Group-Theoretic Buckling Analysis of Symmetric Plane Frames

This paper presents a computationally efficient formulation based on group theory, for the buckling analysis of symmetric plane frames. Numerical examples ranging from simple frames with one vertical plane of symmetry to more complex configurations with multiple symmetry planes are considered. In contrast to conventional procedures for accounting for symmetry, group theory uses the full symmetry of the configuration, resulting in higher reductions of computational effort. Typically, the n-dimensional problem is decomposed into smaller problems that are independent of each other, permitting the buckling loads and mode shapes to be computed through the solution of problems of much smaller dimension. The approach also yields insights on the character of the buckling modes before detailed computations are carried out.