The hp-d -adaptive finite cell method for geometrically nonlinear problems of solid mechanics

2011 ◽  
Vol 89 (9) ◽  
pp. 1171-1202 ◽  
Author(s):  
D. Schillinger ◽  
A. Düster ◽  
E. Rank
Keyword(s):  
Solid Mechanics ◽  
Nonlinear Problems ◽  
Geometrically Nonlinear ◽  
Finite Cell Method ◽  
Cell Method ◽  
Finite Cell

The finite cell method for geometrically nonlinear problems of solid mechanics

2010 ◽  
Vol 10 ◽  
pp. 012170 ◽  
Author(s):  
Dominik Schillinger ◽  
Stefan Kollmannsberger ◽  
Ralf-Peter Mundani ◽  
Ernst Rank
Keyword(s):  
Solid Mechanics ◽  
Nonlinear Problems ◽  
Geometrically Nonlinear ◽  
Finite Cell Method ◽  
Cell Method ◽  
Finite Cell

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

2021 ◽  
Author(s):  
Simeon Hubrich
Keyword(s):  
Basis Function ◽  
Large Deformations ◽  
Nonlinear Problems ◽  
Equation System ◽  
Integration Process ◽  
Finite Cell Method ◽  
Cell Method ◽  
Strain Measures ◽  
Finite Cell ◽  
Goal And Scope

In this thesis, several approaches are discussed in order to further enhance the performance of the finite cell method (FCM). Thereby, novel moment fitting quadrature schemes are introduced that allow to reduce the effort of the numerical integration process significantly. Further, a basis function removal scheme is proposed to improve the conditioning behavior of the resulting equation system. Finally, an innovative remeshing strategy is presented that overcomes the problem of severely distorted elements for simulations with large deformations. Contents 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Goal and scope of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Basic elements of continuum mechanics 6 2.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Motion and deformation . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Strain measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Equilibrium and stress measures . . . . . . . . ....

The finite cell method for three-dimensional problems of solid mechanics

2008 ◽  
Vol 197 (45-48) ◽  
pp. 3768-3782 ◽  
Author(s):  
A. Düster ◽  
J. Parvizian ◽  
Z. Yang ◽  
E. Rank
Keyword(s):  
Solid Mechanics ◽  
Three Dimensional ◽  
Finite Cell Method ◽  
Cell Method ◽  
Finite Cell

scholarly journals Finite cell method for functionally graded materials based on V-models and homogenized microstructures

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Benjamin Wassermann ◽  
Nina Korshunova ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
Gershon Elber
Keyword(s):  
Functionally Graded Materials ◽  
Large Scale ◽  
Functionally Graded ◽  
Material Behavior ◽  
Modeling Framework ◽  
Finite Cell Method ◽  
Geometric Framework ◽  
Graded Materials ◽  
Cell Method ◽  
Finite Cell

AbstractThis paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM—which is heterogeneously micro-structured—characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach.

scholarly journals Hierarchical multigrid approaches for the finite cell method on uniform and multi-level hp-refined grids

2021 ◽  
Vol 386 ◽  
pp. 114075
Author(s):  
J. Jomo ◽  
O. Oztoprak ◽  
F. de Prenter ◽  
N. Zander ◽  
S. Kollmannsberger ◽  
...  
Keyword(s):  
Finite Cell Method ◽  
Cell Method ◽  
Multi Level ◽  
Finite Cell
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