Tessellated continuum mechanics: A Galerkin finite element method

Nonlinear Continuum Mechanics for Finite Element Analysis

A novel modification of decouple scaled boundary finite element method in fracture mechanics problems

In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics (LEFM), the SIFs and energy of cracked media may be estimated. This study presents the novel modification of decoupled scaled boundary finite element method (DSBFEM) to model cracked media. In this metho...

Quantum Mechanics and the Finite Element Method

dx = 0 (1) Here ψ(x) is some sort of wavefunction that somehow describes the properties of the particle, V (x) is the potential the particle moves in, and E is the particle energy. The term ∇ψ(x) ·∇ψ(x) measures the curvature of the wavefunction. In some way it is a surrogate for the (kinetic) energy of the particle. Schrödinger never came to terms with the physical meaning of ψ(x). From this e...

An optimally convergent discontinuous-Galerkin-based extended finite element method for fracture mechanics

The extended finite element method (XFEM) enables the representation of cracks in arbitrary locations of a mesh. We introduce here a variant of the XFEM rendering an optimally convergent scheme. Its distinguishing features are: a) the introduction of singular asymptotic crack tip fields with support on only a small region around the crack tip, the enrichment region, b) only one and two enrichme...

A Weak Galerkin Mixed Finite Element Method for Biharmonic Equations

This article introduces and analyzes a weak Galerkin mixed finite element method for solving the biharmonic equation. The weak Galerkin method, first introduced by two of the authors (J. Wang and X. Ye) in [52] for second order elliptic problems, is based on the concept of discrete weak gradients. The method uses completely discrete finite element functions and, using certain discrete spaces an...