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Improving the robustness of the finite cell method for problems with large deformations

Wadhah Garhuom

Series: Mechanik/Bruchmechanik

Volume 359 2024

Results in this title

„… finite strain problems. Compu-tational Mechanics, 69(5):1225–1240, 2022.[64] S. Gnegel. The finite cell …” „… moment fitting applied to finite strain problems. Proceedings in AppliedMathematics and Mechanics, 18:e …” „… incompressible finite strain plasticity problems with complex geometries. Com-puters & Mathematics with …”

Non-negative moment fitting quadrature for cut finite elements and cells S. 27-58

„… plastic strain574 Non-negative moment fitting quadrature for cut finite elements and cellsᾱ at the …” „… 4 Non-negative moment fittingquadrature for cut finite elements andcellsImmersed boundary domain …” „… methods such as the finite cell method simplify the meshingprocedure significantly. This is because the …”

Titelei/Inhaltsverzeichnis S. I-VIII

„… Fortschritt-Berichte VDIGarhuom, Wadhah, M.Sc.HamburgImproving the robustness of the finite cell method for problems …” „… finite cell method for problems with large deformationsReihe 18Mechanik/BruchmechanikBlackL_240107_F51 …” „… , M.Sc.Improving the robustness of the finite cell method for problems with large deformationsFortschritt-Berichte …”

Publications resulting from this project S. 134

„… robustness of the finite cell method for finite strain problems. Computational Mechanics69, pp. 1225–1240 …” „… in the finite cell method. Computers & Mathematics with Applications 80, pp.2379–2398, 2020. doi …” „… . Wollner, C. Kuhn, and T. Heister. A selection of benchmark problems in solidmechanics and applied …”

Remeshing strategy for large deformations in the FCM S. 89-129

„… strain problems in solid mechanics are still adifficult challenge using numerical techniques such as the …” „… . In an analysisbased on finite strain hyperelastic deformations, the important quantities that need to …” „… transferoperator I as followsHn+1 = I (Hn) . (6.23)For the analysis based on finite strain elastoplasticity, the …”

Introduction S. 1-5

„… significantdeformations is still ongoing research. When performing a large deformation analysis with finite strains, the …” „… . Finally, different benchmarks and numerical applications in finite strains areoutlined to show the …” „… 1 Introduction1.1 MotivationThe finite element method (FEM) is a numerical approach used to solve …”

Eigenvalue stabilization technique to increase the robustness of the FCM S. 59-88

„… applications in finite strainsIn this section, we consider several nonlinear applications including both …” „… discretization can be seen in Figure 5.15.785.4 Nonlinear applications in finite strainsFigure 5.15: Single Cube …” „… affecting the solution.805.4 Nonlinear applications in finite strains0 1 2 3 4 5 600.250.50.751(a)0 1 2 3 4 …”

doi.org/10.51202/9783186359186

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Partitioned Fluid-Structure Interaction Simulation of Maritime Applications

Jorrid Lund

Series: Mechanik/Bruchmechanik

Volume 360 2024

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Structural mechanics S. 5-20

„… fluid mechanic problems,namely the finite volume method (FVM) and the boundary element method (BEM …” „… Green-Lagrange strain tensor for one finite element can be written in Voigt notation as [27,p. 124]δEe = Blh …” „… static problems.Nonetheless, a sufficiently high number of master nodes will still allow for a …”

Bibliography S. 124-138

„… interactions: models, analysis and finite elements, Vol.118, Springer, 2017. doi:10.1007/978-3-319-63970-3.[9 …” „… . Boyle, Solvers for large-displacement fluid–structure interac-tion problems: segregated versus …” „… analyzing multiphysics prob-lems, Engineering with Computers 34 (04 2018). doi:10.1007/s00366-017-0548-4.[13 …”

Introduction S. 1-4

„… ), and the finite volumemethod (FVM), it is possible to accurately solve nonlinear dynamic problems with …” „… for this purpose are focused on eithersolving fluid or structural problems.The development of FSI …” „… coupled problems.The BEM panMARE [24] was developed at the “Institute for Fluid Dynamics and ShipTheory …”

Titelei/Inhaltsverzeichnis S. I-VIII

„… : Fluid-Struktur-Interaktion, partitionierte Kopplung, Finite-Elemente-Methode, numerische Strömungsmechanik, maritime …” „… , faserverstärkter KunststoffKeywords: fluid-structure interaction, partitioned coupling, finite element method …” „… assessing local strains, thrust, and torque. Finally, an anisotropic ship propeller made of …”

doi.org/10.51202/9783186360182

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Generic Topology Optimization Based on Local State Features

