Abstract During the last decades, the modeling of flexures undergoing large deflections has been the subject of many investigations. Various rigid body models have been proposed in an effort to reproduce with high accuracy the path followed by the free-end section of the flexible element. Systems with multiple degrees of freedom have been also presented considering the possible occurrence of an inflection point. However, as the number of DoFs increases, optimization techniques must be implemented to define the characteristic parameters. In this investigation, a one-DoF rigid body model is developed focusing on the pole of the displacements associated to the poses of the free-end section. Two different cases are analyzed, depending on whether the pole is a proper point or an improper point. Strain energy is evaluated to calculate the stiffness coefficients of the rigid body model. Considering end moments and combined loads, two different formulations are elaborated to achieve analytical and numerical solutions, respectively. The proposed model is load dependent and provides an exact solution of the modeling problem, both in the case of rotation and in the case of translation of the free-end section. Occurrence of an inflection point is also considered and various examples are presented.

中文翻译：

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基于有限位移和应变能的拟刚体模型

摘要 在过去的几十年中，经历大挠度的弯曲建模已成为许多研究的主题。为了高精度地再现柔性元件的自由端部分所遵循的路径，已经提出了各种刚体模型。考虑到可能出现的拐点，还介绍了具有多个自由度的系统。但是，随着 DoF 数量的增加，必须实施优化技术来定义特征参数。在这项研究中，开发了一个单自由度刚体模型，重点关注与自由端部分姿势相关的位移极点。根据极点是正确点还是错误点，分析了两种不同的情况。评估应变能以计算刚体模型的刚度系数。考虑到端力矩和组合载荷，详细阐述了两种不同的公式以分别实现解析解和数值解。所提出的模型依赖于载荷，并且在旋转和自由端部分平移的情况下都提供了建模问题的精确解决方案。还考虑了拐点的出现，并提供了各种示例。在旋转和自由端部分平移的情况下。还考虑了拐点的出现，并提供了各种示例。在旋转和自由端部分平移的情况下。还考虑了拐点的出现，并提供了各种示例。