On solutions of two-dimensional linear elastostatic and heat-transfer problems in the vicinity of singular points

Singular points associated with the linear theories of steady-state heat transfer and elasticity are discussed. Exact solutions for a set of benchmark problems consisting of crack tips, wedge corners of different angles and materials and internal multi-material interfaces in isotropic as well as anisotropic materials are provided and described in detail. Both the generalized flux/stress intensity factors (GFIFs/GSIFs) and the eigenfunctions are explicitly presented. The efficiency, robustness and accuracy of new numerical methods based on the p-version of the finite element method are demonstrated on the basis of the benchmark problems.

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