This paper applies an energy method based on the high-order smooth curvature model to address the challenges of kinetostatically modeling the complicated nonlinear post-buckling behavior of inclined compliant beams. The proposed energy method is grounded in the principle of minimum strain energy, implying that the total strain energy is minimized at the equilibrium configuration. In this work, the high-order smooth curvature model is adopted to accurately model the bending strain energy of large deformation beams. Subsequently, the Lagrange multiplier method is employed to ascertain the minimum of strain energy while concurrently determining the corresponding tip loads. Additionally, the deformation shape and maximum stress are determined via the smooth curvature model. The proposed method is introduced for the first time in modeling compliant bistable mechanisms, and it is proven that the method can be used for modeling compliant beams with inclined angles ranging from 0 to 90 degrees. Following the modeling, finite element analysis and experimental tests are conducted to verify the accuracy of the proposed energy method. A comprehensive comparative analysis between proposed method and existing methods is conducted. The comparison results prove that the model is more computationally efficient without compromising modeling accuracy The proposed modeling method can not only be used for modeling compliant bistable mechanisms but also has extendable applications in modeling initially-curved compliant beams, contact-aid design problems, and distributed load problems.The present work not only advances the practical application of the proposed energy method but also lays the foundation for future research in modeling compliant mechanisms.

中文翻译：

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柔顺双稳态机构建模：基于高阶平滑曲率模型的能量方法


本文应用基于高阶平滑曲率模型的能量方法来解决对倾斜柔顺梁的复杂非线性后屈曲行为进行运动静力学建模的挑战。所提出的能量方法基于最小应变能原理，这意味着总应变能在平衡配置下最小化。在这项工作中，采用高阶光滑曲率模型来精确模拟大变形梁的弯曲应变能。随后，采用拉格朗日乘子法来确定应变能的最小值，同时确定相应的尖端载荷。此外，变形形状和最大应力是通过平滑曲率模型确定的。该方法首次被引入柔顺双稳态机构建模中，并证明该方法可用于倾斜角度范围为0~90度的柔顺梁建模。建模之后，进行有限元分析和实验测试，以验证所提出的能量方法的准确性。对所提出的方法与现有方法进行了全面的比较分析。比较结果证明该模型在不影响建模精度的情况下计算效率更高。所提出的建模方法不仅可以用于建模顺应双稳态机构，而且在建模初始弯曲顺应梁、接触辅助设计问题和分布式目前的工作不仅推进了所提出的能量方法的实际应用，而且为未来建模柔顺机构的研究奠定了基础。