Nikola Aulig

Series: Rechnerunterstützte Verfahren

Volume 468 2017

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Introduction S. 1-7

„… finite element analysis for the prediction of structural performance measures have made computer-aided …” „… replaces experience-based engineering practices. Many engineering problems can be addressed as optimization …” „… problems with strongly non-linear characteristics for which a specialized optimization approach is …”

Studies on the Minimum Compliance Problem S. 84-120

„… with other potential features like elemental stresses or strains. For all experiments, forward finite …” „… The two-dimensional cantilever beam is one of the standard test problems agreed on in the topology …” „… estimation using forward finite differentiation (as in (4.11)) for all design variables. The optimization …”

Topology Optimization by Predicting Sensitivities S. 48-83

„… additional N evaluations for each design point. For small problems, such a naive, finite differentiation can …” „… anything but small-scaled problems. Furthermore, almost none of the existing evolutionary computation …” „… of optimization problems, yet a method that incorporates domain knowledge usually has better …”

Titelei/Inhaltsverzeichnis S. I-XVIII

„… provide concept designs even for problems involving complex, black-box simulations. A self-contained …” „… by Finite-Difference Sampling 75 4.4.2 Aggregated Sensitivity-Sampling . . . . . . . . . . . 78 4.4.3 …” „… : Example for displacements of element nodes when a finite element analysis is performed. . . . . . 57 List …”

Topology Optimization of Crashworthiness Objectives S. 121-149

„… subject to non-elastic strain, up to failure, or multiple contacts. This results in complex and …” „… interest in optimization is increasing. In sizing or shape design optimization problems a limited number of …” „… simplified problems and as a consequence, heuristic approaches for crashworthiness topology optimization have …”

doi.org/10.51202/9783186468208

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The hierarchical finite cell method for problems in structural mechanics

Meysam Joulaian

Series: Mechanik/Bruchmechanik

Volume 348 2017

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Bibliography S. 140-154

„… staggered coupling schemes for problems of thermoelasticity at finite strains. Computers & Mathematics with …” „… finite element method for elasto-plastic problems. Applied Mathematics and Mechanics, 35(10):1239–1248 …” „… . Fixed grid finite elements in elasticity problems. Engineering Computations, 16(2):145–164, 1999. [75] A …”

Finite cell method for problems in solid mechanics S. 5-26

„… 5 Chapter 2 Finite cell method for problems in solid mechanics In this chapter, we focus on the …” „… × ] 0, t̂ [ (2.1) 6 2 Finite cell method for problems in solid mechanics where ∼σ is the stress tensor …” „… 2 Finite cell method for problems in solid mechanics ξ η ζ ξ1 ξ2 ξ3 ξ4 ξ5 ξ6 ξ7 ξ8 Ωe x y z x1 x2 …”

Local enrichment of the FCM S. 72-110

„… , or problems containing singularities resulting from reentrant corners or cracks, just to name a few …” „… applied in finite element based methods. In other words, if the non-smooth part of the solution appears …” „… and a jump in the strains at material interfaces. This kind of discontinuity in the solution is known …”

The spectral cell method S. 111-132

„… loadings. This falls into the category of wave propagation problems. Important applications in this field …” „… cracks [17], to name a few. In order to account for problems like this, the numerical model must be able …” „… difficult to obtain a proper mesh for them. Thus, the numerical analysis of problems in this category poses …”

Numerical integration algorithms for the FCM S. 27-71

„… , and they may appear in almost any finite element-based method that involves non-conforming meshes, e.g …” „… . in the eXtended/generalized finite element method or in the partition of unity based approaches [27 …” „… problems using the FCM. Another class of numerical integration methods is based on constructing an …”

doi.org/10.51202/9783186348180

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Bauingenieur

Browse Volumes: Bauingenieur

Bauingenieur Volume 99 (2024) Issue 04 ISSN Online: 0005-6650

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Aleksandar Kostadinovic, Julian Sigmund, Dietmar Adam Numerische Modellierung eines tiefen Schlitzwandschachtes im überkonsolidierten Boden des Wiener Raums/Numerical modelling of a deep excavation in the overconsolidated soil of Vienna S. 123-137

„… numerische 2D- und 3D-Be-rechnungsmodelle, basierend auf der Finiten-Elemente-Metho-de, einander …” „… Hardening Soil Modell (mit und ohne small strain stiffness) – verwendet. Die Bodensteifigkeitsparameter des …” „… Matzleinsdorfer Platz. Numerical 2D- and 3D-mo-dels, based on the finite element method and incorporating …”

doi.org/10.37544/0005-6650-2024-04

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Bauingenieur

Browse Volumes: Bauingenieur

Bauingenieur Volume 94 (2019) Issue 04 ISSN Online: 0005-6650

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Ali Hussein, Blaž Hudobivnik, Peter Wriggers Berechnung von Risswachstum mittels der Methode der virtuellen Elemente/Modeling of Brittle Crack Propagation using the Virtual Element Method S. 147-154

