bluuebunny/crossref_metadata_2025_split huggingface dataset:
Energy‐momentum conserving discretization of mixed shell elements for large deformation problems
Authors: Janz Alexander , Betsch Peter 
Published: October 2015

AbstractIn the present paper we consider structure‐preserving integration methods in the context of mixed finite elements. The used low‐order mixed finite elements typically exhibit improved coarse mesh accuracy. On the other hand energy‐momentum (EM) consistent time‐stepping schemes have been developed in the realm of nonlinear structural dynamics to enhance the numerical stability properties. EM schemes typically exhibit superior robustness and thus offer the possibility to use large time steps while still producing physically meaningful results. Accordingly, combining mixed finite element discretizations in space with EM consistent discretizations in time shows great promise for the design of numerical methods with superior coarse mesh accuracy in space and time. Starting with a general Hu‐Washizu‐type variational formulation we develop a second‐order accurate structure‐preserving integration scheme. The present approach is applicable to a large number of mixed finite element formulations. As sample application we deal with a specific mixed shell element. Numerical examples dealing with large deformations will show the improved coarse mesh accuracy in space and time of the advocated approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A high‐order enrichment strategy for the finite cell method
Authors: Joulaian Meysam , Zander Nils , Bog Tino , Kollmannsberger Stefan , Rank Ernst , Düster Alexander 
Published: October 2015

AbstractThanks to the application of the immersed boundary approach in the finite cell method, the mesh can be defined independently from the geometry. Although this leads to a significant simplification of the mesh generation, it might cause difficulties in the solution. One of the possible difficulties will occur if the exact solution of the underlying problem exhibits a kink inside an element, for instance at material interfaces. In such a case, the solution turns out less smooth – and the convergence rate is deteriorated if no further measures are taken into account. In this paper, we explore a remedy by considering the partition of unity method. The proposed approach allows to define enrichment functions with the help of a high‐order implicit representation of the material interface. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A surface oriented solid formulation based on a hybrid Galerkin‐collocation method
Authors: Klinkel Sven , Chen Lin , Dornisch Wolfgang 
Published: October 2015

AbstractThe contribution is concerned with a numerical method to analyze the mechanical behavior of 3D solids. The method employs directly the geometry defined by the boundary representation modeling technique, which is frequently used in CAD to define solids. It combines the benefits of the isogeometric analysis methodology with the scaled boundary finite element method. In the present approach, only the boundary surfaces of the solid are discretized. No tensor‐product structure of three‐dimensional objects is exploited to parametrize the physical domain. The weak form is applied only on the boundary surfaces. The governing partial differential equations of elasticity are transformed to an ordinary differential equation (ODE) of Euler type. The isogeometric Galerkin approach is employed to approximate the displacement response at the boundary surfaces. It exploits the two‐dimensional NURBS objects to parametrize the boundary surfaces. To solve the Euler type ODE, the NURBS based collocation approach is applied. The accuracy of the method is validated against the analytical solutions. The presented method is able to analyze solids, which are bounded by an arbitrary number of surfaces. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A projection approach to optimal control of elastic beam dynamics
Authors: Kostin Georgy 
Published: October 2015

AbstractControlled lateral motions of an elastic beam – extended body with a cuboid shape – are studied. A generalized statement of the initial‐boundary value problem is given in the frame of 3D linear elasticity based on the integral formulation of constitutive relations. A numerical approach relying on the Fourier method and semi‐discretization technique is proposed to design the optimal boundary control that moves the beam to a given final state and minimizes a quadratic cost function. Some results of numerical simulation and quality analysis are presented and discussed. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A stress‐velocity least‐squares mixed finite element formulation for incompressible elastodynamics
Authors: Nisters Carina , Schwarz Alexander , Steeger Karl , Schröder Jörg 
Published: October 2015

AbstractIn the framework of solving elastodynamic problems using a least‐squares mixed finite element method (LSFEM) the implementation of a stress‐velocity formulation for small strains is introduced and discussed in the present contribution. The element formulation is based on a first‐order div – grad system, with the balance equation of momentum and the constitutive law as the governing equations. Application of the L2‐norm to the two residuals leads to a functional depending on stresses and velocities. Different time discretization schemes are considered, a scalar weighting is introduced and chosen in dependency of the different time discretization methods. In a numerical example the influence of the time integration method, the chosen time step width and the related weighing factor are investigated for a two‐dimensional problem. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Mixed Tetrahedral Elements for the Analysis of Structures with Material and Geometric Nonlinearities
Authors: Nodargi Nicola A. , Bisegna Paolo 
Published: October 2015

