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

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Simeon Hubrich

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

Series: Mechanik/Bruchmechanik

Volume 355 2021

Results in this title

The finite cell method S. 23-35

„… 3 The finite cell method This chapter is intended to give a brief overview of the finite cell …” „… context of the finite cell method. To this end, let us take a look to the boundary value problem depicted …” „… voxel-based models provided by quantitative computer 23 3 The finite cell method α = 0 α = 0 α = 1 Ω Ωe\Ω Ωe …”

Bibliography S. 154-169

„… , 41:121– 133, 2007. [20] A. Düster, J. Parvizian, Z. Yang, and E. Rank. The finite cell method for …” „… . Düster, and E. Rank. The hp-d-adaptive finite cell method for geometrically nonlinear problems of solid …” „… . Schillinger, M. Ruess, A. Düster, and E. Rank. The Finite Cell Method for large deformation analysis …”

Introduction S. 1-5

„… , CutFEM, or CutIGA. In the context of this thesis, we apply the finite cell method (FCM) which was …” „… them as finite cells – giving the method its name – in order to distinguish them from …” „… further research opportunities in connection with the finite cell method. 5 …”

Titelei/Inhaltsverzeichnis S. I-VII

„… Mensch-Maschine-Systeme 23 Technische Gebäudeausrüstung ISBN 978-3-18-335518-1 The hierarchical finite cell method for …” „… _Reihe_18_355_Umschlag.pdf · Seite 2 2 2 The hierarchical finite cell method for nonlinear problems …” „… 20.05.2021 08:03:26 Fortschritt-Berichte VDI The hierarchical finite cell method for nonlinear problems …”

Summary and outlook S. 150-153

„… 7 Summary and outlook In the present thesis, the finite cell method, which is a powerful simulation …” „… into further research topics regarding the finite cell method. • In this thesis, we demonstrated that …” „… of finite cells. In the FCM, it is common to apply adaptive Gaussian schemes – which results in a …”

Basis function removal for the FCM S. 79-123

„… discretization methods. In the context of the finite cell method (FCM) [19, 20] – which combines the fictitious …” „… of the mesh size and the location of the interface. In the context of the finite cell method, de …” „… hierarchical basis of the finite cell method (FCM), which can be easily combined with the fictitious material …”

A remeshing strategy for the FCM S. 124-149

„… of the fictitious domain, badly cut finite cells get distorted severely during the deformation …” „… finite element method as well. A promising approach to overcome this problem is based on remeshing …” „… deformations of the fictitious domain, thus leading to severely distorted cut finite cells. These degenerated …”

Moment fitting quadratures S. 36-78

„… finite cell method (FCM) [19–22] or the CutFEM [16, 17] – particular consideration has to be given to the …” „… scope of this chapter, we focus on the numerical integration process of the finite cell method. As …” „… and robustness for linear and nonlinear applications of the finite cell method [31, 33, 122, 126–130 …”

Basic elements of continuum mechanics S. 6-22

„… continuum mechanics that are needed for the formulation of the finite cell method considering quasi-static …” „… , the finite element method – which is based on the weak (or variational) form – is applied to find an …” „… the equilibrium, let us consider the finite partial volume ϕ ( Ω̃ ) with boundary ϕ ( Γ̃ ) of the …”

doi.org/10.51202/9783186355188

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

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Wadhah Garhuom

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

Series: Mechanik/Bruchmechanik

Volume 359 2024

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The finite cell method S. 17-26

„… finite cell methodFigure 3.1: Basic concept of the finite cell method.The same is applied to the weak …” „… 3 The finite cell methodIn recent years, there has been a growing interest in fictitious or …” „… The finite cell methodThe virtual displacement η is approximated using the Bubnov-Galerkin method byη …”

Bibliography S. 135-152

„… integration schemes in facing discontinuities in the finite cell method.International Journal of Computational …” „… . Juhre.Octree-based integration scheme with merged sub-cells for the finite cell method:Application to non-linear …” „… Methods, 10(3):1350002/1–24, 2013.[4] A. Abedian, J. Parvizian, A. Düster, and E. Rank. The finite cell …”

