Abstract

In this work a methodology of meshless finite points method for the analysis of nonlinear material problems with proportional loading based on deformation theory is presented. In finite points method the approximation around each point is obtained by using weighted least square techniques. The discrete system of equation is constructed by means of a point collocation procedure. The non-dependence on a mesh or integration procedures is an important aspect which transforms the finite point method in a truly meshless technique. Hencky's total deformation theory and an elastic approach is used on the determination of stress-strain fields. This approach introduces the concept of effective material properties which are considered as spatial field variables and to be functions of equilibrium stress state and material properties. The present results are in good agreement with those obtained by nonlinear finite element method and previous work in this meshless context. Nevertheless the present methodology is based on a strong formulation, keeping the meshless characteristics of FPM. © 2009 Elsevier Ltd. All rights reserved.