Robust topology optimization of multi-material lattice structures under material and load uncertainties

Abstract

Enabled by advancements in multi-material additive manufacturing, lightweight lattice structures consisting of networks of periodic unit cells have gained popularity due to their extraordinary performance and wide array of functions. This work proposes a density-based robust topology optimization method for meso- or macro-scale multi-material lattice structures under any combination of material and load uncertainties. The method utilizes a new generalized material interpolation scheme for an arbitrary number of materials, and employs univariate dimension reduction and Gauss-type quadrature to quantify and propagate uncertainty. By formulating the objective function as a weighted sum of the mean and standard deviation of compliance, the tradeoff between optimality and robustness can be studied and controlled. Examples of a cantilever beam lattice structure under various material and load uncertainty cases exhibit the efficiency and flexibility of the approach. The accuracy of univariate dimension reduction is validated by comparing the results to the Monte Carlo approach.

Keywords

robust topology optimization / lattice structures / multi-material / material uncertainty / load uncertainty / univariate dimension reduction

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Acknowledgements

Ms. Yu-Chin Chan would like to acknowledge support from the Digital Manufacturing and Design Innovation Institute (DMDII) through award number 15-07-07. Additionally, this material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1842165. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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