A Three-Node Triangular Finite Element for Static Limit Analysis

A three-node triangular finite element is developed for the static theorem of limit analysis to discretize plane strain and stress problems. The element does not provide rigorous lower-bound solutions because the equilibrium equations and mechanical boundary conditions are satisfied on average, but exhibits a remarkable performance as illustrated by standard benchmark tests. Nowhere does the generated stress field violate the traction continuity across the element interfaces and the yield criterion. The stated nonlinear convex optimization problem is cast as second-order cone programming before its solution by a robust interior-point algorithm implemented in the dedicated solver MOSEK.