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Partition of Unity Methods
book

Partition of Unity Methods

by Stéphane P. A. Bordas, Alexander Menk, Sundararajan Natarajan
October 2023
Intermediate to advanced content levelIntermediate to advanced
368 pages
12h 57m
English
Wiley
Content preview from Partition of Unity Methods

5 Applications

Stéphane P. A. Bordas1, Alexander Menk2, and Sundararajan Natarajan3

1 University of Luxembourg, Luxembourg, UK2 Robert Bosch GmbH, Germany3 Indian Institute of Technology Madras, India

In this chapter, we provide some examples of applications of extended finite element method (XFEM) for problems with weak/strong discontinuities and singularities, viz., linear elastic homogeneous isotropic fracture mechanics; anisotropic fracture mechanics and automatic numerical enrichment; simulation of creep and crack initiation and propagation in solder joints; fatigue crack in two dimensions and plate subjected to thermo-mechanical loading. For the first four examples, consider a linear homogeneous body with an internal discontinuity occupying normal upper Omega subset-of bold upper R squared is subjected to mechanical boundary conditions. The boundary normal upper Gamma of normal upper Omega accommodates the following decomposition: normal upper Gamma equals normal upper Gamma Subscript t Baseline union normal upper Gamma Subscript u, where Dirichlet and Neumann boundary conditions are specified. The governing equation for the linear elasto-static problem in the absence of inertia and body forces is given by:

(5.1)

supplemented with the following boundary conditions ...

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Publisher Resources

ISBN: 9780470667088Purchase Link