Robust topology optimization methodology for continuum structures under probabilistic and fuzzy uncertainties

• Published in: International journal for numerical methods in engineering Vol. 122; no. 8; pp. 2095 - 2111
• Main Authors: Meng, Zeng, Wu, Yang, Wang, Xuan, Ren, Shanhong, Yu, Bo
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 30.04.2021; Wiley Subscription Services, Inc
• Subjects: Cantilever beams; Design parameters; fuzzy methodology; hybrid uncertainties; Iterative methods; Material properties; Mathematical models; Optimization; Perturbation methods; probabilistic methodology; Random variables; robust topology optimization; sensitivity analysis; Topology optimization; Uncertainty
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6616

Owing to the variations in geometric dimensions, material properties and external loads in engineering applications, robust topology optimization (RTO) has garnered increasing attention in recent years to account for the uncertain behaviors during the preliminary concept design phases. This paper presents a hybrid RTO method to simultaneously resolve the epistemic and aleatory uncertainties. First, based on the probabilistic and fuzzy methodologies, the hybrid RTO model is formulated with nested double optimization loops using Monte Carlo simulations. Second, an efficient iterative method is proposed based on the perturbation method to accelerate the rate of convergence of the proposed hybrid RTO model. The derivatives of the hybrid robust compliance objective function with respect to the deterministic design variables, random parameters, and fuzzy parameters are then derived using the adjoint variable method. Finally, a T‐shaped beam design, an L‐shaped beam design, and a three‐dimensional cantilever beam design are tested to validate the proposed hybrid RTO method.