A nonlinear dynamic finite element method in 3D space based on the Co-rotational formulation

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (16) : 14-23.

WANG Tao,LIU Degui,HU Anjie

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Abstract

Considering the geometric nonlinear effect of large amplitude vibration of flexible structures in 3 Dimension (3D) space, a nonlinear dynamic FEM time-history Newmark-β method was built based on the Co-rotational formulation theory.In each step of time-history calculation, geometric nonlinearity, time variant effect of stress and gravity in the structure were considered.The equilibrium iteration calculation was used to get the displacement, velocity, acceleration of the nodes in the FE model.An FEM program which used link and beam elements was developed.The methods and calculation flow were discussed.Three numerical examples were designed.The calculation results reflect the nonlinear vibration of the flexible structures in 3D space.And these phenomena were explained by the nonlinear vibration theory.The computational results of the samples were compared with ANSYS.The results indicate that the algorithm and program are reliable and efficient, which can be applied for large amplitude vibration calculation and investigation on flexible construction in 3D space.

Key words

FEM ; / 3D space; / Co-rotational formulation / geometric nonlinearity / dynamic time-history

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WANG Tao,LIU Degui,HU Anjie. A nonlinear dynamic finite element method in 3D space based on the Co-rotational formulation[J]. Journal of Vibration and Shock, 2018, 37(16): 14-23

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