AbstractA new mixed tetrahedral element, particularly suited for the analysis of structures exhibiting nonlinear material and geometric behavior, is here presented. Its derivation is based on a Hu–Washizu type formulation, including also rotation and skew‐symmetric stress fields as independent variables, instrumental to equip the element with nodal rotational degrees of freedom. A Gauss‐point‐discontinuous interpolation is selected for the total strain field, in order to account for its possibly highly nonlinear spatial distribution due to inelastic strains. Accordingly, the resulting tetrahedron can properly describe inelastic effects occurring over a space scale smaller than the element size. An original and efficient iterative procedure is proposed to perform the element state determination. Geometric nonlinearities are treated by means of the corotational approach. A numerical simulation is presented to analyze the element performances. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
XFEM for Deformation Theory of Plasticity
Authors: Omerović Samir , Fries Thomas‐Peter 
Published: October 2015

AbstractIn this work, an approach is presented to improve global accuracy properties for physically non‐linear problems in the frame of elastoplasticity. The work is motivated by the fact that convergence characteristics of a finite element solution are dominated by the regularity of the exact solution. For a material undergoing inelastic deformations, however, very few analytical solutions for the field variables are known, especially for the displacement field. Considering a simple, one‐dimensional example, it is shown that the convergence rates are far from optimal. The reason is explained by establishing ties to a familiar, but more demonstrative problem. In the next section two remedies for the problem, based on the Extended Finite Element Method (XFEM) are presented and discussed, in the last section a 2D‐problem is considered. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Discussion of the Particle Finite Element Method in the Context of Strength of Materials
Authors: Sabel Matthias , York Duran José L. , Sator Christian , Müller Ralf 
Published: October 2015

AbstractIn the context of the particle finite element method (PFEM) a body is considered as a set of particles that are meshed with standard finite elements before every load step. This enables the method to cope with large topological changes where the standard FEM often fails. To mesh the set of particles, its boundary needs to be detected which is accomplished with the α‐shape method, and although this method is often used within the PFEM, the crucial parameter α is not well understood. This article provides a physical interpretation of α and shows its meaning in the context of strength of materials. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Weighted overconstrained least‐squares mixed finite elements for hyperelasticity
Authors: Schwarz Alexander , Steeger Karl , Schröder Jörg 
Published: October 2015

AbstractThe present contribution aims to improve the least‐squares finite element method (LSFEM) with respect to the approximation quality in hyperelasticity. We consider a geometrically nonlinear elastic setup and here especially bending dominated problems. Compared with other variational approaches as for example the Galerkin method, the main drawback of least‐squares formulations is the unsatisfying approximation quality in terms of accuracy and robustness of especially lower‐order elements, see e.g. SCHWARZ ET AL. [1]. In order to circumvent these problems, we introduce an overconstrained first‐order stress‐displacement system with suited weights. For the interpolation of the unknowns standard polynomials for the displacements and vector‐valued Raviart‐Thomas functions for the approximation of the stresses are used. Finally, a numerical example is presented in order to show the improvement of performance and accuracy. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Comparison of a mixed least‐squares formulation using different approximation spaces
Authors: Steeger Karl , Schröder Jörg , Schwarz Alexander 
Published: October 2015

AbstractThe main goal of the present work is the comparison of the performance of a least‐squares mixed finite element formulation where the solution variables (displacements and stresses) are interpolated using different approximation spaces. Basis for the formulation is a weak form resulting from the minimization of a least‐squares functional, compare e.g. [1]. As suitable functions for
$H^1(\cal{B})$
standard interpolation polynomials of Lagrangian type are chosen. For the conforming discretization of the Sobolev space
$H({\rm div}, \cal{B})$
vector‐valued Raviart‐Thomas interpolation functions, see also [2], are used. The resulting elements are named as PmPk and RTmPk. Here m (stresses) and k (displacements) denote the approximation order of the particular interpolation function. For the comparison we consider a two‐dimensional cantilever beam under plain strain conditions and small strain assumptions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Interlaminar stress recovery for arbitrarily curved shells
Authors: Winkler Robert , Haller Herbert , Plakomytis Dimitrios , Gerstmayr Johannes 
Published: October 2015

AbstractAn established postprocessing procedure for the determination of interlaminar shear and normal stresses based on the results of a conventional shell finite element analysis is generalized for arbitrarily curved laminated shells. The method relies on the three‐dimensional equilibrium conditions and an extended lamination theory. Underlying approximations are discussed and exemplary results are presented. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Stability and bifurcation behaviour of a Laval‐Rotor considering fluid forces in compliant liquid seals
Authors: Bäuerle Simon , Hetzler Hartmut 
Published: October 2015

