The Pre-Twisted Thin-Walled Beam Element Stiffness Matrix Considering the Saint-Venant Warping Deformation

Abstract:

Based on the traditional mechanical model of thin-walled straight beam, the paper makes a systematic analysis and research on the pre-twisted thin-walled beam finite element numerical model. Firstly, based on the geometric deformation differential relationship, the paper deduces the pre-twisted thin-walled beam Saint-Venant warping strain. According to traditional thin-walled straight beam finite element mechanical model, the paper establishes its finite element stiffness matrix considering the Saint-Venant warping deformations. Finally, by calculating the pre-twisted elliptical section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted thin-walled beam element stiffness matrix considering Saint-Venant warping deformation has good accuracy.

• Periodical: Advanced Materials Research (Volume 871)
• Pages: 129-134
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.871.129
• Online since: December 2013
• Authors: Chang Hong Chen*, Ying Huang
• Keywords: Pre-Twisted, Saint-Venant, Stiffness Matrix, Thin-Walled Beam, Warping Deformation

References

[1] L D. Certain problems of the theory of rectilinear, naturally twisted beams. Soviet Applied M Magomaev echanics, 1985, 21(9): 901-908.

DOI: 10.1007/bf00886979

[2] J. F. Barnett. A Bridge for the Bridges [C]. Conference Proceedings for Bridges 1999., American: ISBN, 0-9665201-1-4.

[3] Carlo H Sequin. To Build a Twisted Bridge [C]. Conference Proceedings for Bridges 2000. American: ISBN, 0-966501-2-2.

[4] Chen Changhong, Shan Jian, Huang Ying, Research of mechanics properties of pre-twisted rectangular beam [J]．Industrial Construction，2009，39(4)：54-57.

[5] Chen Changhong, Shan Jian, Huang Ying, Research on elastic bending and torsion buckling performance of pre-twisted bar under axial pressure[J] Engineering Mechanics, 2009, 26 (6) : 166-171.

DOI: 10.1109/mace.2011.5988745

[6] Chen Xingshen, Chen Weiheng. Differential geometry lecture notes (Second Edition)[M]. BeiJing: Peking University Press, 2001, 14-17.

[7] E Petrov, M Geradin. Finite element theory for curved and twisted beams based on exact solutions for three dimensional solids. Part 1: Beam concept and geometrically exact nonlinear formulation, Part 2: anisotropic and advanced beam models, Computer Methods in Applied Mechanics and Engineering 1998 (165): 43-127.

DOI: 10.1016/s0045-7825(98)00061-9

[8] Zhang Zhiyong. Proficient MATLAB 6. 5 [M]. Beijing: Beijing University of Aeronautics and Astronautics Press, 2003, 225-227.