In this article, a nonlinear structural formulation that uses a new dimensionless set of generalized displacements is proposed for solving geometrically nonlinear beam problems, being validated by several applications given in literature where a cantilever beam is likely to undergo large displacements. By this approach, useful simplifications and insights are achievable in the analysis process, as the system matrices becoming linear and the reduction of required interpolation continuity degree. The formulation is firstly developed—in a Lagrangian perspective—and the equilibrium equations are then derived using Hamilton's principle. In the sequence, using finite element method, it is substantiated by comparison to examples given in literature in static, dynamic, and finally in an application where piezoelectric effects intervene, in order to assess its multiframework capabilities and deliver a convenient approach whereby beams constituted of smart or conventional materials can be efficiently studied.

中文翻译：

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考虑压电效应的具有一组新广义位移的梁分析的几何非线性结构公式

在本文中，提出了一种非线性结构公式，该公式使用一组新的无量纲广义位移来解决几何非线性梁问题，并通过文献中给出的几个应用程序进行了验证，其中悬臂梁可能会经历大位移。通过这种方法，可以在分析过程中实现有用的简化和见解，因为系统矩阵变为线性并减少所需的插值连续度。首先从拉格朗日的角度发展公式，然后使用哈密顿原理推导出平衡方程。在序列中，使用有限元方法，通过静态、动态和最后在压电效应介入的应用中与文献中给出的实例进行比较来证实，