AbstractThis contribution discusses the influence of fluid forces, stemming from compliant, contact‐free annular rotor seals, on the steady state stability and bifurcation behaviour of a rotor. The model used in this work consists of a Laval‐Rotor where the disc runs in a turbulently streamed seal. The compliance of the seal is reduced to a visco‐elastically supported outer seal ring. In order to account for the fluid seal forces the Childs‐Hirs‐model is used. An investigation of the eigenvalues shows that the compliance of the seal support may lead to a significant increase in the stable operating range. A stability‐loss via Hopf‐, Hopf‐Hopf or secondary Hopf‐Bifurcations can occur depending on the system parameters. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Optimal Impedance Load of a Bistable Energy Harvester
Authors: Heymanns Matthias , Hagedorn Peter 
Published: October 2015

AbstractIn this contribution we investigate a bistable energy harvester with regard to its optimal impedance load. A bistable energy harvester exhibits three different types of oscillation: Single‐well (about a stable equilibrium), cross‐well (between the wells) and inter‐well (about the unstable equilibrium). The occurring oscillation type depends, for instance, on the excitation parameters and the initial conditions. It has already been observed ( [1]) that the optimal impedance, which allows to maximize the power output, varies for each oscillation type. In our investigations we complement these findings with analytical and numerical calculations. For our analysis we examine the non‐dimensionalized coupled equations of a bistable energy harvester. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A DAE formulation for geared rotor dynamics including frictional contact between the teeth
Authors: Jehle Georg , Fidlin Alexander 
Published: October 2015

AbstractA DAE approach is presented for geared rotor dynamics simulations with rigid helical evolvent gears. It includes the normal contact force between the teeth as well as tangential components.Given the evolvent tooth flank geometry of gear 1 and gear 2 [1], the contact line and the velocity difference in the contact are found. The requirement of no penetration of the teeth yields a non‐holonomic constraint and the contact normal force. The friction caused force and moment are obtained by applying Coulomb's friction model.This approach is used to investigate the dynamics of two ideal rotors with translational DoFs, which are connected by gears to one another. The driving rotor has a given angular speed, while the driven rotates unrestrainedly and is connected to a rotational damper. Because of the periodic friction terms, the solution is periodic. A direct time integration or a harmonic approach can be used for the numerical computation. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Vibrational Behavior of Coupled Bladed Disks with Variable Rotational Speed
Authors: Kaptan Ferhat , Panning‐von Scheidt Lars , Wallaschek Jörg 
Published: October 2015

AbstractLow pressure steam turbine blades are subjected to high static and dynamic loads during operation. These loads strongly depend on the turbine's rotational speed, leading to entirely new load conditions. To avoid high dynamic stresses due to the forced vibrations, a coupling of the blades, such as shrouds or snubber coupling, is applied to reinforce the structure. In this work the influence of the rotational speed on the vibration behavior of shrouded blades is investigated. Two fundamental phenomena are considered: the stress stiffening and the spin softening effect. Both effects are caused by centrifugal forces and affect the structural mechanical properties, i.e. the stiffness matrix K, of the rotating system. Since the rotational speed Ω appears quadratically, it is possible to derive the stiffness matrix as a second order matrix polynomial in Ω2 [3].In the case of shrouded blades, contact forces between neighboring blades must be taken into account. The contact status and the pressure distribution in particular is strongly influenced by the rotational speed, respectively, centrifugal forces, caused by the untwisting and radial deformation of the blades. For the calculation, a three dimensional structural mechanical model including a spatial contact model is considered. The solution of the nonlinear equations of motion is based on the well known Multiharmonic Balance Method [2]. Here, the nonlinear forces are computed in the time domain and transferred in the frequency domain by the use of the Fast Fourier Transformation (FFT), also known as the Alternating Frequency Time method (AFT) [1]. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Multi‐mode model of a piezomagnetoelastic energy harvester under random excitation
Authors: Lentz Lukas , von Wagner Utz 
Published: October 2015

AbstractAbstract: The transformation of ambient vibrational energy into electric energy through the use of piezoelectric energy harvesting devices has been the subject of numerous investigations [1]. A commonly studied energy harvesting device performing especially well under broadband excitation, is the piezomagnetoelastic energy harvester investigated by Erturk et al. [2], which is usually discretised for the fundamental vibration mode resulting in a single‐mode model. This contribution presents the study of a multi‐mode model of the piezomagnetoelastic energy harvester under random excitation. The probabilty density function (PDF) is computed to be the solution of the corresponding Fokker‐Planck equation using a Galerkin type method [3,4]. Based on the PDF, the resulting voltage variance is computed as a measurement for the expected power output as demonstrated in [5]. The results of the multi‐mode model are then compared with the results of the single‐mode model. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Control of Nonlinearly Coupled Oscillators Using a Method of Averaging
Authors: Kreuzer Edwin , Radisch Christian 
Published: October 2015

