Three‐dimensional elastoplastic analysis by triple‐reciprocity boundary element method

Abstract

SUMMARYIn general, internal cells are required to solve elastoplastic problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is ease of data preparation, is lost. Triple-reciprocity BEM can be used to solve two-dimensional elastoplasticity problems with a small plastic deformation. In this study, it is shown that three-dimensional elastoplastic problems can be solved, without the use of internal cells, by the triple-reciprocity BEM. An initial strain formulation is adopted and the initial strain distribution is interpolated using boundary integral equations. A new computer program was developed and applied to solving several problems.

Meshless large plastic deformation analysis considering with a friction coefficient by triple-reciprocity boundary element method

“…in the case of a two-dimensional problem is interpolated using the integral equation to transform the domain integral into a boundary integral. The following equations are used for interpolation [5][6][7][8][9][10]:…”

“…where ∇ = ∂ ∂ + ∂ ∂ values on the boundary are zero. We emphasize that eqns (5) and (6) can be used to interpolate the complicated distribution of the initial stress  σ Ijk [ ] 1 . These equations are the same as those used to generate a free-form surface using an integral equation [6,7].…”