The Analysis of Crack Problems in Elasticity Using Integral Equations
Keywords:
Square-Root, Elasticity, Integral Equations, Fracture Mechanics, Boundary Integral FormulationAbstract
This paper presents an analytical investigation of crack problems in linear elasticity using integral equation methods. The study is based on the classical theory of elasticity under assumptions of small deformations and isotropic material behavior, where crack-induced displacement discontinuities and stress singularities play a dominant role. By employing boundary integral formulations derived from fundamental solutions, the governing elasticity equations are reduced to singular and dual integral equations defined along crack surfaces. These equations are solved using analytical and semi-analytical techniques to obtain crack opening displacements, stress distributions, and stress intensity factors. The results demonstrate that the integral equation approach accurately captures the inverse square-root stress singularity near crack tips and yields stress intensity factors in excellent agreement with classical fracture mechanics solutions. The methodology proves to be computationally efficient, numerically stable, and well-suited for analyzing the influence of crack geometry and boundary conditions, thereby providing a robust framework for crack analysis in elastic solids.
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References
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