Element for Beam Dynamic Analysis Based on Analytical Deflection Trial Function

For beam dynamic finite element analysis, according to differential equation of motion of beam with distributed mass, general analytical solution of displacement equation for the beam vibration is obtained. By applying displacement element construction principle, the general solution of displacement...

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Bibliographic Details
Published in:Mathematical problems in engineering 2015-01, Vol.2015 (2015), p.1-10
Main Authors: Wang, Hongzhi, Ju, Jinsan, Jiang, Xiugen, Ding, Min, Cao, Qiongqiong, Zhang, Peng
Format: Article
Language:English
Subjects:
Accuracy
Beams (structural)
Civil engineering
Construction
Deformation
Differential equations
Displacement
Dynamic tests
Dynamics
Earthquakes
Efficiency
Energy
Equations of motion
Equilibrium
Error analysis
Exact solutions
Finite element analysis
Finite element method
Functions (mathematics)
Interpolation
Load
Mass matrix
Mathematical analysis
Matrix methods
Numerical analysis
Potential energy
R&D
Research & development
Seismic engineering
Stiffness matrix
Vibration
Vibration analysis
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Summary:For beam dynamic finite element analysis, according to differential equation of motion of beam with distributed mass, general analytical solution of displacement equation for the beam vibration is obtained. By applying displacement element construction principle, the general solution of displacement equation is conversed to the mode expressed by beam end displacements. And taking the mode as displacement trial function, element stiffness matrix and element mass matrix for beam flexural vibration and axial vibration are established, respectively, by applying principle of minimum potential energy. After accurate integral, explicit form of element matrix is obtained. The comparison results show that the series of relative error between the solution of analytical trial function element and theoretical solution is about 1×10-9 and the accuracy and efficiency are superior to that of interpolation trial function element. The reason is that interpolation trial function cannot accurately simulate the displacement mode of vibrating beam. The accuracy of dynamic stiffness matrix method is almost identical with that of analytical trial function. But the application of dynamic stiffness matrix method in engineering is limited. The beam dynamic element obtained in this paper is analytical and accurate and can be applied in practice.
ISSN:1024-123X
1563-5147
DOI:10.1155/2015/582326