Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 122, Issue 8, Pages 2095-2111Publisher
WILEY
DOI: 10.1002/nme.6616
Keywords
fuzzy methodology; hybrid uncertainties; probabilistic methodology; robust topology optimization; sensitivity analysis
Funding
- Natural Science Foundation of Anhui Province [2008085QA21]
- Fundamental Research Funds for the Central Universities of China [JZ2020HGPA0112, JZ2020HGTA0080]
- National Natural Science Foundation of China [11972143]
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This paper presents a hybrid RTO method to address epistemic and aleatory uncertainties in engineering applications, using Monte Carlo simulations and a perturbation method to accelerate convergence. Derivatives of the robust compliance objective function are derived using the adjoint variable method. The proposed method is validated through testing on various beam designs.
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.
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