The hypersingular boundary contour method for two-dimensional linear elasticity

This paper presents a novel method called the Hypersingular Boundary Contour Method (HBCM) for two-dimensional (2-D) linear elastostatics. This new method can be considered to be a variant of the standard Boundary Element Method (BEM) and the Boundary Contour Method (BCM) because: (a) a regularized form of the hypersingular boundary integral equation (HBIE) is employed as the starting point, and (b) the above regularized form is then converted to a boundary contour version based on the divergence free property of its integrand. Therefore, as in the 2-D BCM, numerical integrations are totally eliminated in the 2-D HBCM. Furthermore, the regularized HBIE can be collocated at any boundary point on a body where stresses are physically continuous. A full theoretical development for this new method is addressed in the present work. Selected examples are also included and the numerical results obtained are uniformly accurate.