Analisi limite ed a shakedown mediante il metodo simmetrico degli elementi di contorno

Abstract

A reformulation of the static approach to evaluate directly the shakedown and limit multipliers by using the Symmetric Boundary Element Method for multidomain type problems [1,2] is shown. The present formulation utilizes the self-equilibrium stress equation [3-5] connecting the stresses at the Gauss points of each substructure (bem-e) to plastic strains through a stiffness matrix (self stress matrix) involving all the bem-elements in the discretized system. The numerical method proposed is a direct approach because it permits to evaluate the multiplier directly as lower bound through the static approach. The analysis has been performed as a costrained optimization problem, solved through mathematical programming methods. In this approach the optimization problem has been rephrased in the canonic form of a Convex Optimization, in terms of discrete variables, and implemented by using Karnak.sbem code [6] coupled with the MatLab.