Elastic stability of Euler columns with a continuous elastic restraint using variational iteration method

Computers and Mathematics with Applications

Volumn 58, Issue 11-12, 2009, Pages 2528-2534

  Atay, Mehmet Tarik ^a   Coşkun, Safa Bozkurt ^a  

^a NIGDE UNIVERSITY   (Turkey)

Author keywords

Buckling; Continuous restraint; Elastic stability; Euler column; Variational iteration method

Indexed keywords

ANALYTICAL SOLUTIONS; CONTINUOUS RESTRAINT; CRITICAL BUCKLING LOADS; ELASTIC FOUNDATION MODEL; ELASTIC RESTRAINT; ELASTIC STABILITY; END CONDITIONS; ENGINEERING PRACTICES; EULER COLUMN; EULER COLUMNS; EXACT SOLUTION; FOUNDATION ENGINEERS; HIGHLY NONLINEAR; VARIATIONAL ITERATION METHOD;

BUCKLING; ITERATIVE METHODS; NONLINEAR EQUATIONS; OSCILLATORS (MECHANICAL);

STABILITY CRITERIA;

EID: 70350574070     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.03.051     Document Type: Article

References (33)

1. Euler L. Die altitudine colomnarum sub proprio pondere corruentium. Acta Acad Petropol (1778) (in Latin)
2. Greenhill A.G. Determination of the greatest height consistent with stability that a vertical pole on mast can be made and of the greatest height to which a tree of given proportions can grow. Proceedings of the Cambridge Philosophical Society IV (1883)
3. Dinnik A.N. Design of columns of varying cross-section. Transactions of the ASME 51 (1929)
4. Karman T.R., and Biot M.A. Mathematical Methods in Engineering (1940), McGraw Hill, New York
5. Timoshenko S.P., and Gere J.M. Theory of Elastic Stability (1961), McGraw Hill, New York
6. Wang C.M., Wang C.Y., and Reddy J.N. Exact Solutions for Buckling of Structural Members (2005), CRC Press LLC, Florida
7. H. Bleich, Buckling Strength of Metal Structures, McGraw-Hill, New York, pp. 187-191
8. Dinnik A.N. Design of columns of varying cross-section. Transactions of the ASME, Applied Mechanics 51 (1932)
9. Elishakoff I., and Pellegrini F. Exact and effective approximate solution solutions of some divergent type non-conservative problems. Journal of Sound and Vibration 114 (1987) 144-148
10. Elishakoff I., and Pellegrini F. Application of Bessel and Lomel functions and undetermined multiplierGalerkin method version for instability of non-uniform column. Journal of Sound and Vibration 115 (1987) 182-186
11. Elishakoff I., and Pellegrini F. Exact solution for buckling some divergence type non-conservative systems in terms of Bessel and Lomel functions. Computer Methods in Applied Mechanics and Engineering 66 (1988) 107-119
12. Eisenberger M. Buckling loads for variable cross-section members with variable axial force. International Journal of Solids and Structures 27 (1991) 135-143
13. Gere J.M., and Carter W.O. Critical buckling loads for tapered columns. Journal of Structural Engineering ASCE 88 1 (1962) 1-11
14. Arbabi F., and Li F. Buckling of variable cross-section columns - integral equation approach. Journal of Structural Engineering ASCE 117 8 (1991)
15. Siginer A. Buckling of columns of variable flexural rigidity. Journal of Engineering Mechanics, ASCE 118 3 (1992) 543-640
16. Li Q.S., Cao H., and Li G. Stability analysis of bars with multi-segments of varying cross section. Computers and Structures 53 5 (1994) 1085-1089
17. Li Q.S., Cao H., and Li G. Stability analysis of bars with varying cross section. International Journal of Solids and Structures 32 21 (1995) 3217-3228
18. Li Q.S., Cao H., and Li G. Static and dynamic analysis of straight bars with variable cross-section. Computers and Structures 59 (1996) 1185-1191
19. Sampaio Jr. J.H.B., and Hundhausen J.R. A mathematical model and analytical solution for buckling of inclined beam columns. Applied Mathematical Modelling 22 (1998) 405-421
20. Keller J.B. The shape of the strongest column. Archive for Rational Mechanics and Analysis 5 (1960) 275-285
21. Tadjbakhsh I., and Keller J.B. Strongest columns and isoperimetric inequalities for eigenvalues. Journal of Applied Mechanics ASME 29 (1962) 159-164
22. Taylor J.E. The strongest column - an energy approach. Journal of Applied Mechanics ASME 34 (1967) 486-487
23. He J.H. Variational iteration method - A kind of nonlinear analytical technique: Some examples. International Journal of Nonlinear Mechanics 34 4 (1999) 699-708
24. He J.H. A review on some new recently developed nonlinear analytical techniques. International Journal of Nonlinear Science Numerical Simulation 1 1 (2000) 51-70
25. He J.H. Variational iteration method-some recent results and new interpretations. Journal of Computational and Applied Mathematics 207 1 (2007) 3-17
26. Momani S., and Abuasad S. Application of He's variational iteration method to Helmholtz equation. Chaos, Solitons and Fractals 27 5 (2006) 1119-1123
27. Abulwafa E.M., Abdou M.A., and Mahmoud A.A. Nonlinear fluid flows in pipe-like domain problem using variational iteration method. Chaos, Solitons and Fractals 32 4 (2007) 1384-1397
28. Sweilan N.H., and Khader M.M. Variational iteration method for one dimensional nonlinear thermoelasticity. Chaos, Solitons and Fractals 32 1 (2007) 145-149
29. Xu L. Variational iteration method for solving integral equations. Computers and Mathematics with Applications 54 (2007) 1071-1078
30. He J.H., Wazwaz A.M., and Xu L. The variational iteration method: Reliable, efficient and promising. Computers and Mathematics with Applications 54 7-8 (2007) 879-880
31. Xu L., He J.H., and Wazwaz A.M. Variational iteration method - reality, potential and challenges. Journal of Computational and Applied Mathematics 207 1 (2007) 1-2
32. Coşkun S.B., and Atay M.T. Analysis of convective straight and radial fins with temperature-dependent thermal conductivity using variational iteration method with comparison with respect to finite element analysis. Mathematical Problems in Engineering 2007 (2007) Article ID: 42072
33. Atay M.T., and Coşkun S.B. Effects of nonlinearity on the variational iteration solutions of nonlinear two-point boundary y value problems with comparison with respect to finite element analysis. Mathematical Problems in Engineering 2008 (2008) Article ID: 857296