A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains

ZHUO Yingpeng; WANG Gang; QI Zhaohui; ZHANG Jian

doi:10.21656/1000-0887.420290

Volume 43 Issue 9

Sep. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(9): 987-1003

ZHUO Yingpeng, WANG Gang, QI Zhaohui, ZHANG Jian. A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains[J]. Applied Mathematics and Mechanics, 2022, 43(9): 987-1003. doi: 10.21656/1000-0887.420290

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A Spatial Geometric Nonlinearity Spline Beam Element With Nodal Parameters Containing Strains

doi: 10.21656/1000-0887.420290

1.
State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116023, P.R.China
2.
School of Ocean Science and Technology, Dalian University of Technology, Panjin, Liaoning 124221, P.R.China

Received Date: 2021-09-22
Rev Recd Date: 2021-12-17

Available Online: 2022-08-01

Publish Date: 2022-09-30

Abstract

Abstract

Many slender rods in engineering can be modeled as Euler-Bernoulli beams. For the analysis of their dynamic behaviors, it is necessary to establish the dynamic models for the flexible multi-body systems. Geometric nonlinear elements with absolute nodal coordinates help solve a large number of dynamic problems of flexible beams, but they still face such problems as shear locking, nodal stress discontinuity and low computation efficiency. Based on the theory of large deformation beams’ virtual power equations, the functional formulas between displacements and rotation angles at the nodes were established, which can satisfy the deformation coupling relationships. The generalized strains to describe geometric nonlinear effects in this case were derived. Some parameters of boundary nodes were replaced by axial strains and sectional curvatures to obtain a more accurate and concise constraint method for applying external forces. To improve the numerical efficiency and stability of the system’s motion equations, a model-smoothing method was used to filter high frequencies out of the model. The numerical examples verify the rationality and effectiveness of the proposed element.
- flexible multibody system,
- geometric nonlinearity beam,
- Cardan angle,
- mixed coordinate,
- spline interpolation

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References

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