Computing the vertex stress intensity factors in three-dimensional Laplace problems with vertex singularities using the singular function boundary integral method

The purpose of this work is to solve three-dimensional Laplace problems with vertex singularities using the Singular Function Boundary Integral Method (SFBIM). In the SFBIM, the solution is approximated by the first terms of the local asymptotic solution expansion, whose coefficients are the unknown singular coefficients or vertex stress intensity factors. The application of Green’s theorem reduces the discretized Galerkin equations to boundary integrals, and the essential boundary conditions are imposed weakly by Lagrange multipliers, whose values constitute additional unknowns in the linear system. Numerical experiments for a special case are presented, and the convergence of the solution with both the numbers of Lagrange multipliers and vertex stress intensity factors is demonstrated and discussed. An analysis of the features and the limitations of the method is also provided.