A polynomial dimensional decomposition-based method for robust topology optimization

• Published in: Structural and multidisciplinary optimization Vol. 64; no. 6; pp. 3527 - 3548
• Main Authors: Ren, Xuchun, Zhang, Xiaodong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2021; Springer Nature B.V
• Subjects: Approximation; Civil engineering; Computational Mathematics and Numerical Analysis; Decomposition; Derivatives; Design optimization; Engineering; Engineering Design; Mathematical analysis; Methods; Polynomials; Probability; Random variables; Reaction-diffusion equations; Research Paper; Response functions; Robustness; Sensitivity analysis; Theoretical and Applied Mechanics; Topology optimization; Topology optimization; Stochastic moments; Topology derivatives; Polynomial dimensional decomposition; Robust design
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-021-03036-5

This paper implements a novel integration of the polynomial dimensional decomposition (PDD), topology derivative, and level-set method for robust topology optimization subject to a large number of random inputs. With this method, the influence of a large number of random inputs can be easily captured in an accurate manner. In addition, the stochastic moments and their sensitivities can be obtained from analytical expressions based on the PDD approximation of response functions and the deterministic topology derivative. Only a single stochastic analysis is required for evaluating the moments and their sensitivities in each iteration. The topology is described by the level-set function and its evolution is driven by solving the reaction-diffusion equation of the level-set function. An augmented Lagrange penalty formulation dovetails the stochastic topology derivatives of objective and constraints into the reaction term in the reaction-diffusion equation, which generates a new topology during the iteration process. The practical examples illustrate that the proposed method can render meaningful optimal designs for structures subject to several or a large number of random inputs.