The use of cyclic symmetry in two-dimensional elastic stress analysis by BEM

Abstract

Rotationally periodic (or cyclic) symmetry is exploited in the elastic stress analysis of two-dimensional structures under arbitrary load conditions by the BEM. It is proved that the coefficient matrices of the global boundary element equations for the rotationally periodic system are block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted. Furthermore, the computational convenience and efficiency which can be achieved by exploiting this property and the structural geometric symmetry in the different phases of numerical implementation is demonstrated, and an efficient algorithm is presented. Numerical examples are given to illustrate the advantages of such exploitation of symmetry in the context of the BEM.