A BOUNDARY-ELEMENT APPROACH TO THE SOLUTION OF 3-DIMENSIONAL PROBLEMSOF THE THEORY OF ELASTICITY BY THE GEOMETRICAL IMMERSION METHOD

A basic formulation of the geometrical immersion method (GIM) for solv ing three-dimensional boundary-value problems in the differentially fo rmulated theory of elasticity is given. If the canonical domain is tak en to be the entire Euclidean space, the differential formulation redu ces to the corresponding boundary integral equation whose kernel is th e Kelvin-Somigliana tenser. The integral equation obtained is realized numerically using the boundary-element approximation. Numerical exper iments confirm the theoretical convergence of the GIM iterative proces s. The efficiency of this approach compared with the traditional metho ds of boundary integral equations for solving three-dimensional proble ms on the theory of elasticity is due to the absence of computationall y intensive steps which invert densely-packed matrices of the influenc e coefficients in the direct solution of algebraic systems of equation s, and the choice of parameters that ensure convergence when iterative methods are used.