Computation of stress intensity factors for through cracks in plates 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 this task, hierarchical degenerated plate/shell and crack-tip singular plate/shell elements were developed. The hierarchical degenerated plate shell element has four corner 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. p-Version shape functions up to order seven were used for defining the displacement field. Enriching the displacement field with the asymptotic displacement field near the crack tip, a crack-tip singular plate/shell element was developed. Some benchmark problems were analyzed and compared. Analyses were performed to obtain the stress intensity factors of plate with through-thickness crack using singular hierarchical degenerated plate/shell element around the crack tip. 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. Copyright © 2007 John Wiley & Sons, Ltd.