On the mechanical inconsistency of symmetrization of unsymmetric coupling matrices for BEFEM discretizations of solids

摘要

For several technical problems discretization of the boundary of a part of a solid by the BEM and of the remaining part of the solid by the FEM is useful in order to exploit the complementary advantages of the BEM and of the FEM optimally. A characteristic feature of the employed “local FEM approach” for the coupling of such discretizations are “coupling matrices” representing load-stiffness matrices which are associated with displacement-dependent node forces acting on the interface of the two parts of the solid. Because of the nature of the employed BEM these matrices are unsymmetric. It is proved theoretically that symmetrization of such coupling matrices is mechanically inconsistent. It is also demonstrated that this symmetrization may lead to a significant deterioration of the quality of numerical