Structural design optimization of nonlinear symmetric structures using thegroup theoretic approach

Among multidisciplinary analysis and optimization problems, structural opti mization of geometrically nonlinear stability problems is of great importan ce, especially in structures used in space applications, because of their l ong and slender configurations. in this study, application of the group the oretic approach (GTA) in structural optimization of geometrical Nonlinear p roblems under system stability constraint has been investigated. According to GTA, the number of displacement degrees of Freedom in the initial config uration can be reduced significantly by using the set of symmetry transform ations of the undeformed structure to construct a projection matrix from fu ll space to a reduced subspace spanned by the symmetry modes. A structural optimization algorithm is developed for shallow structures undergoing large deflections subject to system stability constraint. The method combines th e nonlinear buckling analysis, based on the displacement control technique using GTA, with the optimality criteria approach, based on the potential en ergy of the system. A shallow dome truss structure has been designed to ill ustrate the proposed methodology. This paper demonstrates that structural o ptimization of nonlinear symmetric structures using GTA is computationally efficient, and excellent agreement exists between optimal results in full s pace and those in the reduced subspace. Also, it is shown that structural d esign based on the generalized eigenvalue problem (linear buckling) highly underestimates the optimum mass, which may lead to structural failure.