Application of the variational iteration method to the boundary value problems with jump discontinuities arising in solid mechanics

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 8, Issue 4, 2007, Pages 513-518

  Ozer, Halil ^a  

^a ZONGULDAK KARAELMAS UNIVERSITY   (Turkey)

Author keywords

Generalized functions; Jump discontinuity; Variational iteration method

Indexed keywords

EID: 36248955605     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2007.8.4.513     Document Type: Article

References (32)

1. Sokolnikof IS, Redheffer RM. Mathematics and Physics of Modern Engineering, McGraw-Hill, (1966).
2. Yavari A, Sarkani S. On applications of generalized functions to the analysis of Euler-Bernoulli beam-columns with jump discontinuities, Int. J. Mech. Sci. 43 (2001) 1543-1562.
3. Kanwal RP. Generalized Functions Theory and Applications, Academic Press, New York, (1983).
4. Yavari A, Sarkani S, Reddy JN. Generalized solutions of beams with jump discontinuities on elastic foundations, Arch. Appl. Mech. 71 (2001) 625-639.
5. Stankovic B, Atanacković TM. Generalized Solutions to a linear discontinuous differential equation, J. Math. Anal. Appl. 324 (2006) 1462-1469.
6. Failla G, Santini A. On Euler- Bernoulli discontinuous beam solutions via uniform-beam Green's functions, Int. J. Solids Struct. (2007), in press.
7. Biondi B, Caddemi S.Closed form solutions of Euler- Bernoulli beams with singularities, Int. J. Solids Struct. 42 (2005) 3027-3044.
8. Biondi B, Caddemi S. Euler- Bernoulli beams with multiple singularities in the flexural stiffness, Eur. J. Mech. A-Solids (2007), in press.
9. He JH. The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput. 151 (2004) 287-292.
10. Al-Hayani W, Casasús L. On the applicability of the Adomian method to initial value problems with discontinuities, Appl. Math. Lett. 19 (2006) 22-31.
11. Casasús L, Al-Hayani W. The decomposition method for ordinary differential equations with discontinuities, Appl. Math. Comput. 131 (2002) 245-251.
12. Clebsch A. Theorie der Elasticitat Fester Korper, Teubner, (1862).
13. Macaulay WH. A note on the deflection of beams, Messenger Math. 48 (1919) 129.
14. Reddy JN. Energy and Variational Methods in Applied Mechanics, John Wiley & Sons, (1984).
15. He JH. Semi-inverse method and generalized variational principles with multi-variables in elasticity, Appl. Math. Mech.-Engl. 21 (7) (2000) 797-808.
16. Pedregal P.On the Generality of Variational Principles, Milan J. Math. 71 (2003) 319-356.
17. Ozer H. A variational formulation and analysis of polar orthotropic circular plates using an energy principle, part I: thin Plates, Sci. Eng. Compos. Mater. (2007), in press.
18. Ozer H. A variational formulation and analysis of polar orthotropic circular plates using an energy principle, part II: thick Plates, Sci. Eng. Compos. Mater. (2007), in press.
19. He JH. Variational iteration method -a kind of non-linear analytical technique: some examples, Int. J. NonLinear Mech. 34 (1999) 699-708.
20. Wazwaz AM. The variational iteration method for exact solutions of Laplace equation, Phys. Lett. A. 363 (2007) 260-262.
21. Abdou MA, Soliman AA. New applications of variational iteration method, Phys. D 211 (2005) 1-8.
22. Bildik N, Konuralp A. The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations, Int. J. Nonlinear Sci. 7 (1) (2006) 65-70.
23. Yusufoglu E. The variational iteration method for construction of some compact and noncompact structures of Klein-Gordon equations, Int. J. Nonlinear Sci. 8 (2) (2007) 153-158.
24. He JH. Some Asymptotic methods for strongly nonlinear equations, Int. J. Mod. Phys. B 20 (10) (2006) 1141-1199, and 20 (18)(2006) 2561-2568
25. Kanwal RP. Generalized Functions Theory and Technique, Birkhäuser, Boston, (1998).
26. Schwartz L. Théorie des Distributions, Hermann, Paris, (1966).
27. Zemanian AH. Distribution Theory and Transform Analysis, McGraw-Hill, New York, (1965).
28. Tari H, Ganji DD, Rostamian M. Approximate solutions of K (2,2), KdV and modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method Int. J. Nonlinear Sci., 8 (2): 203-210 2007
29. Ozis T, Yildirim A. Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method, Int. J. Nonlinear Sci., 8 (2): 239-242 2007
30. Ganji DD, Sadighi A. Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, Int. J. Nonlinear Sci., 7 (4): 411-418 2006
31. Odibat ZM, Momani S. Application of variational iteration method to Nonlinear differential equations of fractional order, Int. J. Nonlinear Sci., 7(1): 27-34 2006
32. He JH.Variational iteration method - Some recent results and new interpretations, J. Comput. Appl. Math., 207(1)(2007) 3-17