One approach to the derivation of exact integration formulae in the boundary element method

An approach to the derivation of analytical formulae for exact integration in the boundary element solution of two-dimensional elasticity problems is proposed. The integration over an arbitrary boundary element reduces to the integration over a specific element, and this simplifies the derivation of the formulae. Integrals involving fundamental functions are considered, as well as integrals containing derivatives of the fundamental functions, the latter integrals being necessary for stress evaluation. Exact formulae have been obtained to calculate regular and singular integrals. Constant and discontinuous linear elements are considered. The accuracy of the solution obtained with the use of the formulae derived is verified against two test problems.