Optimal Design of Structures with Kinematic Nonlinear Behavior

Abstract

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 first‐order necessary condition is derived and used as the basis of a fixed‐point iteration method to search for the optimal design. A fixed‐point iteration algorithm is used based on the criterion that at optimum design the nonlinear strain energy is equal in all members. A nonlinear analysis procedure for three‐dimensional structures is discussed and used in developing the optimization algorithm. Several examples are given to evaluate the validity of the underlying assumptions and to demonstrate some of the characteristics of the proposed procedures. The procedure is verified using two well‐known examples.