Algorithm of structural topology optimization under loading uncertainty

Structural topology optimization under loading uncertainty was studied, where the uncertainty was described by the probabilistic approach. 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 cases, 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 topology optimization to minimize the weighted sum of expectation and standard deviation of compliance was proposed and verified by numerical examples. The numerical examples also demonstrate the robustness of topology optimization results under loading uncertainty. The proposed algorithm can be readily generalized into 3D cases.