Group theory provides an efficient and systematic means for exploiting the full symmetry of physical systems, resulting in a substantial simplification of the quantitative analysis of their properties. For a given problem exhibiting symmetry properties, this simplification is achieved by a decomposition of the vector space of its arbitrary functions into a number of mutually-independent subspaces each spanned by a set of symmetry-adapted functions, such that within each subspace, the number of unknowns (i.e. symmetry-adapted functions) is only a fraction of that associated with a conventional analysis of the problem. In the present paper, the technique is applied to the structural analysis of symmetrical plane frames by the well-known direct stiffness method, and the computational superiority of the group-theoretic procedure over its conventional counterpart is shown through a simple illustrative example.

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