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The hierarchical finite cell method for problems in structural mechanics / Titelei/Inhaltsverzeichnis
The hierarchical finite cell method for problems in structural mechanics / Titelei/Inhaltsverzeichnis
Contents
Chapter
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Page
I–X
Titelei/Inhaltsverzeichnis
I–X
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1–4
1 Introduction
1–4
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1.1 Motivation
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1.2 Scope and outline of this work
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5–26
2 Finite cell method for problems in solid mechanics
5–26
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2.1 The strong and weak form of the governing equations
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2.2 The finite element method
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2.3 Mesh generation and the finite cell method
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2.4 Numerical challenges of the finite cell method
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2.4.1 Fast algorithms to introduce the indicator function
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2.4.2 Imposition of boundary conditions
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2.4.2.1 Neumann boundary conditions
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2.4.2.2 Dirichlet boundary conditions
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2.4.3 Numerical integration of cut cells
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2.4.4 Material interfaces and weak discontinuities
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2.4.5 Efficient iterative solvers
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2.5 Some applications of the FCM
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2.5.1 Elastostatic analysis of a one-dimensional rod
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2.5.2 Perforated plate
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2.5.3 Porous domain
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27–71
3 Numerical integration algorithms for the FCM
27–71
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3.1 Numerical integration of unbroken cells
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3.2 Performance of Gaussian quadrature rules in facing discontinuities
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3.3 Composed integration
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3.3.1 Composed integration based on conforming local meshes
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3.3.2 Composed integration based on uniform sub-cell division
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3.3.3 Composed integration based on spacetrees
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3.3.4 Resolution of the integration mesh
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3.3.5 Composed integration with an hp-refinement procedure
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3.4 Moment fitting method
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3.4.1 Step 1: Selection of the basis functions
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3.4.2 Step 2: Setting up the position of the quadrature points
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3.4.3 Step 3: Computation of the right-hand side
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3.4.3.1 Computing the right-hand side on B-rep models
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3.4.3.2 Computing the right-hand side on voxel models
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3.4.3.3 Computing the right-hand side on implicitly described geometries
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3.4.4 Step 4: Solving the equation system
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3.4.5 Recovery of the Gauss quadrature rule
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3.5 Performance of the suggested numerical integration schemes
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3.5.1 Cell cut by a planar surface
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3.5.2 Cell cut by several planar surfaces
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3.5.3 Cell cut by a curved surface
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3.5.4 Cell cut by several curved surfaces
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3.5.5 Numerical integration on voxel models
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3.6 Performance of the numerical integration methods in the FCM
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3.6.1 Perforated plate
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3.6.2 Sphere under hydrostatic stress state
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3.6.3 Porous domain under pressure
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72–110
4 Local enrichment of the FCM
72–110
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4.1 FCM for problems with material interfaces
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4.2 Local refinement and adaptivity
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4.3 Describing material interfaces using the level set function
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4.3.1 Smooth level set functions
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4.3.2 Non-smooth level set functions
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4.4 Local enrichment with the aid of the PU method
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4.4.1 Enrichment function for problems with material interfaces
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4.4.1.1 Stable XFEM/GFEM
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4.4.1.2 Blended enrichment
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4.5 Local enrichment with the aid of the hp-d method
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4.6 Selection of proper enrichment strategy
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4.7 Numerical examples
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4.7.1 Elastostatic analysis of a bi-material one-dimensional rod
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4.7.2 Bi-material perforated plate with curved holes
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4.7.3 Interplay between the fictitious domain and the enrichment zone
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4.7.4 3D cube with cylindrical inclusion
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4.7.5 Heterogeneous material
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111–132
5 The spectral cell method
111–132
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5.1 Temporal discretization and lumped mass matrix
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5.2 Spectral cell method and mass lumping in cut cells
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5.2.1 Row-sum technique for cut cells
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5.2.2 Mass scaling technique
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5.2.3 Diagonal scaling technique
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5.3 Numerical examples
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5.3.1 Lamb waves in a 2D plate
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5.3.2 Lamb waves in a perforated plate
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5.3.3 Lamb waves in a 2D porous plate
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5.3.4 Wave propagation in a sandwich plate
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133–135
6 Summary and Outlook
133–135
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136–137
A Gaussian quadrature rules
136–137
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A.1 Gauss-Legendre quadrature
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A.2 Gauss-Legendre-Lobatto quadrature
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138–138
B Polynomial integrands
138–138
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139–139
C Chen-Babuška points
139–139
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140–154
Bibliography
140–154
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The hierarchical finite cell method for problems in structural mechanics , page I - X
Titelei/Inhaltsverzeichnis
Autoren
Meysam Joulaian
DOI
doi.org/10.51202/9783186348180-I
ISBN print: 978-3-18-334818-3
ISBN online: 978-3-18-634818-0
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