Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids

By Theofanis Strouboulis, Lin Zhang, Ivo Babuska. 2003

111 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/d9d4be90b980aea96283e4349e32dc6416c5de06

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A two-scale approach for the analysis of propagating three-dimensional fractures (2012, result): “in contrast with other recently proposed multi-scale methods which rely on, e.g., analytically derived boundary conditions for fine-scale problems [ 55 ,56].”
Stability of incompressible formulations enriched with X-FEM (2008, methodology): “The method was used to simulate structures containing thousands of holes or/and micro-cracks, and the approximation can be enriched with handbook functions [ 19 ].”
The piecewise polynomial partition of unity functions for the generalized finite element methods (2008, methodology): “However, they are generally very large and in some cases, the stiffness matrices become singular (for example, see [17], [18]).”
Analysis of Interacting Cracks Using the Generalized Finite Element Method With Global-Local Enrichment Functions (2008, methodology): “Custom-built enrichment functions that are solutions of local boundary value problems can be used as well [8, 9, 26].”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “Later, the approach is extended to a large number of voids and also shifts in [174].”
Arbitrarily smooth generalized finite element approximations (2006, unknown): “, [4,16,18,19,53,55,56, 68,70,71].”
GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE (2004, unknown): “Vekua (1967) and I.”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, methodology): “This is the basic idea of the GFEMgl [40], the GFEM with mesh-based handbooks [74], the GFEM with numerically defined harmonic enrichment functions [75], the method of Menk and Bordas for fracture of bi-material systems [76], the spider-XFEM [77], and the reduced basis enrichment for the XFEM [78] o”