Nonlinear large-deformation modeling of planar compliant mechanisms and model-based design optimization
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Date
2025-12-31
Authors
Liu, Tinghao
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Publisher
University College Cork
Published Version
Abstract
Compliant mechanisms achieve motion and force transmission through elastic deformation, offering advantages of compactness, precision, low friction, and structural simplicity. These properties make them attractive for a wide range of applications, including precision engineering, biomedical and surgical devices, aerospace and space systems, and robotics. However, their reliance on large elastic deformations introduces highly nonlinear behavior, which poses significant challenges for accurate analysis and design. Conventional finite element simulations, while reliable, are often computationally expensive and provide limited capability of being applied in structural optimization, whereas over-simplified analytical models may fail to capture the essential nonlinear characteristics. Accordingly, this dissertation aims to further contribute to the development of the field of compliant mechanism design by addressing these key challenges, thereby laying a foundation for future theoretical development and engineering applications. Guided by this mission, the dissertation advances along three mutually reinforcing parts.
First, an energy method based on high-order smooth curvature model (High-order SCME) is proposed, in which high-order Legendre polynomials are employed to approximate curvature and derive bending energy expressions. The model provides low-dimensional, differentiable, and efficient solutions for large-deformation compliant mechanisms, achieving high accuracy with significantly reduced computational cost.
Second, recognizing that high-order SCME method neglects axial deformation, a Comprehensive SCME (CoSCME) method is further developed to resolve this issue. By incorporating axial strain energy and bending-axial coupling into a unified framework, CoSCME enables precise predictions of nonlinear responses across pre-buckling and post-buckling regimes. Its accuracy and generality are validated in scenarios including compresural beams, tensural beams, bistable mechanism, general lumped-compliance beams and initially-curved beams. The modeling results are in strong agreement with the finite element analysis results.
Third, a bi-level optimization framework driven by CoSCME is established for systematic mechanism design. The upper-level optimization aims to achieve mechanism configuration search through genetic algorithms, while the lower-level optimization evaluates kinetostatic behavior using the CoSCME method. This bi-level optimization framework successfully achieves optimal designs such as bistable mechanisms with symmetric switching forces and constant negative-stiffness behavior, thereby broadening the functional landscape of compliant mechanisms.
Together, these contributions deliver not only efficient modeling tools and a practical optimization paradigm but also a unifying framework that bridges theoretical modeling, numerical simulation, and experimental validation. By systematically advancing the smooth curvature modeling approach and extending it into comprehensive and optimization-oriented formulations, this thesis deepens the theoretical understanding of large-deformation mechanics in compliant mechanisms. At the same time, it provides engineering methodologies capable of guiding the design of complex, multi-functional, and programmable compliant systems. Collectively, these outcomes underscore the dual significance of this work: establishing a solid theoretical foundation for compliant mechanism research and enabling practical engineering applications across robotics, biomedical devices, and deployable structures.
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Keywords
Compliant mechanisms , Mechanism design , Structural optimization
Citation
Liu, T. 2025. Nonlinear large-deformation modeling of planar compliant mechanisms and model-based design optimization. PhD Thesis, University College Cork.