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

• Published in: Frontiers of Mechanical Engineering 2019-06, Vol.14 (2), p.141-152
• Main Authors: CHAN, Yu-Chin, SHINTANI, Kohei, CHEN, Wei
• Format: Article
• Language: English
• Subjects: Engineering; lattice structures; load uncertainty; material uncertainty; Mechanical Engineering; multi-material; Research Article; robust topology optimization; Structural Topology Optimization; univariate dimension reduction
• ISSN: 2095-0233; 2095-0241
• DOI: 10.1007/s11465-019-0531-4

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.