Bayesian Optimization of Target Buckling Shapes in Constrained Elastomeric Beams With Geometric Uncertainty

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.