Truss topology design optimization with guaranteed kinematic stability

Kinematic stability of the truss topology design and sizing optimization (TTDSO) problems is a crucial aspect which is often overlooked in the mathematical optimization models. In this paper, we propose a novel mathematical optimization model for the discrete TTDSO problem with Euler buckling constraints. Random perturbations of external forces are used to obtain kinematically stable structures. We prove that by considering the perturbed external forces, the resulting structure is kinematically stable with probability one. Furthermore, we show that necessary conditions for kinematic stability can be used to speed up the solution of discrete TTDSO problem. While mixed integer linear optimization (MILO) solvers for existing models are not able to even find a feasible solution for Michell trusses with more than 182 bars in a reasonable amount of time, our model provides high-quality solutions for those problems in the same time window.

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