Robust Multi-material Topology Optimization for Lattice Structure Under Material Uncertainties

Abstract

Recent advances in additive manufacturing have enabled the manufacture of hollow shapes with complex external geometry and multiple materials using networks of small periodic cells known as lattice structures. The porosity and high number of elements in these structures generate lightweight designs with improved performance and functionality. This paper proposes a design approach for lattice structures considering both multi-material design and uncertainty in material properties. A density-based multi-material topology optimization method is proposed to find the optimal geometry and material layout. In addition, a new interpolation scheme for using multiple and arbitrary materials is presented. For robustness of structural compliance against uncertainty in material properties, a weighted sum of the mean and standard deviation is chosen as an objective function. To estimate statistical moments by the material uncertainty, the univariate dimension-reduction (UDR) method combined with Gauss-type quadrature sampling is employed. Two numerical examples demonstrate the efficiency of the proposed approach and the effect of material uncertainty on the robust design results.