Buckling Restrained Sizing and Shape Optimization of Truss Structures

Abstract

An integrated strategy for sizing and shape optimization of truss structures, taking buckling constraints implicitly into truss design, is demonstrated here. Because the associated objective functional is not convex, a derivative-free directionality-based global optimization scheme is adopted. As required by the problem, the change of measure–based evolutionary optimization (COMBEO) optimization scheme is appropriately enhanced in this work to incorporate complex inequality constraints without affording any violation. The applied scheme arrests buckling through a forward model via capturing geometric nonlinear responses of the structure. For this purpose, each truss element is modeled using two corotational beam elements with moment releases at hinged ends. Local and global imperfections are introduced to induce buckling of a single member and global buckling of the structure, respectively. These imperfections are randomly generated using Gaussian distribution to arrive at a resilient structure. While past research used large numbers of buckling constraints explicitly to optimize truss weight, the proposed scheme eliminates the same by adding buckling implicitly in the forward model. Present formalism also includes capturing nonlinear responses of the structure to eliminate structural failure due to geometric nonlinearity. Robustness of the proposed scheme is demonstrated extensively using four different types of trusses. The proposed formalism can be used to solve many other structural optimization problems involving geometric nonlinearity and imperfections.