Estimation of Fracture Parameters for Cracked Mindlin–Reissner Plates by a Hierarchical Quadrature Element Method

Abstract

This paper presents an integration of the hierarchical quadrature element method (HQEM), characterized by p-convergence, with the virtual crack closure method (VCCM) for evaluating stress resultant intensity factors of through-cracked plates. A HQEM formulation, free from shear locking and applicable to both thin and moderately thick plates, is developed based on the Mindlin–Reissner plate theory. Building upon the conventional framework of VCCM, a universal formula for calculating fracture parameters is derived for the proposed element formulation with an arbitrary number of boundary nodes. Both the calculation formula and its corresponding numerical implementation are simple and straightforward. Several representative numerical examples demonstrate the accuracy and effectiveness of combining HQEM and VCCM for fracture parameter calculation in through-cracked plates. Furthermore, the results indicate that a relatively coarse mesh is sufficient to obtain highly accurate moment and shear force intensity factors for cracked plates, whether thin or thick, thereby greatly simplifying the preprocessing procedure.