The hierarchical finite cell method for problems in structural mechanics

Meysam Joulaian

doi:10.51202/9783186348180

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Bibliographic data

Copyright year: 2017
ISBN-Print: 978-3-18-334818-3
ISBN-Online: 978-3-18-634818-0
Publisher: VDI Verlag, Düsseldorf
Series: Mechanik/Bruchmechanik
Volume: 348
Language: German
Pages: 154
Product type: Book Titles

Titelei/Inhaltsverzeichnis Partial access Pages I - X Download chapter (PDF)
1. Motivation No access
2. Scope and outline of this work No access
1. The strong and weak form of the governing equations No access
2. The finite element method No access
3. Mesh generation and the finite cell method No access
4. 1. Fast algorithms to introduce the indicator function No access
  2. 1. Neumann boundary conditions No access
    2. Dirichlet boundary conditions No access
  3. Numerical integration of cut cells No access
  4. Material interfaces and weak discontinuities No access
  5. Efficient iterative solvers No access
5. 1. Elastostatic analysis of a one-dimensional rod No access
  2. Perforated plate No access
  3. Porous domain No access
1. Numerical integration of unbroken cells No access
2. Performance of Gaussian quadrature rules in facing discontinuities No access
3. 1. Composed integration based on conforming local meshes No access
  2. Composed integration based on uniform sub-cell division No access
  3. Composed integration based on spacetrees No access
  4. Resolution of the integration mesh No access
  5. Composed integration with an hp-refinement procedure No access
4. 1. Step 1: Selection of the basis functions No access
  2. Step 2: Setting up the position of the quadrature points No access
  3. 1. Computing the right-hand side on B-rep models No access
    2. Computing the right-hand side on voxel models No access
    3. Computing the right-hand side on implicitly described geometries No access
  4. Step 4: Solving the equation system No access
  5. Recovery of the Gauss quadrature rule No access
5. 1. Cell cut by a planar surface No access
  2. Cell cut by several planar surfaces No access
  3. Cell cut by a curved surface No access
  4. Cell cut by several curved surfaces No access
  5. Numerical integration on voxel models No access
6. 1. Perforated plate No access
  2. Sphere under hydrostatic stress state No access
  3. Porous domain under pressure No access
1. FCM for problems with material interfaces No access
2. Local refinement and adaptivity No access
3. 1. Smooth level set functions No access
  2. Non-smooth level set functions No access
4. 1. 1. Stable XFEM/GFEM No access
    2. Blended enrichment No access
5. Local enrichment with the aid of the hp-d method No access
6. Selection of proper enrichment strategy No access
7. 1. Elastostatic analysis of a bi-material one-dimensional rod No access
  2. Bi-material perforated plate with curved holes No access
  3. Interplay between the fictitious domain and the enrichment zone No access
  4. 3D cube with cylindrical inclusion No access
  5. Heterogeneous material No access
1. Temporal discretization and lumped mass matrix No access
2. 1. Row-sum technique for cut cells No access
  2. Mass scaling technique No access
  3. Diagonal scaling technique No access
3. 1. Lamb waves in a 2D plate No access
  2. Lamb waves in a perforated plate No access
  3. Lamb waves in a 2D porous plate No access
  4. Wave propagation in a sandwich plate No access
Summary and Outlook No access Pages 133 - 135
1. Gauss-Legendre quadrature No access
2. Gauss-Legendre-Lobatto quadrature No access
Polynomial integrands No access Pages 138 - 138
Chen-Babuška points No access Pages 139 - 139
Bibliography No access Pages 140 - 154