Robust and Reliability-Based Structural Topology Optimization Using a Continuous Adjoint Method

Abstract

AbstractA unified framework for robust and reliability-based structural topology optimization, considering structural model and loading uncertainties, is presented using a continuous adjoint formulation. The topology optimization is formulated for objective functions related to uncertainty measures of the compliance or displacements of the structure. Uncertainty measures, such as mean, standard deviation, and level exceedance probability or failure probability, involve the estimation of multidimensional integrals over the uncertain parameter space. These integrals are evaluated using (1) sparse grid quadrature techniques for the mean and standard deviation and (2) the approximate first-order reliability method (FORM) for failure probability. A unified continuous adjoint formulation is presented for the different objective function formulations. Simplifications are proposed that result in increased computational efficiency and accuracy for special cases of uncertainties and structural performance measures....