Optimal Design of Geometrically Nonlinear Structures Under a Stability Constraint

This paper suggests an optimization-based methodology for the design of minimum weight structures with kinematic nonlinear behavior. Attention is focused on three-dimensional reticulated structures idealized with beam elements under proportional static loadings. The algorithm used for optimization is based on a classical optimality criterion approach using an active-set strategy for extreme limit constraints on the design variables. A fixed-point iteration algorithm based on the criterion that at optimum the nonlinear strain energy is equal for all members is used. Several examples are given to evaluate the validity of the underlying assumptions and to demonstrate some of the characteristics of the proposed procedure.