MULTI-DOMAIN BOUNDARY ELEMENT METHOD FOR AXISYMMETRIC PROBLEMS IN POTENTIAL THEORY AND LINEAR ISOTROPIC ELASTICITY

The paper presents an approach based on reduced boundary element methods to resolve axisymmetric problems in potential and linear isotropic elasticity theories. The singular integral equations for these problems are received using fundamental solutions. Initially three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So the three-dimensional axisymmetric problems are reduced to systems of singular integral equations requiring the evaluation of linear integrals only. The fundamental solutions and their derivatives are expressed in terms of complete elliptic integrals. The effective algorithm for treatment of the singular integrals is proposed. The multi-domain boundary element method is applied for the numerical simulation. As examples, the following problems are considered: fluid induced vibrations of a compound cylindrical-spherical elastic shell partially filled with an ideal incompressible liquid, and axisymmetric elasticity problems for an isotropic body with rigid or elastic circular cylindrical inclusions.