Two-Scale Topology Optimization with Isotropic and Orthotropic Microstructures

Abstract

Advances in additive manufacturing enable the fabrication of complex structures with intricate geometric details, which bring opportunities for high-resolution structure design and transform the potential of functional product development. However, the increasingly delicate designs bring computational challenges for structural optimization paradigms, such as topology optimization (TO), since the design dimensionality increases with the resolutions. Two-scale TO paves an avenue for high-resolution structural design to alleviate this challenge. This paper investigates the efficacy of introducing function-based microstructures into the two-scale TO. Both isotropic and orthotropic microstructure are considered to develop this TO framework. Implicit functions are exploited to model the two classes of cellular materials, including triply periodic minimal surfaces (TPMS) and Fourier series-based functions (FSF). The elasticity tensor of microstructures is computed with numerical homogenization. Then, a two-scale TO paradigm is formulated, and a gradient-based algorithm is proposed to simultaneously optimize the micro-scale structures and macro-scale material properties. Several engineering benchmark cases are tested with the proposed method, and experimental results reveal that using proposed microstructures leads to, at most, a 36% decrease in the compliance of optimal structures. The proposed framework provides achievable directionality and broader design flexibility for high-resolution product development.