APPLICATION OF THE FINITE ELEMENT METHOD FOR THE SOLUTION OF STABILITY PROBLEMS OF THE TIMOSHENKO BEAM WITH EXACT SHAPE FUNCTIONS

V. V. Lalin; A. V. Yavarov; E. S. Orlova; A. R. Gulov

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APPLICATION OF THE FINITE ELEMENT METHOD FOR THE SOLUTION OF STABILITY PROBLEMS OF THE TIMOSHENKO BEAM WITH EXACT SHAPE FUNCTIONS

机译：有限元法在具有精确形状函数的TIMOSHENKO梁的稳定性问题中的应用

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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.

机译：在本文中，通过应用精确的形状函数，通过有限元方法解决了季莫申科梁的稳定性问题。这些形状函数从均质平衡方程的解中得出。本文介绍了刚度矩阵和Timoshenko梁的几何刚度的表达式。所使用的方法可以排除剪切（锁定）效应，并以少量有限元获得数值和解析解之间的高度对应。

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来源
《Hydrotechnical Construction》 |2019年第4期|449-454|共6页
作者
V. V. Lalin; A. V. Yavarov; E. S. Orlova; A. R. Gulov;
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作者单位

Peter the Great St. Petersburg Polytechnic University St. Petersburg Russia;

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正文语种 eng
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关键词
Timoshenko beam; exact shape functions; stiffness matrix; geometric stiffness matrix; critical force;

机译：季莫申科光束;精确的形状函数;刚度矩阵几何刚度矩阵临界力;

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专利

1. The Exact Two-Node Timoshenko Beam Finite Element Using Analytical Bending and Shear Rotation Interdependent Shape Functions [J] . Ini B. Edem International Journal for Computational Methods in Engineering Science and Mechanics . 2006,第6期

机译：精确的两节点Timoshenko梁有限元，使用解析弯曲和剪切旋转相互依赖的形状函数
2. Violin string shape functions for finite element analysis of rotating Timoshenko beams [J] . A.S. Vinod Kumar, Ranjan Ganguli Finite Elements in Analysis and Design . 2011,第9期

机译：小提琴琴弦形状函数，用于旋转提莫申科梁的有限元分析
3. Improvement in accuracy of the finite element method in analysis of stability of Euler-Bernoulli and Timoshenko beams [J] . Z. Wieckowski, M. Golubiewski Thin-Walled Structures . 2007,第10a11期

机译：Euler-Bernoulli和Timoshenko梁稳定性分析中有限元方法精度的提高
4. EIGENSOLUTIONS OF BEAMS CARRYING AXIALLY MOVING MATERIAL CALCULATED BY USE OF EXACT FINITE ELEMENTS [C] . J. H. Sallstrom, B. A. Akesson International Modal Analysis Conference . 2004

机译：通过使用精确有限元计算轴向移动材料的光束的尖锐型
5. Solutions of Potential Fields Using Flexible Finite Element Methods with Applications in Flow Through Porous Media and Electrospinning [D] . Li, Yalong. 2017

机译：利用柔性有限元方法求解势场及其在多孔介质流动和静电纺丝中的应用
6. Application of Inverse Finite Element Method to Shape Sensing of Curved Beams [O] . Pierclaudio Savino, Francesco Tondolo, Marco Gherlone, 2020

机译：逆有限元法在弯曲梁形状传感中的应用
7. Discussion: “Dynamic Stability of Timoshenko Beams by Finite Element Method” (Thomas, J., and Abbas, B. A. H., 1976, ASME J. Eng. Ind., 98, pp. 1145–1149) [O] . C. V. Smith 1976

机译：讨论：“由有限元方法的”Timoshko梁的动态稳定性“（托马斯，J.和Abbas，B.A.H.，1976，Asme J. Eng。Ind.，98，PP。1145-1149）
8. Sensitizing the Timoshenko Beam and the Reissner-Mindlin Plate Finite Element211 Solution [R] . Freund, J., Salonen, E. M. 1998

机译：敏化Timoshenko梁和Reissner-mindlin板有限元211解决方案

APPLICATION OF THE FINITE ELEMENT METHOD FOR THE SOLUTION OF STABILITY PROBLEMS OF THE TIMOSHENKO BEAM WITH EXACT SHAPE FUNCTIONS

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