Analysis and Synthesis of Nonlinear-Elastic Compliant Mechanisms
Open Access
- Author:
- Hargrove, Brianne
- Graduate Program:
- Mechanical Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 28, 2024
- Committee Members:
- Robert Kunz, Professor in Charge/Director of Graduate Studies
Zoubeida Ounaies, Major Field Member
Paris von Lockette, Special Member
Mary Frecker, Chair, Minor Member & Dissertation Advisor
Reginald Hamilton, Outside Unit & Field Member
Jared Butler, Major Field Member
Jovana Jovanova, Special Member - Keywords:
- Compliant mechanisms
Material nonlinearity
Large deformations
Analytical model
Superelasticity
Synthesis
Optimization
Additive manufacturing - Abstract:
- Compliant mechanisms (CMs) are comprised of flexible components that allow them to have greater mobility over rigid-link mechanisms, commonly made up of pin joints and linkages. The design freedom of the additive manufacturing (AM) process has created new avenues for CMs to have more complex geometries and functionality than conventional manufacturing methods offer. However, in comparison to their use in applications involving shape-morphing, energy absorption, and bio-inspired structures, CMs have mostly been modeled under the assumptions of linear-elastic mechanical behavior and small deformations. These applications are typically characterized by large shape changes and large deformations that linear-elastic materials may not withstand. Due to the development of new types of materials that respond and change adaptively due to external stimuli, as seen in smart materials, the introduction of material nonlinearity in the design of CMs allows for a controlled and tailorable response. Thus, it is necessary to develop a methodology that captures both large deformations and nonlinear-elastic materials to understand how smart materials can be leveraged in CM design. Examples of nonlinear-elastic materials that are useful in the design of CMs are shape memory alloys (SMAs). SMAs, such as Nitinol (NiTi), tolerate large amounts of mechanical or thermal strain with little permanent distortion of the shape of the mechanism. In other words, the mechanism recovers its shape when an applied load is removed. This property of SMAs is controlled by stress-induced and temperature-induced phase transformation within the material, known as superelasticity and the shape memory effect respectively. While nonlinear-elastic CMs undergoing large deformations have been researched using FEA-based approaches, there is a notable trade-off between accuracy and solver time that makes FEA a computationally expensive method. For this reason, a fast analytical model is proposed to analyze deflection of different superelastic CMs made from a chain of basic beam elements. The analytical model is then generalized for any type of nonlinear-elastic material model using a multilinear model approximation. The generalization of the model is critical to extending current analytical models for CMs, which often assume symmetric mechanical properties, to include asymmetric tensile and compressive properties that reflect the actual behavior of the material. Equally important to the analysis of nonlinear-elastic CMs is the design of new types of CMs through synthesis. Synthesis involves the creation of CM for a desired function given constraints, for example, on its dimensions, total volume, and material distribution. Analysis of the force-deflection response of CMs requires a prescribed set of geometric and mechanical parameters. Yet, for inverse design or synthesis, these parameters may be difficult for the designer to select without trial-and-error and prototyping. This is a notable challenge in the assumption of “free complexity” for additively manufactured CMs. To address this issue, CM synthesis has become automated over the years through structural optimization using continuum-based methods, kinematic approaches such as rigid body replacement or the pseudo-rigid body model (PRBM), genetic algorithms, and basic elements known as building blocks to arrive at an optimal structure. To introduce nonlinear-elastic materials and large deformations into the synthesis of CMs, an optimization approach using building blocks derived from the beam elements studied in the analytical model is proposed. Designs generated by the model highlight the optimization of the building block selection, size, shape, and topology to achieve different deflected states and nonlinear stiffness response. The introduction of the superelasticity, in particular, has been shown to enhance the flexibility of the optimized mechanism to reach such target shapes and also improve energy absorption properties associated with high nonlinear stiffness. The synthesis process can then be supplemented by analysis and also AM to validate the behavior of the final CM design both analytically and experimentally. To formulate a methodology for analysis and synthesis of nonlinear-elastic CMs, two methods for predicting the deflection of a cantilever beam and a folding CM design are explored first for analysis. The first approach involves the use of a segmented PRBM to predict the tip deflection of the folding CM, with the novelty of capturing both large deformations and nonlinear elasticity. The second approach incorporates large-deflection beam theory in modeling a superelastic cantilever beam that is used as the basis for predicting the tip deflection of more nonuniform structures, such as initially curved beams and arcs. The analytical model is generalized to include other nonlinear-elastic materials, such as thermoplastic polyurethane (TPU), such that the analytical model can be validated against experimental studies of a 3D-printed folding CM design. The synthesis model is an extension of the analytical model with the addition of an optimization-based approach to construct CMs from basic building blocks. The superelastic beam is used as a fundamental building block from which the full building block library, or pool of available geometries that can be selected for synthesis, is constructed. A hybridized approach using the genetic algorithm as a global search strategy, and the nonuniform patternsearch algorithm as a local search is proposed as the optimization approach. The 2D nonlinear-elastic CMs produced by the synthesis model can be applied to applications such as tailoring the nonlinear stiffness of unit cells of cellular compliant mechanism (CCM) arrays and metastructures to enhance energy absorption properties. While the research objectives being considered are currently limited to only the superelastic property of NiTi, future work will aim to explore the addition of the shape memory effect to introduce thermomechanical control to CMs. Other ways to introduce nonlinearity can be studied such as adding self-contacting members in the CM, as in cellular contact-aided compliant mechanisms (C3Ms). Lastly, for the modeling of 2D CMs, the 1D beam models used for analysis restrict the CM to in-plane motion. However, future research may include extending the 1D model to a fully 3D formulation to capture both in-plane and out-of-plane bending and twisting.