A novel centroid-enriched edge-based smoothed radial point interpolation method for upper bound limit analysis

Abstract

This paper presents a novel centroid-enriched edge-based smoothed radial point interpolation method (CE-ESRPIM) to overcome the volumetric locking problem and increase the numerical accuracy for upper bound limit analysis. Based on the edge-based smoothed radial point interpolation method (ESRPIM), the centroid of the triangle element is used as a field node to discretize the problem domain. Simultaneously, the local support node selection scheme, which is established based on a modified centroid-enriched triangle mesh (CE-TScheme), is proposed to realize local radial point interpolation (RPIM). Using the Mohr–Coulomb yield criterion and associated flow rule, the upper bound theorem in the plane strain condition is discretized into a standard second-order cone programming (SOCP) problem through the CE-ESRPIM, which is solved using the primal–dual interior-point algorithm (PDIP). The proposed approach with the enriched centroid considered as the field node is straightforward and efficient and can directly inherit the formulation framework of the traditional ESRPIM. Moreover, this method has been proven to be effective in eliminating the volumetric locking problem under incompressible conditions.