Layout optimization of continuum structures considering the probabilistic and fuzzy directional uncertainty of applied loads based on the cloud model

• Published in: Structural and multidisciplinary optimization Vol. 53; no. 1; pp. 81 - 100
• Main Authors: Liu, Jie, Wen, Guilin, Xie, Yi Min
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2016; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Engineering; Engineering Design; Evolutionary algorithms; Finite element method; Layouts; Loads (forces); Research Paper; Statistical analysis; Theoretical and Applied Mechanics; Topology optimization; Uncertainty; Topology optimization; Bi-directional evolutionary structural optimization (BESO); Cloud model; Directional uncertainty; Probabilistic and fuzzy uncertainty
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-015-1334-9

This paper reports an efficient approach for uncertain topology optimization in which the uncertain optimization problem is equivalent to that of solving a deterministic topology optimization problem with multiple load cases. Probabilistic and fuzzy property of the directional uncertainty of the applied loads is considered in the topology optimization; the cloud model is employed to describe that property which can also take the correlations of the probability and fuzziness into account. Convergent and mesh-independent bi-directional evolutionary structural optimization (BESO) algorithms are utilized to obtain the final optimal solution. The proposed method is suitable for linear elastic problems with uncertain applied loads, subject to volume constraint. Several numerical examples are presented to demonstrate the capability and effectiveness of the proposed approach. In-depth discussions are also given on the effects of considering the probability and fuzziness of the directions of the applied loads on the final layout.