Material penalization and filtering schemes are key strategies applied to topology optimization (TO) to promote more discrete and manufacturable designs. However, these modifications introduce fluctuations in the design landscape that amplify non-convexity and influence the local minima identified by TO. Harnessing the machine learning approach of generative adversarial networks (GAN), we investigate the role of penalization and filtering by comparing the designs between TO and GAN-based TO surrogates. A total of 17 GANs were constructed to predict 2D minimum compliance topologies across a set of penalization factors and filters, each interpolating a design space of 270,000 boundary condition and loading scenarios. The prevalence of GAN-predicted topologies with better compliance than TO-calculated topologies was estimated via a random sampling of the design space. GAN ‘over-performance’ occurs across material penalization and filtering conditions, where the frequency tends to increase as penalization increases. Analysis of this test set is leveraged to highlight trends regarding the conditions under which this ‘over-performance’ occurs, and the geometric characteristics these designs exhibit. Collectively, this study presents an alternative method to characterize the effects of penalization and filtering on design outcomes and motivates the use of data-driven surrogates to augment traditional approaches.
Additive manufacturing has enabled the fabrication of complex, architected materials, which have shown great promise in fields such as acoustics, mechanical logic gates, and energy trapping, due to their unique properties derived from repeating unit cells. The force-displacement performance of one such unit cell, the bistable elastomeric beam, has been characterized experimentally and subsequently tuned by the introduction of a Fourier series-based design parameterization that enables a wider range of available energy performance characteristics and secondary stable configurations. Here, another characteristic of this beam that has not yet been explored, namely the shape during post-buckling deformation between the two stable states, is optimized under the same Fourier series-based parameterization. Nonlinear finite element analysis reveals that the performance is highly sensitive to even modest profile error incurred on the beam’s upper and lower sides during manufacturing. Various methods of quantifying performance are compared, and Bayesian optimization is employed in two case studies to achieve desired post-buckled shapes. A novel acquisition function, which considers a candidate design’s robustness to profile error, is used to find the design that achieves the desired performance consistently, even in the face of the variability associated with additive manufacturing. Finally, Monte Carlo simulations are used to quantify the performance of optimal beams found with and without the new acquisition function, and reveal the importance of considering geometric uncertainty during the optimization process.
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