„… erlaubt, bruchmechanische Probleme mit Risswachstum mit ausreichender Genauigkeit zu berechnen. 3.1 VEM …” „… isoparametrischen finiten Elementen – durch eine Funktion in den Koordination X = {x; y} gegeben, die die …” „… Problems finden sich in Bild 10. Der Balken weist eine Länge von 20 mm und eine Höhe von 8 mm auf. Der …”

doi.org/10.37544/0005-6650-2019-04

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The hierarchical finite cell method for nonlinear problems: Moment fitting quadratures, basis function removel, and remeshing

Simeon Hubrich

Series: Mechanik/Bruchmechanik

Volume 355 2021

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Introduction S. 1-5

„… applications in finite strain is studied by considering several problems of different complexity. • In Chapter …” „… , e.g. applications to elastic and plastic problems in small and large strain [19, 20, 23–33 …” „… . • Further, the FCM suffers from severely distorted finite cells for applications in finite strain. When …”

Titelei/Inhaltsverzeichnis S. I-VII

„… – Nonlinear problems – Finite strain problems In this thesis, several approaches are discussed in order to …” „… strain elastoplasticity . . . . . . . . . . . . . . . . . . . . . . 92 5.3 Finite strain problems …” „… _Reihe_18_355_Umschlag.pdf · Seite 2 2 2 The hierarchical finite cell method for nonlinear problems …”

Summary and outlook S. 150-153

„… modes, which is an important issue, especially considering applications in finite strain problems …” „… was demonstrated by considering several finite strain problems in elasticity. Here, it could be shown …” „… highly accurate results. Moreover, considering several finite strain applications in elasticity as well …”

Basis function removal for the FCM S. 79-123

„… last load step λ = 1.5. 96 5.3 Finite strain problems 5.3 Finite strain problems In this section, we …” „… study the effect of the basis function removal for finite strain problems. In general, FCM computations …” „… used without basis function removal. 98 5.3 Finite strain problems Figure 5.16: Single cube connector …”

A remeshing strategy for the FCM S. 124-149

„… problems in finite strain. In general, the FCM analysis for such kind of problems suffers from large …” „… per target point nn whose indices are deposited in set N , 136 6.3 Finite strain problems • the number …” „… choice. 6.3 Finite strain problems In this section, we investigate the performance of the remeshing …”

Basic elements of continuum mechanics S. 6-22

„… and elastoplastic material models for problems with small and finite strain. Therefore, this section …” „… problems in finite strain. A more detailed description of the theory can be found in [81–84]. The …” „… . This behavior defines a fundamental property that strain measures have to satisfy when problems with …”

Bibliography S. 154-169

„… nearly incompressible finite strain plasticity problems with complex geometries. Computers & Mathematics …” „… broken finite cells based on moment fitting applied to finite strain problems. Proceedings in Applied …” „… . Düster, and E. Rank. The hp-d-adaptive finite cell method for geometrically nonlinear problems of solid …”

Moment fitting quadratures S. 36-78

„… applications of the finite cell method to linear problems. Figure 4.3: Gauss-Legendre points. 4.1.3 Computation …” „… various applications of the finite cell method considering three-dimensional problems. Thereby, we study …” „… 4.3 Applications to the finite cell method 4.3.2.2 Small strain elastoplasticity In the second test …”

doi.org/10.51202/9783186355188

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Partitioned solution strategies for electro-thermo-mechanical problems applied to the field-assisted sintering technology

Patrick Erbts

Series: Mechanik/Bruchmechanik

Volume 345 2016

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Bibliography S. 186-204

„… . Accelerated staggered coupling schemes for problems of thermoelasticity at finite strains. Computers …” „… . Heißerer. High-order finite elements for material and geometric nonlinear finite strain problems. PhD thesis …” „… numerical aspects in weak-compressible finite strain thermo-elasticity. Journal of Theoretical and Applied …”

Titelei/Inhaltsverzeichnis S. I-XVI

„… / Bruchmechanik Reihe 18 Partitioned solution strategies for electrothermo-mechanical problems applied to the …” „… field-assisted sintering technology Partitioned solution strategies for electro-thermo-mechanical problems …” „… VDI Partitioned solution strategies for electrothermo-mechanical problems applied to the …”

