Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity

Abstract

This paper discusses the formulation and implementation of the symmetric Galerkin boundary integral method for two dimensional linear elastic orthotropic fracture analysis. For the usual case of a traction-free crack, the symmetry of the coef®cient matrix can be effectively exploited to signi®cantly reduce the computational work required to construct the linear system. In addition, computation time is reduced by employing ef®-cient analytic integration formulas for the analysis of the orthotropic singular and hypersingular integrals. Preliminary test calculations indicate that the method is both accurate and ef®cient.

3D Boundary Element Analysis for Composite Joints with discrete Damage. Part 1.

“…A symmetric Galerkin algorithm for fracture, in the context of twodimensional potential theory, was recently presented by Gray, Balakrishna, and Kane [1995]. This method, effectively a combination of displacement discontinuity [Crouch and Starfield 1983] and the hypersingular BEM [e.g., Gray 1990] ideas, employs the hypersingular equation on the crack surface as described above in Section 1.3.…”

“…For the present project, we have explored techniques to improve the computational efficiency, and have extended the approach to plane orthotropic elastostatics. Some of this work has been presented in Gray and Paulino [1996].…”

Influence functions of the displacement discontinuity method for anisotropic bodies

“…The complete Green's functions and BEM formulation have been derived by Pan [10] in the generalized anisotropic half-plane problems. Some various kinds of singular integrals in boundary element methods have been developed by Gray [11] and Sladek [12].…”

The meshless standard and hypersingular boundary node methods—applications to error estimation and adaptivity in three‐dimensional problems

“…References [32;38;39]), in symmetric Galerkin boundary element formulations (e.g. References [40][41][42]), to obtain the hypersingular boundary contour method (e.g. References [43; 44]), and for adaptive analysis (e.g.…”