Reliability-based topology optimization by ground structure method employing a discrete filtering technique

When conventional filtering schemes are used in reliability-based topology optimization (RBTO), identified solutions may violate probabilistic constraints and/or global equilibrium. In order to address this issue, this paper proposes to incorporate a discrete filtering technique termed the discrete filtering method (Ramos Jr. and Paulino 2016) into RBTO using the elastic formulation of the ground structure method. The discrete filtering method allows the optimizer to achieve more physically realizable truss designs in which thin bars are eliminated while ensuring global equilibrium. The method uses a potential-energy-based approach with Tikhonov regularization to solve the singular system of equations that may result from imposing the discrete filter. Combining this method with RBTO allows us to use the reliability-based truss sizing optimization for the purpose of topology optimization under uncertainties. Furthermore, a single-loop approach is adopted to enhance the computational efficiency of the proposed RBTO method. Numerical examples of two- and three-dimensional engineering designs demonstrate useful features of the proposed method and illustrate the influence of the discrete filter and parameter uncertainties on the optimization results. In order to check if the optimal topologies obtained by the proposed approach satisfy the constraints on the failure probabilities, structural reliability analysis is also performed using the first-order reliability method and Monte Carlo simulations.