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Topology optimization of programmable lattices with geometric primitives

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Abstract

This work presents a topology optimization method for the design of programmable lattice materials whose struts can be activated/deactivated by some actuation mechanism. The proposed method simultaneously determines the spatial layout of struts in the unit cell, and two or more programs corresponding to the open/close states of the struts in order to attain desired effective properties. A high-level parametric description of the cylindrical struts in the unit cell is smoothly mapped onto a fixed mesh for analysis via the geometry projection method. Desired material symmetries are imposed by reflections with respect to the symmetry planes in the computation of the projected density. The open/close state of a strut is modeled by assigning a state variable per program to each strut, and a discreteness constraint in the optimization ensures these variables are zero or unity in the optimal design. To aid manufacturability, a no-cut constraint is imposed to preclude partial cuts of the struts by the symmetry planes or the unit cell boundaries and thus ensure that struts are whole in the optimal design. The effectiveness of the proposed method is demonstrated with examples of minimal volume design for two and three programs with target bulk moduli and for two programs with a bulk modulus target and a Poisson’s ratio target.

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Acknowledgements

Support from the National Science Foundation, award CMMI-1634563 to conduct this work is gratefully acknowledged. We also thank Niels Aage and collaborators for their parallel implementation of MMA Aage et al. (2017), which we used for the optimization.

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Authors and Affiliations

  1. University of California San Diego, 9500 Gilman Drive, La Jolla, CA, 92093, USA

    Hesaneh Kazemi

  2. The University of Connecticut, 191 Auditorium Road, U-3139, Storrs, CT, 06269, USA

    Julián A. Norato

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  1. Hesaneh Kazemi
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  2. Julián A. Norato
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Correspondence to Julián A. Norato.

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The MATLAB code implementing the method described in this manuscript is available from the corresponding author upon reasonable request and for non-commercial purposes.

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Kazemi, H., Norato, J.A. Topology optimization of programmable lattices with geometric primitives. Struct Multidisc Optim 65, 33 (2022). https://doi.org/10.1007/s00158-021-03094-9

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