Abstract This paper presents a consistent corotational formulation for the geometric nonlinear dynamic analysis of 2D sliding beams. Compared with the works of previously published papers, the same cubic shape functions are used to derive the elastic force vector and the inertia force vector. Consequently, the consistency of the element is ensured. The shape functions are used to describe the local displacements to establish an element-independent framework. Moreover, all kinds of standard elements can be embedded within this framework. Therefore, the presented method is more versatile than previous approaches. To consider the shear deformation, the sliding beam (a system of changing mass) is discretized using a fixed number of variable-domain interdependent interpolation elements (IIE). In addition, the nonlinear axial strain and the rotary inertia are also considered in this paper. The nonlinear motion equations are derived by using the extended Hamilton's principle and solved by combining the Newton-Raphson method and the Hilber-Hughes-Taylor (HHT) method. Furthermore, the closed-form expressions of the iterative tangent matrix and the residual force vector are obtained. Three classic examples are given to verify the high accuracy and efficiency of this formulation by comparing the results with those of commercial software and published papers. The simulation results also show that the shear deformation and the rotary inertia cannot be neglected for the large-rotation and high-frequency problem.

中文翻译：

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滑梁非线性动力分析的一致共转公式

摘要 本文提出了二维滑动梁几何非线性动力学分析的一致共转公式。与之前发表的论文的作品相比，使用相同的三次形状函数来推导弹性力矢量和惯性力矢量。因此，确保了元件的一致性。形状函数用于描述局部位移以建立与单元无关的框架。此外，所有类型的标准元素都可以嵌入到这个框架中。因此，所提出的方法比以前的方法更通用。为了考虑剪切变形，使用固定数量的可变域相互依赖插值元素 (IIE) 对滑动梁（质量变化系统）进行离散化。此外，本文还考虑了非线性轴向应变和转动惯量。利用扩展的哈密顿原理推导出非线性运动方程，并结合牛顿-拉夫森方法和希尔伯-休斯-泰勒(HHT)方法求解。进一步得到迭代切线矩阵和残余力矢量的闭式表达式。给出了三个经典实例，通过与商业软件和已发表论文的结果进行比较，验证了该公式的高精度和高效性。仿真结果还表明，对于大旋转和高频问题，不能忽略剪切变形和旋转惯量。s 原理并通过结合 Newton-Raphson 方法和 Hilber-Hughes-Taylor (HHT) 方法求解。进一步得到迭代切线矩阵和残余力矢量的闭式表达式。给出了三个经典实例，通过与商业软件和已发表论文的结果进行比较，验证了该公式的高精度和高效性。仿真结果还表明，对于大旋转和高频问题，不能忽略剪切变形和旋转惯量。s 原理并通过结合 Newton-Raphson 方法和 Hilber-Hughes-Taylor (HHT) 方法求解。进一步得到迭代切线矩阵和残余力矢量的闭式表达式。给出了三个经典实例，通过与商业软件和已发表论文的结果进行比较，验证了该公式的高精度和高效性。仿真结果还表明，对于大旋转和高频问题，不能忽略剪切变形和旋转惯量。给出了三个经典实例，通过与商业软件和已发表论文的结果进行比较，验证了该公式的高精度和高效性。仿真结果还表明，对于大旋转和高频问题，不能忽略剪切变形和旋转惯量。给出了三个经典实例，通过与商业软件和已发表论文的结果进行比较，验证了该公式的高精度和高效性。仿真结果还表明，对于大旋转和高频问题，不能忽略剪切变形和旋转惯量。