Note on the removal of rigid body motions in the solution of elastostatic traction boundary value problems by SGBEM

Abstract

A study of errors appearing in traction boundary value problems on simply connected domains solved by the symmetric Galerkin boundary element method (SGBEM) is presented. Two methods for the removal of rigid body motions from the nullspace of the discretised SGBEM system matrix, one based on the direct enforcement of additional point supports and the other based on the Fredholm theory of linear operators, are analysed. The fulfillment of the global equilibrium conditions by the discretised load has been found to be the key point in the different behaviour of the errors in displacements obtained applying these two methods. The main objective of this paper is to compare the application of these methods with the SGBEM and with the classical collocation BEM, clarifying in particular a different role of the equilibrium of the discretised load in the SGBEM and classical collocational BEM linear systems. Conclusions of the theoretical analysis presented are confirmed by numerical examples, where the conditions of the global equilibrium are either fulfilled or slightly violated by the discretised load.