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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

Reihe: Mechanik/Bruchmechanik

Band 355 2021

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Bibliography S. 154-169

„… , 225:1347–1387, 2007. [16] E. Burman and P. Hansbo. Fictitious domain finite element methods using cut elements …” „… , 199(41-44):2680–2686, 2010. [17] E. Burman and P. Hansbo. Fictitious domain finite element methods using cut elements …” „… . Rank. The finite cell method for the J2 flow theory of plasticity. Finite Elements in Analysis and …”

Titelei/Inhaltsverzeichnis

„… € 55,80. Keywords: Finite cell method – Fictitious domain approach – High-order finite element methods …” „… elements are denoted as finite cells – thus giving the method its name – in order to distinguish them from …” „… Mensch-Maschine-Systeme 23 Technische Gebäudeausrüstung ISBN 978-3-18-335518-1 The hierarchical finite cell method for …”

Introduction S. 1-5

„… simulation tools in the development phase. Here, the application of the finite element method (FEM) is one of …” „… , CutFEM, or CutIGA. In the context of this thesis, we apply the finite cell method (FCM) which was …” „… introduced in [19–22]. The FCM combines the fictitious domain approach with finite elements using shape …”

Basis function removal for the FCM S. 79-123

„… methods, the generalized or extended finite element method (GFEM/XFEM), or the B-Spline finite element …” „… element method, Béchet et al. [138] proposed a special preconditioner for enriched finite elements. In …” „… approach is similar to the finite element tearing and interconnecting method (FETI) presented by Farhat and …”

The finite cell method S. 23-35

„… body-conforming discretization methods like the classical finite element method (FEM). In the following, we …” „… define a widely used standard within the context of the finite element method. However, Gaussian …” „… 3 The finite cell method This chapter is intended to give a brief overview of the finite cell …”

A remeshing strategy for the FCM S. 124-149

„… finite element method as well. A promising approach to overcome this problem is based on remeshing …” „… [158–160]. The basic idea of the remeshing approach is simple. Whenever a finite element violates certain …” „… shape functions from the ansatz, as shown in the previous chapter. When considering problems in finite …”

Moment fitting quadratures S. 36-78

„… extended finite element method (GFEM/XFEM) [90–94], or fictitious domain methods [8, 11, 13, 14] like the …” „… . Note that for the FCM only, in contrast to the standard finite element method, one finite cell with an …” „… finite cell method (FCM) [19–22] or the CutFEM [16, 17] – particular consideration has to be given to the …”

Basic elements of continuum mechanics S. 6-22

„… , the finite element method – which is based on the weak (or variational) form – is applied to find an …” „… continuum mechanics that are needed for the formulation of the finite cell method considering quasi-static …” „… 2 Basic elements of continuum mechanics In this chapter, we briefly outline the basic elements of …”

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

Reihe: Mechanik/Bruchmechanik

Band 359 2024

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Bibliography S. 135-152

„… functions in the finite element methods. Computer Methods inApplied Mechanics and Engineering, 343:690–720 …” „… method for the J2flow theory of plasticity. Finite Elements in Analysis and Design, 69:37–47, 2013.[5] A …” „… . Abedian, J. Parvizian, A. Düster, and E. Rank. Finite cell method comparedto h-version finite element …”

Titelei/Inhaltsverzeichnis

„… Finite-Elemente-Methode (FEM) dar. Die Finite-Cell-Methode (FCM) kombiniert den fiktiven Gebietsansatz mit hierarchischen …” „… 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 …”

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 …”

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

„… 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 …” „… remeshing method, Lee and Bathe [109]recommended the use of a macro-element mesh generator to produce a new …”

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

„… standard discretizationmethods such as the finite element method. Nevertheless, the simplification in 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 …”

Introduction S. 1-5

„… 1 Introduction1.1 MotivationThe finite element method (FEM) is a numerical approach used to solve …” „… inthe work of Saul’ev [140]. In addition, XFEM (extended finite element methods [119]), andEPUM …” „… as the finite cell method (FCM)[29, 47, 48, 126, 142], CutFEM [21–24], or CutIGA [53], gained great …”

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 …”

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

„… ], andLoehnert and Beese [116] in the context of the extended finite element method (XFEM).Recently, the method …” „… method,also known as the α-method to improve the condition number of the system within theframework of the FCM …” „… 5 Eigenvalue stabilization technique toincrease the robustness of the FCMDiscretization methods …”

doi.org/10.51202/9783186359186

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

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Patrick Erbts

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

Reihe: Mechanik/Bruchmechanik

Band 345 2016

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Bibliography S. 186-204

„… the finite element method for three-dimensional curved thin walled structures. International Journal …” „… Hamburg-Harburg, 2010. [46] A. Düster and E. Rank. The p-version of the finite element method compared to an …” „… newton-raphson method in non-linear finite element analysis. Computational Mechanics, 36(2):100– 116, 2005. 192 …”

