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Approximation schemes for stochastic compliance-based topology optimization with many loading scenarios

In this paper, approximation schemes are proposed for handling load uncertainty in compliance-based topology optimization problems, where the uncertainty is described in the form of a set of finitely many loading scenarios. Efficient approximate methods are proposed to approximately evaluate and differentiate either 1) the mean compliance, or 2) a class of scalar-valued function of the individual load compliances such as the weighted sum of the mean and standard deviation. The computational time complexities of the proposed algorithms are analyzed, compared to the exact approaches and then experimentally verified. Finally, some mean compliance minimization problems and some risk-averse compliance minimization problems are solved for verification.