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Accuracy and Efficiency Analysis of the Beam Elements for Nonlinear Large Deformation

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Abstract

Purpose

The purpose of this paper is to study that which beam element should be adopted to achieve the required high accuracy and efficiency in different projects. Three kinds of beam elements commonly used to analyze the nonlinear dynamics of flexible multibody systems are compared and analyzed, which are fully parameterized beam and gradient-deficient beam elements based on the absolute nodal coordinate formulation, and geometrically exact beam element, respectively.

Methods

The governing equations are established based on the fully parameterized beam element, the gradient-deficient beam element and the geometrically exact beam element, and the generalized-α implicit time stepping algorithm is used to study the dynamic responses of system.

Results and Conclusion

In this study, the solution accuracy and efficiency of the three kinds of element are analyzed in both statics and dynamics in detail and compared with each other. It is found that the geometrically exact beam element is superior to other two elements when the discretized element is subjected to axial deformation and torsion. Both gradient-deficient beam element and geometrically exact beam element show the high accuracy and efficiency when the element is bent. Moreover, the Young’s modulus and time step have a great effect on displacement responses when the beam element is in dynamic state. All the results should be helpful for selection of a high-precision calculation method in engineering applications.

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Funding

This work is supported in part by the National Natural Science Foundation of China (Grant No.12102041; 52130512) and China Postdoctoral Science Foundation (Grant No. 2021M690401) and Graduate Technological Innovation Project of Beijing Institute of Technology (Project No. 2019CX10005).

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Authors and Affiliations

  1. School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Zhen Wang, Changle Xiang, Hui Liu & Ming Liu

  2. Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing, 100081, China

    Ming Liu

Authors
  1. Zhen Wang
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  2. Changle Xiang
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  3. Hui Liu
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  4. Ming Liu
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Correspondence to Ming Liu.

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Wang, Z., Xiang, C., Liu, H. et al. Accuracy and Efficiency Analysis of the Beam Elements for Nonlinear Large Deformation. J. Vib. Eng. Technol. 11, 319–328 (2023). https://doi.org/10.1007/s42417-022-00581-1

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  • DOI: https://doi.org/10.1007/s42417-022-00581-1

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