Robust topology optimization of thermoelastic metamaterials considering hybrid uncertainties of material property

Abstract

Metamaterials with extreme thermoelastic properties (i.e. thermal expansion and stress) offer significant value in applications that require maintaining thermal geometric stability, e.g., aerospace equipment. However, material uncertainty has a great impact on the thermoelastic properties of such multiphase composites. Thus, a robust topology optimization design for the thermoelastic composites under hybrid uncertainties of material property is investigated. The distribution of base materials in the periodic unit cell is achieved by multi-phase solid isotropic material with penalization method and the equivalent properties of composites are evaluated by the numerical homogenization method. To obtain a clear material interfaces in the unit cell, a filtering method named the element perimeter control method is proposed. Considering the uncertainties of material property, the linear thermal expansion coefficients of two constituent materials are assumed to be a random variable and an interval variable, respectively. A robust topology optimization model based on Polynomial-Chaos-Chebyshev-Interval method is proposed, where the Polynomial chaos and Chebyshev interval functions are integrated to perform uncertainty analysis. The robust objective function is formulated by a combination of average mean, average and bandwidth of standard deviation of the objective value. The effectiveness of the proposed robust topology optimization methodology is illustrated with several numerical examples.