Formulating a new efficient simple element for statics, buckling and free vibration analysis of Timoshenko’s beam

Document Type : Research Article

Authors

1 Department of civil engineering, Faculty of engineering, University of Torbat Heydarieh, Torbat Heydarieh, Iran.

2 Civil Engineering Department, Engineering Faculty, University of Torbat Heydarieh, Torbat Heydarieh, Iran.

3 Civil Engineering Department, Larestan Branch Islamic Azad University, Larestan, Iran.

Abstract

The beams are really useful for a large number of engineering structures. In this article, a simple, robust beam element will be formulated. Other researchers utilized several theories such as Euler-Bernoulli, Timoshenko and higher-order shear for analyzing the beams. The proposed formulation will be written based on satisfying the equilibrium equation. Using the equilibrium equation reduces the number of unknowns in addition to improving the efficiency of the new element. The suggested element has only two nods and two degrees of freedom per node. The third and second-order polynomials will be used for vertical displacement and rotation fields, respectively. After calculating the matrix of shape functions, the governing equations of statics, free vibration and buckling analysis can be written. Finally, using the suggested element, static analysis, free vibration and buckling were performed on several problems. To prove the efficiency of the new element, a large number of benchmark tests will be utilized. These numerical tests have various support conditions and different aspect ratios. With the help of these tests, rapid convergence and high accuracy of the proposed element will be shown. The new element has high efficiency in all of the static, free vibration and buckling analysis for both thin and thick beams besides its simplicity. Good element answers of other researchers will be available to have a better comparison.

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References

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Amirkabir Journal of Civil Engineering
Volume 53, Issue 9
December 2021
Pages 4061-4080

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