Solution of coupled problems S. 79-144

„… multi-level Newton algorithm. Thermo-plasticity is also considered in [142] and for finite strain …” „… the cuff. However, this split is unconditionally stable and can also be applied to finite strain …” „… finite strain viscoelasticity is considered, and the nonlinear heat conduction problem is treated in [143 …”

Numerical methods S. 45-78

„… quasi-stationary problems, only the heat equation needs to be discretized in time. To this end, the global finite …” „… spatial discretization of the body B using the finite element method (FEM) is described and the time …” „… finite volume method (FVM) is employed to discretize the fluid domain Σ which can be viewed as the …”

Numerical examples S. 145-170

„… applied to multiphysical problems with nf > 2 fields. The general purpose is to find the best suited …” „… problemwith finite deformations is studied, where thermal radiation is approximated as a boundary condition in …” „… . Because the layers consist of different materials, the thermal strains in the layers differ from each …”

Introduction S. 1-7

„… problems often requires a solution of coupled multi-field systems. Nowadays, commercial solvers can be used …” „… to carry out coupled simulations for a large number of different problems. However, these solvers are …” „… to thermal strains that cause thermal stresses. Due to the temperature dependency of several material …”

Governing equations S. 8-44

„… engineering problems require a mathematical formulation of the process and a substantiated background in the …” „… . Basic continuum mechanics 11 the deformation of the body, which will lead to stress and strain. This …” „… Strain tensors In order to describe a stress state of a deformable body, it is necessary to introduce …”

doi.org/10.51202/9783186345189

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Bauingenieur

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Bauingenieur Volume 92 (2017) Issue 06 ISSN Online: 0005-6650

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Viet Hung Le, Frank Rackwitz, Stavros Savidis Verformungsakkumulation bei Monopilegründungen in Sand mit Lastrichtungswechseln/Accumulation of monopile deformation in sand due to change in load direction S. 263-270

„… in sand. Finite element modeling has been performed using an explicit accumulation model (HCA-Model …” „… hypoplastic model with intergranular strain as well as the isoelasticity model for implicit calculation steps …” „… Integrationspunkt der Finiten Elemente aufgezeichnet. Daraus wird anschließend die Dehnungsamplitude eampl …”

doi.org/10.37544/0005-6650-2017-06

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Bauingenieur

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Bauingenieur Volume 98 (2023) Issue 11 ISSN Online: 0005-6650

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Verena Curoșu, Georgia Kikis, Christian Krüger, Frank Liebold, Domen Macek, Leonie Mester, Jakob Platen, Stephan Ritzert, Sascha Stüttgen, Michael Kaliske, Sven Klinkel, Stefan Loehnert, Hans-Gerd Maas, Stefanie Reese, Daniel Robertz Ansätze für numerische Methoden zur Inspiration, Analyse und Bewertung neuartiger Carbonbetonstrukturen/Approaches for Numerical Methods for Inspiration, Analysis and Evaluation of Novel Structures for Carbon-Reinforced Concrete S. 368-377

„… Fasern angibt (Bild 3 (Mitte unten)) in ein Finite-Elemente-(FE-)Netz gelegt. Für jedes Element wird ein …” „… , werden zwei FE-Probleme simultan gelöst [21]. Hier wird die makrosko-pische Skala, also die Schale, mit …” „… wird im-plizit durch die Verwendung der Erweiterten Finiten-Elemente-Methode (XFEM) [27] diskretisiert …”

Fadi Aldakheel, Michael Haist, Ludger Lohaus, Peter Wriggers Maschinelles Lernen für die numerische Homogenisierung von Beton/Machine Learning for the Numerical Homogenization of Concrete S. 354-360

„… modeling for parame-tric, anisotropic finite strain hyperelasticity based on machine learning with …” „… macro-variables for heterogeneous solids at finite strain. In: Proceedings of the Royal Society of London (Series …” „… Zementleim-Matrix besteht. Um die Trai-ningsdaten zu generieren, werden Standard-Finite-Elemente-Si-mulationen (FEM …”

doi.org/10.37544/0005-6650-2023-11

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Bauingenieur

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Bauingenieur Volume 91 (2016) Issue 02 ISSN Online: 0005-6650

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Peter Wriggers Modelle in der Strukturmechanik/Models in Structural Mechanics S. 41-45

„… .: Three dimensional finite strain rod model. Part II: computational aspects. In: Computer Methods in …” „… Problemstellungen der Statik durchgesetzt hat. Im Rahmen der Entwicklung der FEM sind eine Vielzahl finiter …” „… Simulationswerkzeuge – wie zum Beispiel die Methode der finiten Elemente – haben immer ein bestimmtes Modell, das den …”

doi.org/10.37544/0005-6650-2016-02

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Bauingenieur

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Bauingenieur Volume 93 (2018) Issue 04 ISSN Online: 0005-6650

