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Additive manufacturing techniques such as 3D printing, selective laser sintering and others have enabled the fabrication of complex geometries such as meta-materials. Generally, the resulting geometry may be separated into scales, assuming sufficient characteristic length differences. For lattice cell meta-materials, a 'macro-scale' detailing the overall structure and its partitioning into subcells and a 'micro-scale', which describes the geometry of these subcells, may be defined. For Finite Element computations, the dependency of the mechanical behaviour of the macro-scale on the micro-scale geometry necessitates fine meshing, which results in prohibitively high computational costs, especially for multi-query analyses. One viable approach is the usage of effective material parameters obtained via homogenisation approaches, which show high efficiency but are limited to periodic designs. For multi-query analyses such as topology optimisation, a precomputed reduced order model (e.g. response surfaces or neural networks) may be introduced to approximate a unit cell's effective elastic material parameters based on specified design parameters [1],[2]). A downfall of these methods is the significant computational effort required for the training stage for general anisotropic materials. Schwahofer et al. performed Free Material Optimization for orthotropic unit cells and semi-periodic designs based on simplified modelling of a unit cell's trusses via beams, showcasing the promise of beam-based modelling for these applications [3].In this contribution, topology optimisation is conducted for anisotropic unit cells without defining periodicity constraints. The truss-based geometry of the unit cells is modelled in a simplified manner with beam elements, allowing for an efficient evaluation of the structure's performance. This method, while preserving the physicality of the problem, requires no previous computational steps and significantly reduces computational costs.
[1]: C. Imediegwu, R. Murphy, R. Hewson, and M. Santer, “Multiscale structural optimization towards three-dimensional printable structures,” Struct Multidisc Optim, vol. 60, no. 2, pp. 513–525, Aug. 2019, https://doi.org/10.1007/s00158-019-02220-y
[2]: N. Black and A. R. Najafi, “Deep neural networks for parameterized homogenization in concurrent multiscale structural optimization,” Struct Multidisc Optim, vol. 66, no. 1, p. 20, Jan. 2023, https://doi.org/10.1007/s00158-022-03471-y
[3]: O. Schwahofer, S. Büttner, J. Binder, D. Colin, and K. Drechsler, “Multiscale Optimization of 3D‐Printed Beam‐Based Lattice Structures through Elastically Tailored Unit Cells,” Adv Eng Mater, vol. 25, no. 20, p. 2201385, Oct. 2023, https://doi.org/10.1002/adem.202201385