Titelei/Inhaltsverzeichnis S. I-VIII

„… Wadnah GarhuomImproving finite cell method robustnessReihe 18 | Nr. 359Reihe 18 …” „… 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 …”

Publications resulting from this project S. 134

„… in the finite cell method. Computers & Mathematics with Applications 80, pp.2379–2398, 2020. doi …” „… robustness of the finite cell method for finite strain problems. Computational Mechanics69, pp. 1225–1240 …” „… . Düster, and D. Juhre. Octree-based integration scheme with merged sub-cells for the finite cell method …”

Summary and outlook S. 130-133

„… inthis work. For the integration of broken cells using the finite cell method, we developed a …” „… stabilization in combination with the α-method significantly enhancesthe robustness of the finite cell method …” „… a result, we were able to improve the performance of the finite cell method whenapplied to nonlinear …”

Introduction S. 1-5

„… as the finite cell method (FCM)[29, 47, 48, 126, 142], CutFEM [21–24], or CutIGA [53], gained great …” „… configurations, followed by the linearization of the weak forms. In Chapter 3, the finite cell method is briefly …” „… 1 Introduction1.1 MotivationThe finite element method (FEM) is a numerical approach used to solve …”

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

„… of the finite cell method, as proposed in [60]. To continue thenonlinear computation even when the …” „… finite element method, particu-larly when the system contains complicated geometries and significant …” „… formulation (ALE). The firstwho worked on this, among others, in the context of the finite element method are …”

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

„… methods such as the finite cell method simplify the meshingprocedure significantly. This is because the …” „… standard discretizationmethods such as the finite element method. Nevertheless, the simplification in the …” „… .One commonly used method to perform the integration for the broken cells is basedon the spacetree decomposition …”

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

„… . The α-method involves imposing a very soft material into thefictitious domain of each broken cell …” „… stabilize itusing the α-method. Here, the domain is discretized with one cell and a quadrature order ofpq …” „… ], andLoehnert and Beese [116] in the context of the extended finite element method (XFEM).Recently, the method …”

doi.org/10.51202/9783186359186

Meysam Joulaian - The hierarchical finite cell method for problems in structural mechanics

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Meysam Joulaian

The hierarchical finite cell method for problems in structural mechanics

Series: Mechanik/Bruchmechanik

Volume 348 2017

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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 …” „… basics of the finite cell method (FCM) such as the governing equations, the mesh generation and the …” „… × ] 0, t̂ [ (2.1) 6 2 Finite cell method for problems in solid mechanics where ∼σ is the stress tensor …”

Bibliography S. 140-154

„… integration schemes in facing discontinuities in the finite cell method. International Journal of …” „… finite cell method for the J2 flow theory of plasticity. Finite Elements in Analysis and Design, 69:37–47 …” „… , 2013. [16] A. Abedian, J. Parvizian, A. Düster, and E. Rank. Finite cell method compared to hversion …”

Titelei/Inhaltsverzeichnis S. I-X

„… The hierarchical finite cell method for problems in structural mechanics The hierarchical …” „… finite cell method for problems in structural mechanics Vom Promotionsausschuss der Technischen …” „… . ISSN 0178-9457 ISBN 978-3-18-334818-3 Joulaian, Meysam The hierarchical finite cell method for …”

Local enrichment of the FCM S. 72-110

„… applied in finite element based methods. In other words, if the non-smooth part of the solution appears …” „… – there is expected to be a reduction in the convergence rate of the method too if the cells include such …” „… Ω1 Ω2 E1 E2 fb(x) Discretization with 1 finite cell Figure 4.1: A bi-material one-dimensional rod …”

Introduction S. 1-4

„… successful methods based on the fictitious domain approach is the finite cell method (FCM) which employs …” „… 1 Chapter 1 Introduction 1.1 Motivation The standard finite element method (FEM) is surely a widely …” „… , 122], the generalized finite element method (GFEM) [53, 165, 166], and the eXtended finite element …”

Numerical integration algorithms for the FCM S. 27-71

„… physical boundaries in the scope of this method, we may encounter two types of cells during the simulation …” „… , 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 …”

