Group theory provides a systematic means of exploiting the physical symmetry of a structure in the course of analysis, with the result that all the symmetry elements of the configuration are taken into account. This is achieved by a decomposition of the vector space of the arbitrary functions of the problem, into mutually-independent subspaces of symmetry-adapted functions, within each of which the number of unknowns is only a fraction of those of the original problem. Consequently, substantial reductions in computational effort can be achieved. In the present paper, the method is applied to the determination of eigenvalues of a plate by the well-known numerical technique of finite differences, thereby illustrating the significant computational gains of a group-theoretic approach over conventional methods, whenever the physical configuration of the plate structure (or sub-structure) exhibits symmetry properties.

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