A Novel Formulation of Upper Bound Limit Analysis as a Second-order Cone Programming Problem

In this paper we describe an efficient approach to upper bound limit analysis of cohesivefrictional continua, using a finite element discretization in conjunction with second-order cone programming (SOCP). We also introduce the use of linear strain elements, focusing here on 6-node triangles in plane strain, though a directly analogous extension to 10-node tetrahedra in 3D is straightforward. If the vertices of such elements are taken as the flow rule points, it can be proved that the solutions obtained are strict upper bounds on the exact collapse load. Two numerical examples using unstructured meshes show that the linear strain elements give better results than constant strain elements combined with kinematically admissible discontinuities (until now considered to be the only practical choice for a rigorous upper bound analysis using finite elements). The examples also demonstrate that, as in shakedown analysis, the use of SOCP is highly advantageous, allowing very large problems to be solved in 1-2 minutes on a desktop PC. The obvious limitation of this approach is that it can only be applied to quadratic cone-shaped yield functions (e.g. Mohr-Coulomb in plane strain, and Drucker-Prager).