A cell-based smoothed radial point interpolation method applied to lower bound limit analysis of thin plates

Abstract

This paper proposes a novel numerical method based on the cell-based smoothed radial point interpolation method (CS-RPIM) combined with second-order cone programming to perform lower bound limit analysis of elastic-perfectly-plastic thin plates, using only deflection as nodal variable. The problem domain is initially discretized using a simple triangular background mesh, where each triangular cell is subsequently subdivided into multiple smoothing domains. Shape functions are formulated using the radial point interpolation method, allowing direct imposition of essential boundary conditions for deflection. Rotational constraints are conveniently handled through the construction of smoothed curvatures. By utilizing a generalized gradient smoothing technique, complex domain integrals are simplified into boundary integrals over the smoothing domains, thus eliminating the need to compute second-order derivatives of the shape functions. The virtual work principle is employed to enforce the equilibrium conditions for the self-equilibrated residual moment field in a weak sense. The von Mises yield conditions are expressed as conic constraints and the resulting optimization problems are solved using highly efficient primal-dual interior point solvers. Numerical examples demonstrate that it is feasible and effective to conduct lower bound limit analysis of thin plates using the proposed CS-RPIM and second-order cone programming.