Segmental multi-point linearization for topology optimization and reliability analysis

This paper proposes an efficient gradient-based optimization algorithm to solve reliability-based topology optimization (RBTO) of structures under loading and material uncertainties. Topology optimization is a powerful design tool as it can provide the most efficient material layout for structural design problems under given conditions and limitations. However, most attempts are formulated in a deterministic manner, which may be impractical as this formulation ignores the inherent uncertainty and randomness in structural design problems. The objective of RBTO considered in this research is to identify the optimal topology of truss structures with minimum weight which also satisfy certain requirements on the reliability of the structures. As a subtopic of reliability-based design optimization (RBDO), RBTO problems are primarily performed with algorithms based on a first-order reliability method (FORM) which are well developed in the literature for RBDO. However, those algorithms may lead to deficient or even invalid results for RBTO problems since the gradient of probabilistic constraint, calculated by first order approximation, is not accurate enough for RBTO to converge correctly regardless of how accurate the failure probability is approximated. A segmental multi-point linearization (SML) method is proposed for a more accurate estimation of failure probability and its gradient. Numerical examples show that the RBTO algorithm based on the SML is more stable numerically and is able to converge to a solution that is closer to the true optimum than conventional FORM-based algorithms. The obtained optimal topology can serve as a starting point for engineers to make the design of structures both economic and reliable