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U. Häußler-Combe Ein Vergleich aktueller numerischer Rechenverfahren am Beispiel von Scheibentragwerken mit Rissen/Current numerical methods in comparison with the example of cracked plates S. 131-140

„… locking and stability of finite elements in finite deformation plane strain problems. In: Computers …” „… konventionellen Finite-Elemente- Methode stellt die numerische Mechanik in ihren neueren Entwicklungen alternative …” „… Scheiben mit den Methoden „Strong Discontinuity Approach“ (SDA)“, „Extended Finite Elements“ (X-FEM …”

doi.org/10.37544/0005-6650-2018-04

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Identifikation und Optimierung im Kontext technischer Anwendungen

Dirk Schellenberg

Series: Mechanik/Bruchmechanik

Volume 347 2017

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Literaturverzeichnis S. 135-146

„… . und Eglais, V., 1977: New approach for planning out of experiments. Problems of Dynamic and Strength …” „… . Bergström, J. und Boyce, M., 1998: Constitutive Modelling of the Large Strain Time- Dependent Behavior of …” „… : Optismoothing: An optimization-driven approach to mesh smoothing. Finite Elements in Analysis and Design 13(2-3 …”

Identifikation von Materialparametern anhand bauteilnaher Probekörper S. 63-124

„… Deformation der finiten Elemente • Robustes Konvergenzverhalten auch bei ungünstigen Parameterkonstellationen …” „… entarteter finite Elemente, speziell im Bereich des Selbstkontaktes, zu vermeiden. Bevor die …” „… Zugversuch Ogden Plane-Strain-Zugversuch Experiment Plane-Strain-Zugversuch Ogden Simple-Shear-Versuch …”

doi.org/10.51202/9783186347183

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Partitioned Solution Strategies for Strongly-Coupled Fluid-Structure Interaction Problems in Maritime Applications

Marcel König

Series: Mechanik/Bruchmechanik

Volume 351 2018

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Titelei/Inhaltsverzeichnis S. I-XVI

„… Partitioned Solution Strategies for Strongly-Coupled Fluid-Structure Interaction Problems in Maritime …” „… Applications Partitioned Solution Strategies for Strongly-Coupled Fluid-Structure Interaction Problems in …” „… Fluid-Structure Interaction Problems in Maritime Applications M.Sc. Marcel König, Hamburg Mechanik …”

Structural Problems S. 25-41

„… Structural Problems For a strain energy density function of the kind (3.50), the second Piola-Kirchhoff …” „… ⎛ ⎜⎜⎝ η1 ... ηn ⎞ ⎟⎟⎠ ︸︷︷︸ =η , (3.87) 35 3 Structural Problems where the nodal strain …” „… 3 Structural Problems In this chapter, we consider the structural subproblem of the coupled problem …”

Bibliography S. 252-266

„… material and geometric nonlinear finite strain problems”. PhD thesis. Munich, Germany: Technische …” „… anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models at finite strains”. In …” „… . “Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems”. In …”

Fluid Problems S. 5-24

„… 2 Fluid Problems In this chapter, we discuss the governing fluid equations and present two …” „… solution of the Navier-Stokes equations, we briefly revisit the finite volume method (FVM), which …” „… , alongside finite difference and finite element methods, has emerged as one of the most widely-used numerical …”

Benchmark Problems S. 158-217

„… 6 Benchmark Problems In this chapter, we present several numerical examples in order to verify and …” „… between the possibly non-conforming subfield discretizations. All problems are solved using our versatile …” „… pseudo-three-dimensional fluid domain is discretized by 40 × 40 × 1 hexahedral finite volumes and solved using the …”

doi.org/10.51202/9783186351180

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SIMVEC 2022

VDI Wissensforum GmbH (ed.)

Series: VDI-Berichte

Volume 2407 2022

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J. Lee, S. Rehfeldt, H. Klein, D. Bäder, A. Eisenträger, J. Kuhnert, I. Michel Two-phase water evaporation MESHFREE CFD method for wet automotive component dry-out time prediction S. 33-44

„… in the Finite Pointset Method (FPM) to simulate the free water surface evaporation phenomenon at the …” „… water-air interface. The FPM, a General-ized Finite Difference Method (GFDM) implemented in the software …” „… dynamic viscosity. The strain rate tensor for the local deformation rate is given by (6) where is …”

doi.org/10.51202/9783181024072

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