Application of Symmetric Galerkin Boundary Element Method on Elastostatic Neumann Problems

When Symmetric Galerkin boundary element method (SGBEM) is applied to Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion term involved. In this paper, this phenomenon is discussed, and methods for the removal of rigid body motions are introduced and investigated. In geotechnical engineering, half-space problems are encountered quite often, and most of them are Neumann problems. In this study, SGBEM is used to analyze half-space problems by the technique of modelling a truncated free surface mesh. Nevertheless, the solutions obtained are still not satisfactory because of the errors due to the truncation of the free surface. Among the methods investigated, the one using modified boundary integral equations based on Fredholm theory is relatively preferable.