Edge EigenPairs and ESIFs of 3-D Elastic Problems

Abstract

We proceed to elasticity problems in three-dimensional (3-D) polyhedral domains in the vicinity of an edge and provide the solution in an explicit form. It involves a family of eigenfunctions with their shadows, and the associated “edge-stressintensity functions” (ESIFs), which are functions along the edges. Utilizing the explicit structure of the solution in the vicinity of the edge, we extend the use of the quasidual function method (QDFM) presented in Section 11.3 for EFIFs [46, 134] to the extraction of ESIFs. It provides a polynomial approximation of the ESIF along the edge whose order is adaptively increased so to approximate the exact ESIF. The QDFM is implemented as a post-solution operation in conjunction with the p -version finite element method. Numerical examples are provided in which we extract ESIFs associated with traction-free or homogeneous Dirichlet boundary conditions in 3-D cracked domains or 3-D V-notched domains. These demonstrate the efficiency, robustness, and high accuracy of the proposed QDFM.