Topology optimization of steel frame structures with constraints on overall and individual member instabilities

A computationally efficient structural topology optimization framework is proposed for design of steel frame structures with user-defined factors of safety against overall structure (global) and individual member instabilities. The objective function is minimization of either compliance or the maximum of von Mises stresses within the frame structure. Within optimization, overall structure buckling modes are found via an eigenvalue analysis, a subset of “pseudo modes” are identified using a newly proposed methodology and are discarded to obtain a set of real eigenvalues. Moreover, individual member buckling loads are estimated with Euler buckling analysis and are aggregated into a single constraint. The minimum of each instability constraint is then estimated with separate differentiable negative p-norm functions. Sensitivities of these newly developed constraints are explicitly derived for application of gradient-based optimizers. The topology of four frame structures featuring moment-resisting connections and member cross-sectional properties mapped from the American Institute of Steel Construction design manual are optimized with the proposed algorithm to verify its effectiveness in optimizing structural performance while maintaining factors of safety against overall and individual member instabilities. The interaction effects of preventing instabilities at different safety levels and the choice of objective function on the final designs and their performances are investigated.