Exact integrations of two-dimensional high-order discontinuous boundary elements of elastostatics problems

Abstract

High-order boundary elements are efficient for solving problems with high stress gradient and are necessary for adaptive boundary element analysis. This paper derives the exact integrations of the integrals of the discontinuous cubic and quartic boundary element analysis of two-dimensional elstostatics problems. The derived exact integrations enable the non-singular and singular integrals to be evaluated in the same way, making special treatment of the singular integrals unnecessary. This greatly simplifies the computer code and improves solution efficiency as a result. The advantages of the exact integrations are verified against two examples.