Dynamic non-probabilistic reliability-based topology optimization of truss with uncertain-but-bounded parameters

In this paper, non-probabilistic reliability indices for frequency and static displacement constraints are analyzed based on the ellipse convex model of elastic modulus and mass density. The dynamic non-probabilistic reliability-based topology optimization model of a truss is built, where the cross-sectional areas and nodal topology variables are taken as design variables. The objective is to minimize the structural total mass. Constraints are imposed on static stresses and non-probabilistic reliability indices of static displacement and natural frequency. A genetic algorithm is used as the optimization method to find optimal solutions in the outer loop and an analysis method is adopted to seek non-probabilistic reliability index according to implicit forms of the limit state function in the inner loop. Results of numerical examples show that the optimal mass of a non-probabilistic reliability-based topology optimization is larger than that of the deterministic topology optimization and the optimal mass increases with the increase of the non-probabilistic reliability requirement in order to ensure structural safety.