利用开关隧道法进行双稳态复合材料层压板逆向设计的全局优化

Katherine S. Riley, Mark H. Jhon, Hortense Le Ferrand, Dan Wang, Andres F. Arrieta
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摘要

双稳态性使可调挠度的自适应设计成为可能,其应用领域包括变形机翼、机器人抓手和消费品。复合材料层压板在设计时可以表现出双稳态性,这是由于在聚合物基体加工过程中产生了预应力,从而可以在两种稳定形状之间快速重新配置。遗憾的是,由于双稳态层压板的高度非线性行为,设计双稳态层压板具有很大的挑战性。在此,我们提出了切换隧道法来应对这一挑战,该方法交替使用基于梯度的局部最小化和隧道搜索阶段,并加强了目标表达式的切换以改善数值调节。结果表明,与现有优化器相比,切换隧道法具有很高的有效性;在一般复合材料铺层中找到所有能量最小值的成功率高达 99%。此外,我们的方法还有助于反向设计可变预应变场,从而实现传统预应变层压板无法实现的生物启发式正高斯曲率。通过有限元分析和三维打印样品的验证,确认了最佳设计。Wang 博士、Arrieta 博士及其同事报告了一种开关隧道法,用于双稳态复合材料层压板的逆向设计。他们的优化方法解决了双稳态复合材料的高度非线性问题,并成功确定了与目标稳定形状相匹配的可变预应变场。
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Inverse design of bistable composite laminates with switching tunneling method for global optimization
Bistability enables adaptive designs with tunable deflections for applications including morphing wings, robotic grippers, and consumer products. Composite laminates may be designed to exhibit bistability due to pre-strains that develop during the processing of the polymer matrix, enabling fast reconfiguration between two stable shapes. Unfortunately, designing bistable laminates is challenging because of their highly nonlinear behavior. Here, we propose the Switching Tunneling Method to address this challenge by alternating between gradient-based local minimization and tunneling search phases, with the enhancement of objective expression switching to improve numerical conditioning. Results demonstrate high effectiveness compared to existing optimizers; the Switching Tunneling Method achieves a 99% success rate in finding all energy minima across general composite layups. Additionally, our method facilitates the inverse design of variable pre-strain fields, enabling bioinspired, positive Gaussian curvatures, which are not possible with conventional pre-strain laminates. Validations through both finite element analysis and 3D printed samples confirm the optimal designs. Dr Wang, Dr Arrieta, and colleagues report a switching tunneling method for the inverse design of bistable composite laminates. Their optimization methodology addresses the bistable composites’ highly nonlinear nature and successfully identifies the variable pre-strain fields to match the target stable shapes.
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