Pseudo-Lower-Bound Limit Analysis of Structures Using an Enhanced Cell-Based Smoothed Finite Element Method

Abstract

Volumetric locking remains a major obstacle in pseudo-lower-bound limit analysis of near-incompressible structures. To overcome this difficulty, a bubble-enriched cell-based smoothed finite element approach is proposed, in which quadrilateral elements are supplemented with internal enrichment and the equilibrium constraints are imposed in a weak, spatially smoothed form over subcells. The resulting discrete problem is recast as a conic optimization model and solved efficiently using second-order cone programming (SOCP) techniques. Numerical examples confirm that the proposed approach effectively suppresses the locking behavior observed in the standard CS-FEM-Q4 formulation under near-incompressible plane-strain conditions. Computed solutions exhibit errors as low as 0.1% relative to analytical and reference results, while large-scale optimization problems can be solved within a few seconds. These results demonstrate that the proposed method provides an accurate, robust, and efficient computational tool for pseudo-lower-bound limit-state analysis, particularly for structures exhibiting near-incompressible behavior.