A consistent corotational formulation for the nonlinear dynamic analysis of sliding beams

• Published in: Journal of sound and vibration 2020-06, Vol.476, p.115298, Article 115298
• Main Authors: Deng, Lanfeng, Zhang, Yahui
• Format: Article
• Language: English
• Subjects: Axial strain; Corotational method; Deformation; Dynamical systems; Equations of motion; Finite element analysis; Hamilton's principle; Inertia; Interpolation; Mathematical analysis; Matrix algebra; Matrix methods; Newton-Raphson method; Nonlinear analysis; Nonlinear dynamic analysis; Nonlinear dynamics; Nonlinear equations; Nonlinear finite elements; Nonlinear systems; Rotary inertia; Shape functions; Shear deformation; Sliding; Sliding beams; Two dimensional analysis; Variable-domain beam elements
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/j.jsv.2020.115298

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.