A multi-scale discrete material optimization model for optimization of structural topology and material orientations to minimize dynamic compliance

For fiber-reinforced composites, the combination of structural topology optimization and fiber angle design is an excellent way to suppress structural vibration more efficiently and acquire a lighter structure. This paper proposes a concurrent optimization model for fiber-reinforced composite structures, where the mathematical model is built by combining the polynomial interpolation scheme (PIS) and the Heaviside penalization of discrete material optimization (HPDMO). Therein, the former is adopted to avoid the localized mode phenomena due to the mismatch between element stiffness and mass. And the latter is used for multi-candidate fiber orientation design. The objective function is to minimize the integration of the dynamic compliance in a given frequency band subject to macro-volume constraint. In order to ease the heavy computational burden caused by hundreds of frequency steps in each iteration, too many freedom degrees, and discrete design variables in HPDMO, the modal acceleration method is used to obtain a high-precision estimation of displacement response, and a decoupled method suitable for multiphase fiber material sensitivity analysis is also developed. Finally, a modified threshold Heaviside projection is used to obtain a black-and-white design. Several numerical examples are presented to verify the validity and robustness of the proposed model.