Completely Regularized Integral Representations and Integral Equations for Anisotropic Bodies with Initial Strains

Abstract

The present paper is devoted to the boundary formulation for anisotropic bodies subjected to a distribution of initial strains. Concerning both interior and exterior problems, the results are featured by the complete regularization of all the derived expressions: the integral representation of the displacement gradients and the stresses as well as the ordinary or derivative integral equations. The formulation also includes the case of piecewise regular boundary with edges or corners. Furthermore, explicit expressions in terms of physical meaningful boundary quantities such as the stresses related to the normal vector and the tangent derivatives of the displacements are given, which is particularly useful for further numerical implementations.

Weakly-singular, weak-form integral equations for cracks in three-dimensional anisotropic media

“…The singularity-reduced traction integral equation developed by Sládek and Sládek (1982) applies for general anisotropy, but (in addition to the limitations already mentioned) it explicitly involves the stress fundamental solution which is difficult to compute for anisotropic material behavior. More recently, Sládek et al (1998) established completely regularized integral equations for anisotropic media which are applicable to cracks in both unbounded and finite domains. There remains the requirement that the derivative of the relative crack-face displacement be continuous and, further, the integral equations involve both the gradient of the displacement fundamental solution and the stress fundamental solution.…”