A quasi-dual function method for extracting edge stress intensity functions. (English) Zbl 1141.35363

Summary: We present a method for the computation of the coefficients of singularities along the edges of a polyhedron for second-order elliptic boundary value problems. The class of problems considered includes problems of stress concentration along edges or crack fronts in general linear three-dimensional elasticity. Our method uses an incomplete construction of three-dimensional dual singular functions, based on explicitly known dual singular functions of two-dimensional problems tensorized by test functions along the edge and combined with complementary terms improving their orthogonality properties with respect to the edge singularities. Our method is aimed at the numerical computation of the stress intensity functions. It is suitable for a postprocessing procedure in the finite element approximation of the solution of the boundary value problem.


35J25 Boundary value problems for second-order elliptic equations
35B65 Smoothness and regularity of solutions to PDEs
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