Concurrent structural optimization of buckling-resistant trusses and their initial imperfections

This paper presents a new approach for truss optimization against buckling that incorporates both the structural design and the imposed initial imperfections. Euler buckling of slender members, global buckling and stability of sequences of bars are all considered by optimizing the geometric nonlinear response, instead of by imposing a large number of constraints. The proposed optimization problem formulation consists of two alternating steps: (1) Shape optimization that aims to find the worst-case imperfection shape of the joints’ positions; (2) Sizing-topology optimization that aims to find the minimum volume of a buckling-resistant structure with the given optimized imperfection. Sensitivity analysis for the two optimization phases follows the adjoint method and solutions are obtained using first-order sequential approximate methods. It is shown that optimizing the imperfection shape stabilizes the convergence as acute instantaneous buckling is avoided. Several numerical examples demonstrate the capability of the proposed formulation to generate buckling-resistant designs with robustness against imperfections.