Solution of periodic group circular hole problems by using the series expansion variational method

Abstract

SUMMARYThis paper investigates the periodic group circular holes composed of infinite groups with numbering from j = −∞, . . . , −2, −1, 0, 1, 2, . . . to j = ∞ placed periodically in an infinite plate. The same loading condition and the same geometry are assumed for holes in all groups. The series expansion variational method (SEVM) is used for the solution of the periodic group circular hole problems. After using the SEVM, the boundary value problem is then reduced to an algebraic equation for the undetermined coefficients in the series expansion form, which is formulated on the central group. The influences on the central group from central group itself and many neighbouring groups are evaluated exactly. The influences on the central group from remote groups from j = − ∞, −(M + 2), −(M + 1), M + 1, M + 2 to j = ∞ are approximately summed up into one term. This suggested technique is called the remainder estimation technique (RET) hereafter. It is proved from the computed results that the RET is very effective for the solution of the periodic group hole problems. Finally, several numerical examples are given and the interaction between the groups is addressed. Comparison between various sources of computation is presented. In the uniaxial tension in y-direction, the stacking effect of the stacked groups is studied.

Untitled

“…A special boundary element formulation for multiple circular hole problems in an infinite plate was suggested in [Chen 1985]. The multiple circular hole problem for an elastic half-plane and the periodic group circular hole problems were solved by using the series expansion variational method [Chen 1994;Chen and Lin 2007].…”