AbstractContainer cranes belong to the class of underactuated systems for which the design of control laws is a challenging task. We study the stabilization of certain modes of a crane system using a method of averaging. Based on the local approximation to the system dynamics by a second order Taylor series expansion, the effects of nonlinear couplings are exploited to steer degrees of freedom, for which no linear actuation is available. Rotations of the load about the vertical axis are analyzed and a control method is derived and tested experimentally. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Adaptive Fuzzy Sliding Mode Controller and Observer for a Dive Cell
Authors: Bessa Wallace M. , Kreuzer Edwin , Krumm Ludwig , Pick Marc‐André , Solowjow Eugen 
Published: October 2015

AbstractWe present an adaptive fuzzy sliding mode control strategy in combination with a sliding mode observer for a dive cell. Numerical results demonstrate the outperformance of the presented controller compared to a conventional sliding mode approach. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
One‐dimensional simulation of the creep behavior of directionally solidified NiAl‐9Mo
Authors: Albiez Jürgen , Sprenger Ioannis , Heilmaier Martin , Böhlke Thomas 
Published: October 2015

AbstractThe directional solidification (DS) of the eutectic alloy NiAl‐9Mo (at. %) leads to a formation of single‐crystal molybdenum‐rich fibers embedded in a NiAl matrix and has promising high‐temperature properties. Material models describing each phase are necessary to be able to predict the materials behavior of the in‐situ composite under several conditions. Using a one‐dimensional Voigt‐Taylor model based on a phenomenological approach, the creep behavior is simulated and the results are compared to experimental data. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A geometrical approach to remove stress singularities in continuum models of multi‐material structures
Authors: Blech Christopher , Falkenberg Paul , Langer Sabine C. , Vietor Thomas 
Published: October 2015

AbstractIn the frame of stress based topology optimisation multi‐material structures are investigated. At the interface of dissimilar materials an adhesive joint shall be considered. Selecting a continuum approach to model the two adherends and the adhesive, stress singularities occur at the material‐interfaces due to the difference in the impedance [1].This contribution investigates a geometrical opportunity to remove singularities at the interface of two different linear elastic structures. Sensitivities of important parameters are qualitatively shown by a simple example consisting of two cubes under tension. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Characterization of Ni/Al hybrid foam from atomic to microscale
Authors: Chen Zhaoyu , Jung Anne , Heinze Stephan , Düster Alexander , Diebels Stefan 
Published: October 2015

AbstractIn this paper, the Ni/Al hybrid open‐cell foams are characterized on different hierarchical levels by means of experiments and numerical modeling from the atomic to the microscale. In this case, it is possible to compare the elastic‐plastic behavior at different scales in order to attain a deeper understanding of the multiscale properties of the Ni/Al hybrid foams. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
A coupled phase‐field – Cahn‐Hilliard model for lower bainitic transformation
Authors: Düsing Martin , Mahnken Rolf 
Published: October 2015

AbstractThe lower bainitic transformation is highly dependent on carbon diffusion. Bainite consists of bainitic ferrite, residual austenite and carbides. The numerical modeling of the interaction between these phases and the carbon is extremely demanding. The goal of this work is to describe the formation of carbides in lower bainite. To model the evolution of a bainitic sheaf a phase‐field model is coupled with a Cahn‐Hilliard equation simulating the diffusion. The system of equations is solved using the finite element method. Numerical examples show the growth of the ferrite and the following uphill diffusion within this phase. At accumulation points of carbon, carbides are precipitated. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An atomistic scale analysis of ferroelectric nanodomain interfaces
Authors: Endres Florian , Steinmann Paul 
Published: October 2015

AbstractWe discuss numerical results of nanodomain interfaces using a new extended molecular statics algorithm for ferroelectric materials. The new algorithm is able to not only calculate the change of the polarization behavior caused by strain but also the influence on the polarization behavior due to mechanical stress. The size effects of 180° head to head and tail to tail nanodomains have already been investigated. This study also considers 90° domain walls and discusses the impact of mechanical stress on polarization patterns and system energies of nanodomain interfaces. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An Intrinsic Geometric Formulation of the Equilibrium Equations in Continuum Mechanics
Authors: Eugster Simon R. 
Published: October 2015

AbstractThe theory of invariant continuum mechanics is based on the concept that forces and stresses are defined as elements of the cotangent bundle of the configuration manifold. While body and physical space are modeled as differentiable manifolds, the infinite dimensional configuration manifold is given by all configurations of the body in the physical space. In this paper a virtual work principle is postulated which leads together with an induced traction stress and Stokes' theorem directly to the local equilibrium equations and the traction boundary conditions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)