A robust multi-material topology optimization method considering load and material uncertainties with univariate interpolation

Understanding and quantifying uncertainty factors for multi-material topology optimization (TO) are crucial to satisfy realistic engineering requirements. A robust multi-material TO method for structures with bounded load and spatially correlated material uncertainties is proposed. For the first time, a univariate interpolation framework is established to model multi-material uncertainty fields. The process begins by generating topology density fields using a univariate characteristic function, which are then filtered via convolution principle and normalized with the Heaviside function. These filtered fields are incorporated into the Discrete Material Optimization scheme to generate material property weighting functions. An uncertainty analysis model is constructed by combining weight functions with spatially varying material property field for each material using the K–L expansion method. Statistical characteristics of the displacement response are evaluated by solving the polynomial chaos expansion coefficients. A continuation strategy along with MMA is introduced to update design variables. A series of numerical examples considering load and material uncertainties are illustrated. Numerical results show that structural designs generated using the proposed method, demonstrate robustness in the face of hybrid uncertainties. Moreover, it overcomes the challenges of variable quantity dependence on material phases and non-physical material transitions in traditional methods.