Application of the Finite Element Method for the Solution of Stability Problems of the Timoshenko Beam with Exact Shape Functions
- Authors: Lalin V.V.1, Yavarov A.V.1, Orlova E.S.1, Gulov A.R.1
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Affiliations:
- Peter the Great St. Petersburg Polytechnic University
- Issue: Vol 53, No 4 (2019)
- Pages: 449-454
- Section: Article
- URL: https://journals.rcsi.science/1570-145X/article/view/246550
- DOI: https://doi.org/10.1007/s10749-019-01098-6
- ID: 246550
Cite item
Abstract
In this article, the problems of the stability of a Timoshenko beam are solved by the finite element method, with application of exact shape functions. These shape functions are derived from the solution of homogeneous equations of equilibrium. The article presents expressions for elements of stiffness matrixes and the geometric rigidity of a Timoshenko beam. The approach that is used makes it possible to exclude the shear (locking) effect and obtain a high degree of correspondence between the numerical and analytical solutions with a small number of finite elements.
About the authors
V. V. Lalin
Peter the Great St. Petersburg Polytechnic University
Author for correspondence.
Email: vllalin@yandex.ru
Russian Federation, St. Petersburg
A. V. Yavarov
Peter the Great St. Petersburg Polytechnic University
Email: vllalin@yandex.ru
Russian Federation, St. Petersburg
E. S. Orlova
Peter the Great St. Petersburg Polytechnic University
Email: vllalin@yandex.ru
Russian Federation, St. Petersburg
A. R. Gulov
Peter the Great St. Petersburg Polytechnic University
Email: vllalin@yandex.ru
Russian Federation, St. Petersburg