DBEM analysis for an elliptic torsion bar with a double-edge crack

Abstract

It is well known that rank deficiency occurs in BEM for degenerate boundary. The conventional BEM is difficult to solve the problem which contains degenerate boundary without decomposing the domain to multi-regions. Therefore, the hypersingular integral equation is used in the procedure to ensure a unique solution for the problem containing a degenerate boundary. Combing the singular and hypersingular equation, it's termed dual BEM due to its dual frame. By employing the SVD technique to the four influence matrices, it is interesting to find that true information in physics due to rigid body mode is found in the right unitary vector with respect to the corresponding zero singular value while the degenerate boundary information in mathematics is imbedded in the left unitary vector. In this report, we use the dual BEM to determine the torsional rigidity of an elliptic bar containing a double-edge crack. The role of the right and left unitary vectors of SVD in the dual BEM is also discussed in this work.