Plastic Collapse Analysis of Mindlin–Reissner Plates Using a Stabilized Mesh-Free Method

This paper presents a numerical kinematic formulation for computation of collapse load of Mindlin–Reissner plates, that uses a stabilized mesh-free method in combination with second-order cone programming (SOCP). The kinematic formulation is discretized using a moving least squares approximation combined with a stabilized conforming nodal integration scheme, ensuring that shear locking problem at thin plate limit can be removed. The stabilized mesh-free based kinematic formulation is formulated as a conic problem so that it can be solved by an efficient primal-dual interior-point algorithm. To speed up computational progress, an adaptive refinement scheme using dissipation-based error indicator is also performed. The performance of the proposed numerical procedure is illustrated by examining several plates with arbitrary geometries and various boundary conditions.