Computational & Technology Resources
an online resource for computational,
engineering & technology publications
Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 165

Coupling Dynamic Buckling Analysis of Framed Structures Using a Spline Finite Element

H. Yang and A.Y.T. Leung

Department of Building and Construction, City University of Hong Kong, Hong Kong

Full Bibliographic Reference for this paper
H. Yang, A.Y.T. Leung, "Coupling Dynamic Buckling Analysis of Framed Structures Using a Spline Finite Element", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 165, 2008. doi:10.4203/ccp.88.165
Keywords: torque buckling analysis, spline finite element, cubic B-spline, initial stress, framed structure, initial stress stiffness matrix.

Summary
This paper uses B-splines to analyze dynamic buckling problems of framed structures subject to coupled initial end torque and axial force. It was assumed [1] that the torque applied at the end of the beam element is equally shared in x and y axes as initial stresses, which is satisfactory in such a case that the bending rigidities in x and y axes are equal [2]. In the case where the bending rigidities are different, the torque is shared in the x and y axes as initial stresses in the ratio Ix:Iy.

After a brief introduction, assumptions and a basic description of the problem of interest are presented. Next the energy equations are derived for uniform cross-sections, and are non-dimensionalized with the rigidity ratio to define the geometry. Using cubic B-splines, displacement fields are constructed. A derivation of the equation of motion based on Hamilton's principle is presented. Thereafter, the idea of finite element method is used to formulate the system matrices. To simplify the calculation, a coordinate transformation transforms a typical element into a standardized element. Details of how to deal with boundary conditions are described. The solution is given, which is a linear eigenvalue problem to describe the relationship between natural frequency, axial buckling force, and end buckling torque. Numerical examples for a cantilever beam element are discussed, in which numerous interactive diagrams are constructed and analyzed. The paper is concluded with some remarks.

A comprehensive study on the interactive dynamic axial-torsional buckling problem of a doubly symmetric beam element with uniform cross-section has been presented. Extensive interactive diagrams are constructed for analysis purpose. The numerical results indicate that the method is efficient and accurate in comparison with the results in [2,3,4]. Although only a single cantilever beam element has been investigated in the numerical examples, structural frames can be further studied without difficulties since the method is based on the finite element formulation.

References
1
N.-I. Kim, C.C. Fu, M.-Y. Kim, "Stiffness matrices for flexural-torsional/lateral buckling and vibration analysis of thin-walled beam", Journal of Sound and Vibration, 299(4-5), 739-756, 2007. doi:10.1016/j.jsv.2006.06.062
2
H. Ziegler, "Principles of structural stability", 2nd ed, Birkhauser Verlag Basel, Germany, 1977.
3
S.P. Timoshenko, J. Gere, "Theory of Elastic Stability", 2nd ed, McGraw-Hill, New York, 1961.
4
A.Y.T. Leung, "Exact dynamic stiffness for axial-torsional buckling of structural frames", Thin-Walled Structures, 46(1), 1-10, 2008. doi:10.1016/j.tws.2007.08.012

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £145 +P&P)