Analysis and plastic synthesis of frames involving frictional contacts

Abstract

This paper presents novel schemes for the extended limit analysis and plastic synthesis of rigid perfectly plastic frames involving unilateral supports with frictional contacts. The focus is on the Coulomb friction model which embodies a nonassociative complementarity condition. As such, uniqueness of the upper bound solution in the complementarity system is no longer guaranteed. The aim of the extended limit analysis is to compute, for fixed topology and known material distribution, the least upper bound to collapse limit. This is achieved by directly formulating and solving a single nonconvex and nonsmooth optimization problem, known in a literature as a mathematical program with equilibrium constraints (MPEC). Under given design loads, the plastic synthesis can also be carried out using an iterative scheme that determines the safe material distribution such that the total weight of the structure is a minimum.