Topology optimization of trusses incorporating practical local buckling stability considerations

Abstract

For the practical application of optimized truss structures, the local stability of the bar must be considered to obtain stable and realistic structures. However, in the practical design of structures, the initial crookedness of the bars and residual stresses that remain in the bar after the manufacturing process should be taken into account, which makes the buckling strength highly non-connected and non-convex in terms of the cross-sectional properties. Therefore, most conventional truss optimization formulations include only local buckling constraints based on the Euler buckling criterion, while local buckling constraints based on design specifications are rarely incorporated. To treat these problems, a novel topology optimization model for trusses is proposed, where the critical buckling strength is calculated according to the practical design code GB5007-2017. In addition, a linearized iterative allowable stress method is used to solve the optimization model. Since the allowable stresses are calculated at each iteration based on the critical buckling strength, other types of design codes can also be incorporated into the proposed truss topology optimization model. The proposed computational model shows, through several numerical examples, the remarkable effect of including local buckling stability in the optimal design of trusses, while demonstrating that the optimized topology depends on whether the local buckling constraints are derived from the Euler buckling criterion or from actual structural design codes.