Closed-form models are important because they offer more design insights, require less computing time and prevent convergence problems in modeling compliant mechanisms. However, most of the available closed-form models, e.g., beam constraint models, are only appropriate for beam flexures within the intermediate deflection range. In this paper, a method for developing closed-form models based on the chained beam constraint model through the combined use of strain energy and Castigliano's first theorem is proposed. A closed-form model for beam flexures with a large prediction range is derived using this method. By modeling simple beams and compliant mechanisms using the proposed closed-form model, it is shown that the model has a significantly broader prediction range than the beam constraint model and is more efficient than the chained beam constraint model. The large prediction range and high efficiency of the proposed closed-form model make it potentially useful for optimizing compliant mechanisms.

中文翻译：

---

承受大轴向载荷的梁弯曲的非线性闭式模型

封闭式模型很重要，因为它们提供了更多的设计见解，需要更少的计算时间并防止建模合规机制中的收敛问题。然而，大多数可用的封闭模型，例如梁约束模型，仅适用于中间偏转范围内的梁弯曲。本文提出了一种通过结合使用应变能和卡斯蒂利亚诺第一定理来开发基于链梁约束模型的封闭模型的方法。使用该方法导出了具有大预测范围的梁弯曲的闭式模型。通过使用所提出的封闭式模型对简单梁和柔顺机构进行建模，结果表明该模型具有比梁约束模型更宽的预测范围，并且比链式梁约束模型更有效。所提出的封闭式模型的大预测范围和高效率使其对于优化顺从机制具有潜在的用途。