Structural Design Optimization of Nonlinear Symmetric Structures Using the Group Theoretic Approach

Abstract

Among multidisciplinary analysis and optimization problems, structural optimization of geometrically nonlinear stability problems is of great importance, especially in structures used in space applications, because of their long and slender configurations. In this study, application of the group theoretic approach (GTA) in structural optimization of geometrical nonlinear problems under system stability constraint has been investigated. According to GTA, the number of displacement degrees of freedom in the initial configuration can be reduced significantly by using the set of symmetry transformations of the undeformed structure to construct a projection matrix from full 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 the nonlinear buckling analysis, based on the displacement control technique using GTA, with the optimality criteria approach, based on the potential energy of the system. A shallow dome truss structure has been designed to illustrate the proposed methodology. This paper demonstrates that structural optimization of nonlinear symmetric structures using GTA is computationally efficient, and excellent agreement exists between optimal results in full space and those in the reduced subspace. Also, it is shown that structural design based on the generalized eigenvalue problem (linear buckling) highly underestimates the optimum mass, which may lead to structural failure.