Quadrature rule for singular integrals in common engineering problems

Abstract

This paper describes a general method to compute the boundary integral equation for common engineering problems. The proposed procedure consists of a new quadrature rule to evaluate singular and weakly singular integrals. The methodology is based on the computation of the quadrature weights by solving an undetermined system of equations in the minimum norm sense. The Bezier–Bernstein ´ form of a polynomial is also implemented as an approximation basis to represent both geometry and field variables. Therefore, exact boundary geometry is considered, and arbitrary high-order elements are allowed. This procedure can be used for any element node distribution and shape function. The validity of the method is demonstrated by solving a two-and-a-half-dimensional elastodynamic benchmark problem.