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

Abstract

In general, internal cells are required to solve large deformation problems using a conventional boundary element method (BEM). However, in this case, the merit of BEM, which is the ease of data preparation, is lost. Triple-reciprocity BEM enables us to solve elastoplasticity problems with a small plastic deformation. In this study, it is shown that two-dimensional large plastic deformation problems with a friction coefficient can be solved without the use of internal cells, by the triple-reciprocity BEM. Initial stress and strain formulations are adopted and the initial stress or strain distribution is interpolated using boundary integral equations. In this method, only boundary elements are remeshed. A new computer program is developed and used to solve several problems.

On Solving Nonlinear Elasticity Problems Using a Boundary-Elements-Based Solution Method

“…By adopting interpolation (10) for each component of the vectors σ P and {T}, Equation ( 11) is written for an internal collocation center in the following, obvious form:…”

“…In relation (12), [Φ 1 ] and [Φ 2 ] are properly constructed matrices from interpolation functions defined by (10) and…”

“…In Voigt notation, as (10) for each component of the particular displacement vector, with [Φ 3 ] a properly constructed matrix, Equation (12) becomes…”

“…A number of strategies have been developed in order to convert domain integrals into boundary integrals. One can mention the dual reciprocity method [7], the radial integration method [8], the generalized boundary element method [9], and the multiple reciprocity method which has been recently applied in the context of large deformation [10]. Other boundary-element-based approaches have been proven effective for a variety of problems: the local integral equation [11] and the analogue equation method [12].…”