Determination of buckling loads and mode shapes of a heavy vertical column under its own weight using the variational iteration method

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 11, Issue 10, 2010, Pages 851-857

  Okay, Fuad ^a   Atay, Mehmet Tank ^b   Coçkun, Safa Bozkurt ^a  

^a KOCAELI UNIVERSITY   (Turkey)

^b NIGDE UNIVERSITY   (Turkey)

Author keywords

Buckling; Elastic stability; Heavy column; Variational iteration method

Indexed keywords

EID: 78650012449     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2010.11.10.851     Document Type: Article

References (40)

1. Euler, L., Die altitudine colomnarum sub proprio pondere corruentium, Acta Acad. Petropol, 1778 (in Latin)
2. Dinnik, A.N., Design of columns of varying cross-section, Trans. ASME 51, (1929).
3. Karman, T.R, Biot, M.A., Mathematical Methods in Engineering, McGraw Hill, NewYork, 1940.
4. Morley A., Critical loads for long tapering struts, Engineering, (1917), 104-295.
5. Timoshenko, S.P., Gere, J.M., Theory of Elastic Stability, McGraw Hill, NewYork, 1961.
6. Wang, C.M., Wang, C.Y., Reddy, J.N., Exact Solutions for Buckling of Structural Members, CRC Press LLC, Florida, 2005.
7. G.J. Simitses , D. H. Hodges, Fundamentals of structural Stability, Elsevier- Butterworth- Heinemann Publishing, 2005.
8. Ermopoulos, J. C., Buckling of tapered bars under stepped axial loading, J. Structural Eng. ASCE, 112(6), 1346-1354, 1986
9. Li Q. S., Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading, Eur. J Mech. A / Solids 20 (2001), 485-500 (Pubitemid 32512457)
10. Gere, J.M., Carter, W.O., Critical buckling loads for tapered columns, J. Struct. Eng.ASCE, 88 (1962), 1-11.
11. Arbabi. F., Li, F., Buckling of variable cross-section columns - integral equation approach, J Struct. Eng.-ASCE, 117 (8) (1991), 2426-2441 (Pubitemid 21679789)
12. Siginer, A., Buckling of columns of variable flexural stiffness, J. Eng. Mech.ASCE, 118(1992), 543-640.
13. Li, Q.S., Cao, H., Li, G., Stability analysis of bars with multi-segments of varying cross section, Comput. Struct., 53 (1994), 1085-1089.
14. Li, Q.S., Cao, H., Li, G., Stability analysis of bars with varying cross section, Int. J. Solids Struuct., 32 (1995), 3217-3228.
15. Li, Q.S., Cao, H., Li, G., Static and dynamic analysis of straight bars with variable cross-section, Comput. Struct., 59 (1996), 1185-1191. (Pubitemid 126370522)
16. Sampaio Jr., J.H.B, Hundhausen, J.R., A mathematical model and analytical solution for buckling of inclined beam columns, Appl. Math. Model., 22 (1998), 405-421.
17. Keller, J.B., The shape of the strongest column, Archive for Rational Mechanics and Analysis, 5 (1960), 275-285.
18. Tadjbakhsh, I., Keller., J.B., Strongest columns and isoperimetric inequalities for eigenvalues, J. Appl. Mech. ASME, 29 (1962), 159-164.
19. Taylor, J.E., The strongest column - an energy approach, J. Appl. Mech. ASME, 34 (1967), 486-487.
20. Levyakov, S.V., Stability analysis of curvilinear configurations of an inextensible elastic rod with clamped ends, Mechanics Research Communications, 36 ( 2009), 612-617.
21. Atanackovic, T.M., Stability Theory of Elastic Rods (Series on Stability, Vibration and Control of Systems, Vol 1), World Scientific Publishing Company, (1997).
22. Coskun, S.B., Atay M.T., Determination of critical buckling load for elastic columns of constant and variable cross-sections using Variational iteration method .Computers and Mathematics with Applications, 58 (2009), 2260-2266.
23. Atay M.T, Coskun, S.B., Elastic stability of Euler columns with a continuous elastic restraint using Variational iteration method .Computers and Mathematics with Applications, 58 (2009), 2528-2534.
24. Coskun, S.B., Determination of critical buckling loads for Euler columns of variable flexural stiffness with a continuous elastic restraint using Homotopy Perturbation Method, International Journal Nonlinear Sci. and Numer. Simulation , 10 (2) (2009), 191-197.
25. Atay M. T., Determination of critical buckling loads for variable stiffness Euler columns using Homotopy Perturbation Method, Int. Journal Nonlinear Sci. and Numer. Simulation , 10 (2) (2009), 199-206.
26. Coskun, S.B., Analysis of Tilt-Buckling of Euler Columns withVarying Flexural Stiffness Using Homotopy Perturbation Method, Mathematical Modelling and Analysis, 15 (3) (2010), 275-286.
27. He, J.H., Variational iteration method - a kind of non-linear analytical technique: some examples. International Journal of Nonlinear Mechanics, 34(1999); 699-708.
28. He, J.H., Variational iteration method for delay differential equations. Commun. Nonlinear Sci. Numer. Simulation, 2 (4) (1997); 235-236. (Pubitemid 40492054)
29. He, J.H., Some asymptotic methods for strongly nonlinear equations. Internat. J. Modern Phys. B, 20 (2006); 1141-1199.
30. He, J.H., Non-perturbative methods for strongly nonlinear problems. Berlin: dissertation.de-Verlag im Internet GmbH, 2006.
31. He, J.H., Variational iteration method for autonomous ODE systems. Applied Mathematics and Computation, 114 (2000); 115-123.
32. He J.H., Wu XH., Variational Iteration Method : New development and applications , Computers & Mathematics with Applications, 54 (2007), 881-894.
33. He JH., Variational iteration method-Some recent results and new interpretations, Journal of Computational and Applied Mathematics, 207 (2007), 3-17.
34. He J.H., An elementary introduction to recently developed asymptotic methods and nanomechanisms in textile engineering., International Journal of Modern Physics B, 22 (2008), 3487-3578.
35. Hesameddini, E., Latiflzadeh, H. Reconstruction of Variational Iteration Algorithms using the Laplace Transform, Int. J. Nonlinear Sciences and Numerical Simulation, 10(2009): 1377-1382
36. Chun, C. Fourier-series-based Variational Iteration Method for a Reliable Treatment of Heat Equations with Variable Coefficients, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009) 1383-1388
37. Ozturk, B. Free Vibration Analysis of Beam on Elastic Foundation by the Variational Iteration Method, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009): 1255-1262
38. Zayed, E.M.E., Rahman, H.M.A. On solving the KdV-Burger's equation and the Wu-Zhang equations using the modified variational iteration method, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009): 1093-1103
39. Ates, I., Yildirim, A. Application of variational iteration method to fractional initial-value problems, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009) : 877-883
40. Mokhtari, R., Mohammadi, M. Some Remarks on the Variational Iteration Method, International Journal of Nonlinear Sciences and Numerical Simulation, 10(2009): 67-74