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

Simeon Hubrich

doi:10.51202/9783186355188

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Bibliographic data

Copyright year: 2021
ISBN-Print: 978-3-18-335518-1
ISBN-Online: 978-3-18-635518-8
Publisher: VDI Verlag, Düsseldorf
Series: Mechanik/Bruchmechanik
Volume: 355
Language: German
Pages: 169
Product type: Book Titles

Titelei/Inhaltsverzeichnis Partial access Pages I - VII Download chapter (PDF)
1. Motivation No access
2. Goal and scope of this thesis No access
3. Outline of this thesis No access
1. 1. Motion and deformation No access
  2. Strain measures No access
2. 1. Equilibrium No access
  2. Stress measures No access
3. 1. Linear elasticity No access
  2. Hyperelasticity No access
  3. Small strain elastoplasticity No access
  4. Finite strain plasticity No access
4. 1. Strong and weak form in the initial configuration No access
  2. Strong and weak form in the current configuration No access
5. 1. Linearized weak form in the initial configuration No access
  2. Linearized weak form in the current configuration No access
1. 1. Weak forms No access
  2. Linearized weak forms No access
2. 1. Mapping No access
  2. Discretization of the weak forms No access
3. 1. Gaussian quadrature No access
  2. Adaptive Gaussian quadrature scheme No access
1. 1. Basis functions No access
  2. Point distribution schemes No access
  3. Computation of the moments No access
  4. Computation of the weights No access
  5. Optimized points and weights No access
  6. 1. Cell cut by a sphere No access
    2. Recovery of the Gauss-Legendre quadrature No access
2. 1. Moment fitting without solving an equation system No access
  2. Computation of the moment fitting weights No access
3. 1. Hydrostatic sphere No access
  2. 1. Linear elasticity No access
    2. Small strain elastoplasticity No access
  3. Cube with a cylindrical hole No access
  4. Thick-walled plate with a circular hole No access
1. 1. Affected and nonaffected modes of the hierarchical basis No access
  2. Removal criterion of affected modes No access
  3. Implementation scheme No access
2. 1. Linear elasticity No access
  2. Small strain elastoplasticity No access
3. 1. Single cube connector under pressure No access
  2. Complex cube connector under pressure No access
  3. Single pore of a foam-like structure under pressure No access
1. Kinematic relations No access
2. 1. 1. Ratio of Jacobians No access
    2. Orthogonality No access
    3. Inverse aspect ratio No access
    4. Performance of the suggested remeshing criteria No access
  2. Mesh generation No access
  3. Data transfer No access
3. 1. Plate with a circular hole No access
  2. Single cube connector No access
  3. Complex cube connector No access
Summary and outlook No access Pages 150 - 153
Bibliography No access Pages 154 - 169