  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.
