An XFEM frame for plate elements in yield line analyses

Abstract

A high gradient zone (HGZ) comes into existence in both rotation and deflection displacement fields in the vicinity of a yield line in a plate structure with elasto-plastic material. This HGZ makes the displacements non-smooth locally around the yield line. The Extended Finite Element Method (XFEM) has been proved to be an effective numerical method to capture the behavior of a structure with a locally non-smooth displacement field. In this article, a 6-node triangular and a 9-node quadrilateral Mindlin-Reissner plate element with the XFEM formulation are presented to trace the elasto-plastic behavior of a plate in small-deformation analyses. Regularized enrichments are employed to enrich the rotation and the deflection displacement approximation fields simultaneously so that the non-smoothness in a displacement field near a yield line can be captured. The discrete shear gap method (DSG) is adopted to alleviate shear locking phenomena in the present XFEM plate element. Several plate bending examples are simulated to show the robustness of the enrichment in capture the high gradient zone resulted from yield lines and the effectiveness of the application of DSG method in controlling the shear locking in the XFEM plate element.