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Integral equation methods and numerical solutions of crack and inclusion problems in planar elastostatics. (English) Zbl 0934.74006
The paper presents algorithms for crack and inclusion problems in planar linear elastostatics. The algorithms are based on new integral equations. For the pure crack problem, the integral equations are of Fredholm’s second kind. The algorithms show great stability and allow to solve some new problems. The method departs from the Airy stress function in the complex notation, with potentials as Cauchy-type integrals. The problem is formulated in Hilbert space, and several numerical examples are given for illustration.
MSC:
74B05Classical linear elasticity
74R10Brittle fracture
45B05Fredholm integral equations
45E05Integral equations with kernels of Cauchy type
65R20Integral equations (numerical methods)