Topology optimization of truss structure under load uncertainty with gradient‑free proportional topology optimization method

Abstract

This study proposes a method for truss topology optimization (TO) that incorporates uncertain static and dynamic loads based on the efficient gradient‑free proportional topology optimization (PTO) method. The uncertain loads are modeled using probabilistic parameters and the objective function is constructed as the mean structural compliance with the constraint is imposed to the structural material volume. The univariate dimension reduction method and Gauss-type (UDRG) quadrature are used to quantify and propagate the load uncertainty to estimate the objective function. By the UDRG method, the TO of truss structures under uncertain loads can be transformed into a simple deterministic problem. To obviate the necessity for sensitivity analysis, the PTO method with comparable accuracy and efficiency as the gradient-based method is used. The proposed methodology is corroborated through multiple illustrative examples, which also serve to elucidate the ramifications of load uncertainty on optimized truss designs.