Shakedown analysis of incompressible materials under cyclic loads: A locking-free CS-FEM-Q5 numerical approach

Volumetric locking may occur in plastic analysis of incompressible materials using low-order finite elements due to incompressibility constraints. This study presents a locking-free smoothed five-node quadrilateral element-based approach for plastic analysis in structural engineering. The proposed Q5-element employing four cell-based smoothing domains effectively alleviates the volumetric locking issues, here in the problems under plane strain conditions. The resulting large-scale optimization problem is formulated in a conic programming form, enabling efficient use of the interior-point optimizer. Numerical investigations demonstrate the method’s effectiveness in alleviating volumetric locking, accurately predicting collapse and shakedown limits, and generating interaction diagrams for load-carrying capacity and structural collapse mechanisms.