the granulometry of the material. A Voronoi tesselation based description of the structure is proposed that enables the separate modelling of grains and binder as continuous materials and attempts to accurately reproduce those features. First, a neat Voronoi tesselation is created within the modelling domain. These irregular convex polyhedra representing the grains are subsequently subject to a shrinking process and further modified to accurately represent the granulometric distribution of real asphalt types. Now, the space between the grains can be used for a volumetric representation of the binder. Full‐field strain measurements during the indirect tensile test of mastic asphalt, stone mastic asphalt and asphalt concrete have been performed for validation of the approach. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Efficient computation of cellular materials using the finite cell method
Authors: Heinze Stephan , Joulaian Meysam , Egger Herbert , Düster Alexander
Published: December 2014

The application of cellular materials in lightweight structures is a subject of growing interest. As meshing with surface aligned elements is very time consuming and entails a lot of degrees of freedom, we apply the finite cell method (FCM). The FCM is an extension of the known fictitious domain methods based on using high order polynomials for the Ansatz functions. In order to obtain a realistic representation of the geometry, we derive our discretization directly from the voxel data coming from the computer tomography (CT‐scan) of the specimen of interest. Thus, a much coarser Cartesian grid consisting of hexahedral cells can be readily generated in a fully automated fashion. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
FEM‐Simulation of “Die‐Less Hydroforming”
Authors: Metzger Andreas , Ruff Daniel C. , Ummenhofer Thomas
Published: December 2014

The following contribution focuses on the FEM‐simulation of “Die‐Less‐Hydroforming” using LS‐DYNA. That specific forming technology is used to create structures by inflating initial seal‐welded flat 2D blanks as well as 3D hollow bodies without using any die, mould or punch in contrast to conventional hydroforming (e.g. tube hydroforming or hydromechanical deep drawing). (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Advanced Solution Strategies for r‐Adaptive Finite Element Analysis
Authors: Rambausek Matthias
Published: December 2014

In Finite Element Analysis (FEA) the discretisation has wide influence on the quality of the analysis. With r‐adaptive FEA it is aimed to improve the finite element solution by finding the optimal mesh without changing the mesh connectivity and the order of the elements. Thus, this approach belongs to the group of mesh‐moving methods. The r‐adaptivity approach presented is governed by energy minimisation and therefore is called energy‐based. It is built upon a variational Arbitrary Lagrangian‐Eulerian (vALE) formulation whereby the potential energy is varied with respect to spatial and material coordinates. However, even for simple problems the Hessian is likely to be singular or indefinite. This complicates the application of solution schemes based on Newton's method. Motivated by the approaches of [1–4], we try to find appropriate numeric methods for r‐adaptivity. For this purpose, we study the numerical performance of a primal barrier scheme, of an augmented Lagrange barrier scheme and the primal‐dual interior point package IPOPT. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The anisotropic coupling of one‐dimensional problems in linear elasticity
Authors: Schneider Patrick , Kienzler Reinhold
Published: December 2014

We investigate the coupling of the four one‐dimensional problems of linear elasticity (i.e., the rod‐, the two beam‐ and the shaft‐problem), for the case of a cross section that has two orthogonal axes of reflectional symmetry. An analytical proof is given, that the problems are decoupled for a homogeneous orthotropic material and the coupling behavior is given for monoclinic materials in dependence of the orientation of the symmetry plane. For a general anisotropic (aelotropic) material all four problems are coupled. We also identify the driving forces for the four problems, leading to a detailed definition of the admissible load‐cases for the classical problems, so that any three‐dimensional load‐case can be uniquely decomposed into the driving forces of the four problems. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Weak coupling of thin‐walled multi‐patch NURBS structures in the framework of isogeometric analysis
Authors: Ruess Martin , Guo Yujie
Published: December 2014

In the framework of isogeometric analysis, models are typically derived by the use of computer‐aided geometric design (CAGD) tools which often results in a large number of non‐conforming NURBS patches that are connected along arbitrary curved boundaries. A strong coupling on the basis of matching control meshes is rarely possible and limits the modeling process for practical applications. Weak coupling according to the principles introduced by Nitsche is the method of choice if a stable and variationally consistent method is favored which does not require the solution of additional equations to enforce the coupling constraints. We concentrate on the weak coupling of thin‐walled shell structures modeled according to the theory of Kirchhoff‐Love. The proposed concept is free of ad‐hoc decisions for stabilization thus truly supporting a design‐through‐analysis idea. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)