Robust topology optimization design of structures with multiple-uncertainty load cases

The uncertainties existed in practical applications have great effect on the performance of structures, so it is necessary to introduce uncertainty in structural conceptual design. Robust topology optimization under multiple load cases with uncertainty was studied, where the magnitude and direction of each load are treated as random variables and their probability density functions are given. The weighted sum of the mean and standard deviation of the structural compliance is minimized. According to the superposition principle of linear theory, computational method for expected and variance of structural compliance was proposed. Sensitivity analysis method was developed based on the expressions of the expected and variance of compliance. For 2D structure with M load cases, the expected compliance and variance of structures as well as sensitivity information can be obtained for each load case, and then the object function as well as sensitivity can be achieved readily. In each load case, the expected compliance and variance of structures as well as sensitivity information can be obtained by solving the equilibrium equation under 2n deterministic load cases, where n is the number of uncertain loads. Algorithm of structural robust topology optimization to minimize the weighted sum of expectation and standard deviation of compliance under the constraint on the material volume was proposed and verified by numerical examples. The numerical examples also demonstrated the robustness of topology optimization results under multiple load cases with uncertainties. The proposed algorithm can be readily generalized into 3D cases.