Robust topology optimization considering load uncertainty based on a semi-analytical method

Uncertainty is omnipresent in engineering design and manufacturing. This paper dedicates to present a robust topology optimization (RTO) methodology for structural compliance minimization problems considering load uncertainty, which includes magnitude and direction uncertainty subjected to Gaussian distribution. To this end, comprehensible semi-analytical formulations are derived to fleetly calculate the statistical data of structural compliance, which is critical to the probability-based RTO problem. In order to avoid the influence of numerical units on evaluating the robust results, this paper considers a generic coefficient of variation (GCV) as robust index which contains both the expected compliance and standard variance. In addition, the accuracy and efficiency of semi-analytical formulas are validated by the Monte Carlo (MC) simulation; comparison results provide higher calculation efficiency over the MC-based optimization algorithms. Four numerical examples are provided via density-based approach to demonstrate the effectiveness and robustness of the proposed method.