Generalized de-homogenization via sawtooth-function-based mapping and its demonstration on data-driven frequency response optimization

De-homogenization is becoming an effective method to significantly expedite the design of high-resolution multiscale structures, but existing methods have thus far been confined to simple static compliance minimization problems. There are two critical issues in accommodating general design cases: enabling the design of unit-cell orientation and using free-form microstructures. In this paper, we propose a generalized de-homogenization method to address these two issues, significantly holes, we devise a parameterized microstructure composed of bars in different directions to provide more diversity in stiffness while retaining geometrical simplicity. The microstructural geometry-property relationship is then surrogated by a multi-layer neural network to avoid costly homogenization analysis during optimization. A Cartesian representation of the rotationangle is incorporated into homogenization-based optimization to design the unit-cell orientation. Corresponding high-resolutionmultiscale structures are obtained from the homogenization-based designs through a conformal mapping constructed withsawtooth function fields. This allows us to morph complex microstructures into an oriented and compatible tiling pattern, whilepreserving the local homogenized properties. To demonstrate our method with a specific application, we optimize the frequencyresponse of structures under harmonic excitations within a given frequency range. It is the first time that the de-homogenizationframework, enhanced by the sawtooth function, is applied for complex design scenarios beyond static compliance minimization.The examples illustrate that high-resolution multiscale structures can be generated with high efficiency and much better dynamicperformance compared with the macroscale-only optimization. Beyond frequency response design, our proposed framework canbe applied to general static and dynamic problems. (C) 2022 Elsevier B.V. All rights reserved.