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In this paper, the problem of load uncertainty in compliance problems isaddressed where the uncertainty is described in the form of a set of finitelymany loading scenarios. Computationally more efficient methods are proposed toexactly evaluate and differentiate: 1) the mean compliance, or 2) anyscalar-valued function of the individual load compliances such as the weightedsum of the mean and standard deviation. The computational time complexities ofall the proposed algorithms are analyzed, compared with the naive approachesand then experimentally verified. Finally, a mean compliance minimizationproblem, a risk-averse compliance minimization problem and a maximum complianceconstrained problem are solved to showcase the efficacy of the proposedalgorithms. The maximum compliance constrained problem is solved using theaugmented Lagrangian method and the method proposed for handling scalar-valuedfunctions of the load compliances, where the scalar-valued function is theaugmented Lagrangian function.

Robust and stochastic compliance-based topology optimization with finitely many loading scenarios