A polynomial dimensional decomposition-based method for robust topology optimization

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.

Automated summary

This study introduces a novel method for topology optimization by integrating polynomial dimensional decomposition, topology derivative, and level-set method to effectively deal with a large number of random inputs. The approach allows for the analysis of stochastic moments and sensitivities through analytical expressions, while utilizing the level-set function and reaction-diffusion equation for topology evolution.