An efficient method for concurrent multiscale robust structural topology optimization under loading uncertainties

An efficient method is proposed for the concurrent robust topology optimization of a continuum structure in multiscale material distributions under the external load uncertainties of direction and magnitude such that the resultant design illustrates a prominent insensitivity to the loading variations. In this context, the loading direction and magnitude uncertainties are described in stochastic forms independently. By means of decomposition of the external load along the essential directions, the variation of the structural compliance is firstly represented by a multivariable quadratic Taylor series expansion. Then both the expectation and variance of the compliance can be evaluated efficiently through the statistical analyses‌. Furthermore, the concurrent design sensitivity analyses are performed readily upon the Taylor series formulations, and the multiscale robust topology optimization can be performed by a gradient-based strategy. Several benchmark examples are employed to demonstrate the feasibility of the proposed method, and the computational cost for the compliance statistical characteristics can be reduced remarkably in comparison with a stochastic simulation method. The obtained robust topology optimization designs show quite different from the conventional deterministic counterparts in both macro- and microscale structures. As the result, the variation of the structural compliance can be significantly reduced under the uncertain loading conditions.