Reliability-based topology optimization using a new method for sensitivity approximation - application to ground structures

This paper proposes an efficient gradient-based optimization approach for reliability-based topology optimization of structures under uncertainties. Our objective is to find the optimized topology of structures with minimum weight which also satisfy certain reliability requirements. In the literature, those problems are primarily performed with approaches that use a first-order reliability method (FORM) to estimate the gradient of the probability of failure. However, these approaches may lead to deficient or even invalid results because the gradient of probabilistic constraints, calculated by first order approximation, might not be sufficiently accurate. To overcome this issue, a newly developed segmental multi-point linearization (SML) method is employed in the optimization approach for a more accurate estimation of the gradient of failure probability. Meanwhile, this implementation also improves the approximation of the probability evaluation at no extra cost. In general, adoption of the SML method leads to a more accurate and robust approach. Numerical examples show that the new approach, based on the SML method, is numerically stable and usually provides optimized structures that have more of the desired features than conventional FORM-based approaches. The present approach typically does not lead to a fully stressed design, and thus this feature will be verified by numerical examples.