Symmetric Galerkin BEM for bodies with unconstrained contours

The solution via symmetric Galerkin boundary element method of problems in linear elasticity presents a major difficulty when a whole connected component of the boundary is under Neumann condition. In fact, apart from some special cases here discussed in detail, the resulting boundary integral equations are in general insensitive to the rigid body displacement of unconstrained connected boundary-components, even when the displacement is prescribed on some other boundary portions. A simple procedure is here proposed to solve the aforementioned indeterminacy while preserving the symmetry of the integral operator. Representative examples confirm the numerical effectiveness of the proposed method.