A mixed finite-element formulation for the elasto-plastic analysis of shell structures

Abstract

Abstract. Mixed assumed stress finite elements for elastic-perfectly plastic materials require the solution of a Closest Point Projection (CPP) involving all the element stress parameters for the integration of the constitutive equation. Here, a dual decomposition strategy is adopted to split the CPP at the element level into a series of CPPs at the integration points level and in a nonlinear system of equations over the element. The strategy is tested with a four nodes mixed shell finite element, named MISS-4, characterised by an equilibrated stress interpolation and a displacement field assumed only along its boundaries. The recovered elasto-plastic solution preserves all the advantages of MISS-4, namely it is accurate for coarse meshes in recovering the equilibrium path and evaluating the limit load showing a quadratic rate of convergence.