Stabilized displacement and equilibrium meshfree models for computation of collapse loads

Abstract

This paper describes dual limit analysis formulations based on stabilized displacement and equilibrium meshfree models. Displacement and stress fields are approximated using moving least squares technique. A stabilized conforming nodal integration is applied, ensuring that the size of the resulting optimization problem is kept to a minimum, and that equilibrium only needs to be enforced at the nodes while numerical instability problems can be eliminated. The resulting optimizations are the cast in the form of a standard second order cone programming so that solutions can be obtained rapidly.

Keywords:  limit analysis; mesh-free methods; stabilized displacement and equilibrium models; second order cone programming.