Different types of active materials have been used to actuate origami-inspired self-folding structures. To model the highly nonlinear deformation and material responses, as well as the coupled field equations and boundary conditions of such structures, high-fidelity models such as finite element (FE) models are needed but usually computationally expensive, which makes optimization intractable. In this paper, a computationally efficient two-stage optimization framework is developed as a systematic method for the multi-objective designs of such multifield self-folding structures where the deformations are concentrated in crease-like areas, active and passive materials are assumed to behave linearly, and low- and high-fidelity models of the structures can be developed. In Stage 1, low-fidelity models are used to determine the topology of the structure. At the end of Stage 1, a distance measure $U$ is applied as the metric to determine the best design, which then serves as the baseline design in Stage 2. In Stage 2, designs are further optimized from the baseline design with greatly reduced computing time compared to a full FEA-based topology optimization. The design framework is first described in a general formulation. To demonstrate its efficacy, this framework is implemented in two case studies, namely, a three-finger soft gripper actuated using a PVDF-based terpolymer, and a 3D multifield example actuated using both the terpolymer and a magneto-active elastomer, where the key steps are elaborated in detail, including the variable filter, metrics to select the best design, determination of design domains, and material conversion methods from low- to high-fidelity models. In this paper, analytical models and rigid body dynamic models are developed as the low-fidelity models for the terpolymer- and MAE-based actuations, respectively, and the FE model of the MAE-based actuation is generalized from previous work. Additional generalizable techniques to further reduce the computational cost are elaborated. As a result, designs with better overall performance than the baseline design were achieved at the end of Stage 2 with computing times of 15 days for the gripper and 9 days for the multifield example, which would rather be over 3 and 2 months for full FEA-based optimizations, respectively. Tradeoffs between the competing design objectives were achieved. In both case studies, the efficacy and computational efficiency of the two-stage optimization framework are successfully demonstrated.

已经使用不同类型的活性材料来驱动折纸启发的自折叠结构。为了对这种结构的高度非线性变形和材料响应以及耦合场方程和边界条件进行建模，需要高保真模型（例如有限元（FE）模型），但通常计算量大，这使得优化变得很困难。在本文中，开发了一种计算有效的两阶段优化框架作为一种系统方法，用于这种多场自折叠结构的多目标设计，该结构的变形集中在折痕状区域，假定主动材料和被动材料均表现出良好的性能。可以线性地建立结构的低保真度模型和高保真度模型。在第一阶段 低保真模型用于确定结构的拓扑。在第1阶段结束时，测距$ü$用作确定最佳设计的度量标准，然后将其用作第2阶段的基线设计。在第2阶段，与完全基于FEA的拓扑优化相比，从基线设计进一步优化了设计，大大减少了计算时间。首先以一般公式描述设计框架。为了证明其有效性，该框架在两个案例研究中得以实现，即使用基于PVDF的三元共聚物致动的三指软式抓取器，以及使用三元共聚物和磁活性弹性体致动的3D多场示例，其中关键详细说明了各个步骤，包括变量过滤器，选择最佳设计的度量标准，确定设计领域以及从低保真模型到高保真模型的材料转换方法。在本文中，分析模型和刚体动力学模型分别作为基于三元共聚物和MAE的驱动的低保真模型而开发，基于MAE的驱动的FE模型是从以前的工作中得到的。阐述了进一步降低计算成本的其他通用技术。结果，在阶段2结束时获得了比基准设计更好的总体性能的设计，夹具的计算时间为15天，多字段示例的计算时间为9天，而完整的FEA则需要3到2个月以上的计算时间基于的优化。实现了竞争设计目标之间的折衷。在这两个案例研究中，成功​​证明了两阶段优化框架的功效和计算效率。