Multi-material robust topology optimization considering uncertainty of material properties

Abstract

This paper proposes a solution to a multi-material robust topology optimization problem of density type considering material uncertainties based on H1 gradient method. A material interpolation with respect to the density is introduced using the rational approximation of material properties (RAMP) and generalized it for the case with an arbitrary number of materials. Material uncertainty is considered by introducing random variables in the material interpolation scheme. The probability density functions of the random variables are assumed to be given. The topology optimization is formulated using the density which is given by a sigmoid function of the design variable. A weighted sum of the mean and standard deviation of the mean compliance is used as the objective function to control the tradeoff between optimality and robustness. To evaluate statistical moments of the objective function effectively, the univariate dimension reduction (UDR) and the Gauss-type quadrature sampling are introduced. A scheme to solve the robust topology optimization problem is presented using an iterative algorithm based on the H1 gradient method for reshaping. Examples of a two-dimensional cantilever beam under various material uncertainty exhibit the efficiency and flexibility of the approach. The accuracy of UDR is validated by comparing the results to the Monte Carlo approach.

Keywords

• robust topology optimization
• multi-material
• material uncertainty
• h1 gradient method
• univariate dimension reduction
• rational approximation of material properties