Partially mixed lower bound constant stress tetrahedral element for Finite Element Limit Analysis

A numerical analysis of the limit state for solids, with an adequately described structural geometry, is often a computationally demanding task, and there is a need for an effective method. The existing solid elements for Finite Element Limit Analysis (FELA) are either computationally expensive or require a stress cutoff of the yield surface for triaxial stress states.

This paper presents an effective partially mixed lower bound tetrahedral constant stress solid element that converges rapidly and does not require modification of the yield surface. The element is based on a partially relaxed formulation of the lower bound theorem by providing strict equilibrium of the normal tractions on the element faces and a relaxed equilibrium of the shear/tangential tractions at the vertices.

The performance of the element is shown in four examples applying either the von Mises yield criterion, or the Modified Mohr–Coulomb yield criterion with the possible inclusion of reinforcement. The examples show fast convergence and good performance even for relatively coarse meshes.