Optimum design of nonlinear symmetric truss structures under system stability constraint

Abstract

Among the 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. Structural optimization of nonlinear problems is costly due to iterative nature of both the nonlinear analysis and optimization. In this study, application of 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. The limit point during the each optimization iteration has been obtained efficiently and accurately using a combination of the displacement control technique and the GTA. 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, and the optimality criteria approach based on the potential energy of the system. A closed form solution has been introduced to obtain the Lagrange multiplier, which allows the design process to be started in the infeasible region. A shallow dome truss structure has