Summary and Outlook S. 133-135

„… slightly more 134 6 Summary and Outlook computationally expensive than the standard finite element method …” „… cell method, features a lumped mass matrix that makes it easier to exploit the advantages of an …” „… cell method, the shape functions are based on the tensor-product of Lagrange polynomials of order p …”

The spectral cell method S. 111-132

„… 111 Chapter 5 The spectral cell method An intricate field of the numerical analysis is the dynamic …” „… contributes 112 5 The spectral cell method substantially to the complexity to the task of computer modeling …” „… . Due to its simple mesh generation and capability of delivering high convergence rates, the finite cell …”

doi.org/10.51202/9783186348180

Nikola Aulig - Generic Topology Optimization Based on Local State Features

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Nikola Aulig

Generic Topology Optimization Based on Local State Features

Series: Rechnerunterstützte Verfahren

Volume 468 2017

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Structure Representations for Evolutionary Computation S. 29-47

„… variable is assigned to each cell of a finite element mesh discretization of the design space. 3.2.1 …” „… analysis. 3.3.1 Voronoi-cells Motivated by the idea of overcoming the direct coupling of the finite element …” „… continuum topology optimization [101]. Since then, a large variety of specialized methods has been developed …”

Titelei/Inhaltsverzeichnis S. I-XVIII

„… more sophisticated physical simulations. Using methods of evolutionary optimization and machine …” „… regression. In empirical experiments, the novel method reproduces reference structures with minimum …” „… Control Methods and Robotics (RMR) department, who offered to supervise the dissertation in a …”

Topology Optimization by Predicting Sensitivities S. 48-83

„… of optimization problems, yet a method that incorporates domain knowledge usually has better …” „… , specialized method is also possible, i.e. to widen its applicability to be more general by reducing the amount …” „… gradients are available. Concretely, the idea of the proposed method is to utilize a learning process that …”

Fundamentals S. 8-28

„… geometric parameters of a unit cell. The name “homogenization method” stems from the process of homogenizing …” „… evaluating the method proposed in this thesis. In its finite element form the compliance problem can be …” „… and an overview of state-of-the-art optimization methods. Section 2.1 introduces topology optimization …”

Topology Optimization of Crashworthiness Objectives S. 121-149

„… scenario that are considered [157]. Existing gradient-based methods are only applicable for considerably …” „… history [134] or desired acceleration history [137]. However, the method is limited to significantly …” „… optimization with topological changes as presented in the bubble method by Eschenauer et al. [60]. In the …”

doi.org/10.51202/9783186468208

Mathias Würkner - Numerische Homogenisierung von Faserverbundwerkstoffen mit periodischer Mikrostruktur

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Mathias Würkner

Numerische Homogenisierung von Faserverbundwerkstoffen mit periodischer Mikrostruktur

Series: Mechanik/Bruchmechanik

Volume 346 2017

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Literaturverzeichnis S. 122-132

„… .: Die Methode der finiten Elemente in der Festkörpermechanik. VEB Fachbuchverlag Leipzig, 1982 [4 …” „… + Teubner | GWV Fachverlage GmbH Wiesbaden, 2010 [9] Bathe, K.-J. : Finite-Elemente-Methoden …” „… Wiley and Sons, Inc., 1989 [28] Deng, M. ; Feng, Y. : Two-scale finite element method for piezoelectric …”

Einleitung S. 1-8

„… numerischer Berechnungsverfahren, speziell der Finite-Elemente-Methode (FEM), für die kommerzielle …” „… Potentialfunktionen verwenden. Ein weiteres weit verbreitetes Verfahren stellt die Finite-Elemente-Methode dar [106 …” „… 7 der Finite-Elemente-Methode als vorteilhaft erwiesen. Man ist in der Lage, auch komplexe …”

Titelei/Inhaltsverzeichnis S. I-XVI

„… Faserverbundwerkstoffe mit periodischer Mikrostruktur unter Verwendung der Finite-Elemente-Methode. Der Fokus liegt …” „… homogenisation methods which are based on the finite element method (FEM). These methods developed are applicable …” „… numerischen Homogenisierungsverfahren, welche auf der Finite-Elemente-Methode (FEM) basieren. Diese werden zum …”

doi.org/10.51202/9783186346186

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