Computation of stress intensity factor for through cracks in plates and bending of shells using P-version finite element method

Abstract

The present study concerns the analysis of bending of plates and shells subjected to various boundary conditions and load. Bending stress intensity factors for plates containing through thickness crack under edge bending load are evaluated. To accomplish the task, hierarchical degenerated plate/shell element and hierarchical 18-node solid thick shell element are developed. -- The hierarchical degenerated plate shell element has four comer nodes, four mid-side nodes and one central node on the mid-surface of the shell geometry with five degrees of freedom at each node. For defining the geometry, Lagrangian shape functions were employed. P-version shape functions up to order seven were used for defining the displacement field. Crack tip singular plate/shell element was developed by enriching the displacement field of the element with the asymptotic displacement field near the crack tip. A hierarchical 18-node solid thick shell element has been developed. Sixteen nodes consisting 8 comer nodes and 8 mid-side nodes are used to define the geometry and eighteen nodes for defining the displacement field. Each node has three degrees of freedom. -- Some benchmark problems were analyzed in order to check correctness the elements of both plate/shell and thick solid elements. Analyses were performed to obtain the stress intensity factors of plate with through thickness crack using hierarchical degenerated plate/shell element. Numerical results obtained from the present element formulations are compared with analytical/numerical solutions available from literature. It is inferred that numerical results are in good agreement with the benchmark plate and shell problems.