Numerical methods S. 45-78

„… spatial discretization of the body B using the finite element method (FEM) is described and the time …” „… the thermal field with the finite element method, a weak formulation of the heat conduction equation …” „… linear in the electric potential. 3.2 Finite element method The following section serves to summarize the …”

Titelei/Inhaltsverzeichnis

„… finite element method is applied while solving the radiation field using computational fluid dynamic …” „… . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2 Finite element method . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.1 Spatial …” „… FEM Finite Element Method 6, 41 FSI Fluid-Structure Interaction 4, 37 FVM Finite Volume Method 59 GJ …”

Numerical examples S. 145-170

„… discretized with ne = 12 high-order hexahedral finite elements that have a polynomial degree of p = 5. All …” „… volume mesh (gray) of the chamber together with finite element mesh (red) of the bimetallic beam. Table …” „… non-matchingmeshes. The bimetallic beam is discretizedwith a very coarse highorder finite element mesh, whereas the …”

Conclusions and outlook S. 171-173

„… mechanical fields is carried out by means of the finite element method (FEM). Further, the ambient of the …” „… tools is the radiation field, which is discretized by the finite volume method (FVM). In this context …” „… compared to experimental data. To this end, the finite element solver AdhoC for the thermal field is …”

Solution of coupled problems S. 79-144

„… discretized by finite elements give rise to another simple but efficient method: The requested data can be …” „… high-order finite element methods in time see the aforementioned articles and also the literature cited …” „… this split become apparent when considering aspects of the numerical implementationwith finite elements …”

Introduction S. 1-7

„… radiation are provided. Further objectives in this chapter are the introduction of the finite element method …” „… ]. Therein, fully coupled electro-thermo-mechanical simulations using the commercial finite element solver …” „… a summary of the finite volume method (FVM) regarding the aspect of radiation in a participating …”

Governing equations S. 8-44

„… treatment with finite elements [84]. To find the rate of deformation, the time derivative of the deformation …” „… formulate the further equations. In this thesis, the method of choice is the material or Lagrangian …” „… or volume elements dV of the reference configuration to the current configuration: d x = ∼Fd X …”

doi.org/10.51202/9783186345189

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packREPORT

Alle Ausgaben: packREPORT

packREPORT Jahrgang 53 (2021) Heft 9 ISSN Online: 0342-3743

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Melanie Sachs Mit Finite-Elemente-Methode Effizienz steigern S. 66-67

„… virtuell und effizient über die Finite-Elemente- Methode zu simulieren. Hierfür hat der deutsche Hersteller …” „… einer verringerten Dicke. Ein neuer Ansatz für die Verpackungsindustrie: die Finite-Elemente-Methode …” „… (FEM). Thyssenkrupp Rasselstein, Deutschlands einziger Weiß- Mit der Finiten-Elemente-Methode kommt in …”

Stößchen! S. 3

„… Performance. 66 Mit Finite-Elemente-Methode Effizienz steigern Bei Weißblechverpackungen kommt ein neuer …”

doi.org/10.51202/0342-3743-2021-9

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Bauingenieur

Alle Ausgaben: Bauingenieur

Bauingenieur Jahrgang 95 (2020) Heft 04 ISSN Online: 0005-6650

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Hamid Sadegh-Azar, Arthur Feldbusch Nicht-lineare Untersuchungen zur dynamischen Boden-Bauwerk-Interaktion

„… Struktur in einem Finite-Elemente-Modell erfassen und analysieren. Der Schwerpunkt des Beitrages liegt auf …” „… beschriebene Zeitbereichsmethode gelegt. 2 Berücksichtigung der Boden-Bauwerk- Interaktion in Finite-Elemente …” „… - Berechnungen mithilfe von PML-Elementen Bei der Berücksichtigung des Bodens in Finite-Elemente Berechnungen …”

Peter Wriggers, Fadi Aldakheel, Ludger Lohaus, Michael Haist Wasserinduzierte Schädigungsmechanismen zyklisch beanspruchter Hochleistungsbetone/Water-induced damage mechanisms of cyclically loaded High-performance concretes S. 126-132

„… framework for brittle crack propagation based on an efficient virtual element method. In: Finite Elements in …” „… finiten Elemente in ein numerisches Modell umgesetzt, wobei als primäre Variablen die Verschiebung uS …” „… aufgenommen Daten (Bild 2) wurden geometrisch aufbereitet und für eine Berechnung mittels finiter Elemente …”

doi.org/10.37544/0005-6650-2020-04

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