Finite Element Analysis and A Two-Stage Design Optimization Procedure of Multifield Origami-Inspired Structures
Open Access
- Author:
- Zhang, Wei
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- January 10, 2020
- Committee Members:
- Zoubeida Ounaies, Dissertation Advisor/Co-Advisor
Zoubeida Ounaies, Committee Chair/Co-Chair
Paris R von Lockette, Committee Member
Timothy W. Simpson, Committee Member
Francesco Costanzo, Outside Member
Mary I Frecker, Dissertation Advisor/Co-Advisor
Mary I Frecker, Committee Chair/Co-Chair
Karen Ann Thole, Program Head/Chair - Keywords:
- finite element analysis
design optimization
multifield origami
smart materials - Abstract:
- This dissertation focuses on developing predictive models of the folding performance of multifield responsive structures and optimizing these structures based on design objectives. In particular, these origami-inspired structures incorporate smart materials such as electroactive polymers (EAPs) and magnetoactive elastomers (MAEs), which results in self-folding when one or more external fields are applied. Two types of finite element analysis (FEA) models, i.e., continuum modeling and constitutive modeling, are developed to investigate the actuation performance of self-folding multifield origami that are actuated using either or both an electroactive polymer, i.e., PVDF-based terpolymer, and a magneto-active elastomer. In continuum modeling, surface tractions are applied to simulate the actuation effects resulting from the application of the external fields. The finite element analysis captures folding performance of electromechanical actuation for notched configurations and multifield (both magnetic and electric fields) actuation for a bifold structure. Quantitative comparison using the folding angle as the metric shows that FEA results are comparable to experiments for the terpolymer actuated single-notch configuration and the multifield bifold configuration. Geometric parameter studies show that folding angles increase as the notch length or beam length increases, while beam width does not have a notable effect on folding. The constitutive models implemented through the FEA method successfully predict the coupled responses of the active materials, including folding behavior of the terpolymer-based actuation of the unimorph and bimorph configurations, the MAE-based actuation of the bimorph, and simultaneous actuation of the multifield bimorph, where an electric field and a magnetic field are applied simultaneously. In the modeling the multilayer terpolymer benders, glue layers are included between the terpolymer layers in the FEA models, and the material properties of the glue iv layer are well approximated using a parametric study by comparing to the experiments. In the simultaneous actuation the multifield bimorph structure, the anticlastic curvature observed in the experiments is captured in the simulation results, where the curling in the cross-section prevents the bimorph from further deforming with an increasing external field. The history-dependent folding performance due to the anticlastic curvature is successfully simulated by the geometrically nonlinear FEA model. A computationally efficient two-stage optimization procedure is developed as a systematic method for the design of multifield origami-inspired self-folding structures. In Stage 1, low-fidelity models are used within an optimization of the topology of the structure, while in Stage 2, high-fidelity FEA models are used within an optimization to further improve the best design from Stage 1. The design procedure is first described in a general formulation, applicable to any modeling methods. Further, to illustrate the optimization procedure, a specific formulation using a rigid body dynamic model in Stage 1, followed by FEA in Stage 2, is also developed. To demonstrate the applicability and computational efficiency of the proposed two-stage optimization procedure, two case studies are investigated, namely, a three-finger soft gripper actuated using the terpolymer, and an origami-inspired multifield responsive “coffee table” configuration actuated using the terpolymer and the MAE. In Stage 1, low-fidelity models, such as analytical models and rigid body dynamic models, are implemented within an optimization of the topology of the structure, including the placement of the materials, the connectivity between sections and the amount and orientation of external loads. Distance measures and minimum shape error are applied as metrics to determine the best design in Stage 1, which then serves as the baseline design in Stage 2. In Stage 2, the high-fidelity FEA models are used within an optimization to fine-tune the baseline design. As a result, designs with better performance than the baseline design are achieved at the end of Stage 2 with computing times of 15 days for the gripper and 9 days for the v “coffee table”, which would be over 3 months and 2 mothers for full FEA-based optimizations, respectively. In the design of the gripper, the best design exhibits a nearly tapered configuration, where thicker terpolymer and substrate layers are observed in the segments close to the root, while thinner layers close to the tip, which indicates that the segments close to the root exert greater influence on the blocked force and conversely the segments close to the tip play a more important role in enhancing free deflection. In the design of the “coffee table”, wider creases are found favorable for both electric and magnetic actuations for a higher compliance. Moreover, in the electric actuation, thinner terpolyemr and substrate are favorable to achieve a higher bending curvature. To conclude, the applicability and computational efficiency of the two-stage optimization procedure are demonstrated through the two case studies.