Singular Integration in Variationally Coupled FE‐BE Method

Abstract

In the variationally coupled finite element‐boundary element method, the terms involving tractions on the interface are eliminated. A single variational principle is obtained for both the finite element and boundary element subdomains. However, the domain integrals that appear in this principle involve the singular fundamental solution. A new technique is proposed wherein these singular domain integrals are transformed to boundary integrals. Numerical examples show that the present method improves the accuracy of the results remarkably and decreases computation time compared with the domain integral method. In the “coupled patch test,” consisting of a constant strain field in an arbitrarily skewed patch of zones, the maximum errors for the variationally coupled method is 0.03%, whereas in the stiffness coupling and traction‐matching coupling methods, the maximum errors are 16% and 5%, respectively. Excellent results are also obtained for the variationally coupled solution of single‐edged notched specimens.