Abstract: The exact evaluation of nearly singular integrals is a crucial task in Boundary Element Method(BEM).
Usually, the regular integrals arising from BEM implementation can be evaluated by standard Gaussian quadrature accurately. However, when the source point is close to the boundary, conventional method (Gaussian quadrature) gives a lower numerical precision, even wrong result. For a plane problem, using the source point serving as origin, the tangent and normal direction of integral elements to establish local coordinate system, analytical solutions are obtained for all integrals of linear elements. The field variables of all boundary points except for the corner are continuous and bounded, so the sum of corresponding singular terms are zero and these terms can be ignored directly. The accuracy and efficiency of solutions obtained by this method are verified by several numerical examples.