Geometric Nonlinear Spatial Beam Elements With Curvature Interpolations

QI Zhao-hui; FANG Hui-qing; ZHANG Zhi-gang; WANG Gang

doi:10.3879/j.issn.1000-0887.2014.05.004

Volume 35 Issue 5

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QI Zhao-hui, FANG Hui-qing, ZHANG Zhi-gang, WANG Gang. Geometric Nonlinear Spatial Beam Elements With Curvature Interpolations[J]. Applied Mathematics and Mechanics, 2014, 35(5): 498-509. doi: 10.3879/j.issn.1000-0887.2014.05.004

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Geometric Nonlinear Spatial Beam Elements With Curvature Interpolations

doi: 10.3879/j.issn.1000-0887.2014.05.004

State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology, Dalian, Liaoning 116024, P.R.China

Funds: The National Natural Science Foundation of China（11372057）

Received Date: 2014-02-26
Rev Recd Date: 2014-04-10
Publish Date: 2014-05-15

Abstract

Abstract

Beam elements with absolute nodal coordinates played an important role in the geometric nonlinear analysis of structures and dynamics of flexible multibody systems. One of such elements was the beam element based on the exact geometric beam model, in which the process of obtaining internal nodal forces involved interpolations of rotational angles, resulting in some numerical difficulties. Another such element proposed by Shabana, avoided the angular interpolations by replacing the nodal rotation parameters with many newly introduced nodal parameters. In accordance with the exact virtual power equations for beams with large deformations and the relationships between tangents of the beam centroid line and curvatures of the beam sections, a new spatial beam element with absolute nodal coordinates was presented. The nodal parameters of the presented element are the same with those of the element based on the exact geometric beam model, but the internal forces can be obtained without angular interpolations. Numerical examples verify its validity through comparison with the analytical results.
- spatial beam element,
- flexible multibody system,
- geometric nonlinearity,
- curvature interpolation

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References(16)

References

[1]	Kwak H-G, Kim D-Y, Lee H-W. Effect of warping in geometric nonlinear analysis of spatial beams[J].Journal of Constructional Steel Research,2001,57(7): 729-751.
[2]	Pai P F, Anderson T J, Wheater E A. Large-deformation tests and total-Lagrangian finite-element analyses of flexible beams[J].International Journal of Solids and Structures,2000,37(21): 2951-2980.
[3]	Hsiao K M, Lin J Y, Lin W Y. A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams[J].Computer Methods in Applied Mechanics and Engineering,1999,169(1/2): 1-18.
[4]	Teh L H, Clarke M J. Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements[J].Journal of Constructional Steel Research,1998,48(2/3): 123-144.
[5]	Wu S-C, Haug E J. Geometric non-linear substructuring for dynamics of flexible mechanical systems[J].International Journal for Numerical Methods in Engineering,1988,26(10): 2211-2226.
[6]	Simo J C. A finite strain beam formulation. the three-dimensional dynamic problem—part Ⅰ[J].Computer Methods in Applied Mechanics and Engineering,1985,49(1): 55-70.
[7]	Simo J C, Vu-Quoc L. A three-dimensional finite-strain rod model—part Ⅱ: computational aspects[J].Computer Methods in Applied Mechanics and Engineering,1986,58(1): 79-116.
[8]	Beléndez T, Neipp C, Beléndez A. Large and small deflections of a cantilever beam[J].European Journal of Physics,2002,23(3): 371-379.
[9]	Banerjee A, Bhattacharya B, Mallik A K. Large deflection of cantilever beams with geometric non-linearity: analytical and numerical approaches[J].International Journal of Non-Linear Mechanics,2008,43(5): 366-376.
[10]	Yakoub R Y, Shabana A A. Three dimensional absolute nodal coordinate formulation for beam elements: implementation and applications[J].Journal of Mechanical Design,2001,123(4): 614-621.
[11]	Sopanen J T, Mikkola A M. Description of elastic forces in absolute nodal coordinate formulation[J].Nonlinear Dynamics,2003,34(1/2): 53-74.
[12]	Romero I. A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations[J].Multibody System Dynamics,2008,20(1): 51-68.
[13]	Jonker J B, Meijaard J P. A geometrically non-linear formulation of a three-dimensional beam element for solving large deflection multibody system problems[J].International Journal of Non-Linear Mechanics,2013,53: 63-74.
[14]	Reissner E. On one-dimensional finite-strain beam theory: the plane problem[J].Zeitschrift für angewandte Mathematik und Physik ZAMP,1972,23(5): 795-804.
[15]	Reissner E. On one-dimensional large-displacement finite-strain beam theory[J].Studies in Applied Mathematics,1973,52(2): 87-95.
[16]	Mattiasson K. Numerical results from large deflection beam and frame problems analyzed by means of elliptic integrals[J].International Journal for Numerical Methods in Engineering,1981,17(1): 145-153.