Degenerate scale for a torsion bar problem using BEM

Abstract

In this paper, a torsion bar problem is solved by using BEM. It is found that a degenerate scale problem occurs if the conventional BEM is used. In this case, the influence matrix is rank deficient and numerical results become unstable. Three regularization techniques, method of adding a rigid body mode, hypersingular formulation and CHEEF concept, are employed to deal with the rankdeficiency problem. The existence of degenerate scale is proved for the two-dimensional Laplace problem. The addition of a rigid body term, c, in the fundamental solution can shift the original degenerate scale to a new degenerate scale by a factor e−c. A numerical example for circular bar with keyway under torsion, was demonstrated to show the failure of conventional BEM in case of the degenerate scale. After employing the three regularization techniques, the accuracy of the proposed approaches is achieved.