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International Journal of Scientific and Engineering Research
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ISSN Print: 2229-5518 2    
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scirp IJSER >> Volume 3,Issue 2,February 2012
Exact solution of a problem of dynamic deformation and nonlinear stability of a problem with a Blatz-Ko material
Full Text(PDF, )  PP.51-58  
Edouard DIOUF
systems of nonlinear equation, exact solution in dynamic, strength theory of Blatz-Ko material, stability theory of structure
The aim of the paper is to study the phenomena of stability of a hollow tube subjected to combined deformations. The model used is that of Blatz-Ko in compressible and dynamic. Before studying the stability, we have solved a boundary value problem with exact solution. The results could be applied in biomechanics.
[1] W. Hahn, Theory and Application of liapunov’s Direct Method.Prentice-Hall inc., 1963.N.J.

[2] P.A.Glendinning, Stability, instability and chaos: an introduction to the theory of nonlinear differential equations, Cambridge Texts in Applied Mathematics, CUP 1994.

[3] J.K.Hale, Asymptotic Behavior of Dissipative Systems, Providence: Math. Surveys and Monographs, Amer. Math.Soc.1988.

[4] R. Temam. Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New-York 1988 (1st edition) and 1996 (2nd edition).

[5] D.Henry, Geometric theory of Semilinear Parabolic Equation, Springer Lecture Notes in Mathematics, Vol.840, Springer Verlag, Berlin 1984.

[6] H.S.Shen, T.Y.Chen, Buckling and postbuckling behavior of cylindrical shells under combined pressure and axial compression, Thin-Walled Struct. 12 (1991) 321-334.

[7] M.Barush,J.Singer, Effet of eccentricity of stiffners on the general instability of stiffened cylindrical shells under hydrostatic pressure, J. Mech. Eng. Sci. 5 (1963) 23-27.

[8] T.Y.Ng, Y.K.Lam, K.M.liew, J.N.Reddy, Dynamic stability analysis of functionally grated Cylindrical shells under periodic axial loading, Int.J. Solids Struct. 38 (2001) 1295-1300.

[9] D.G. Roxburgh and R.W. Ogden. Stability and vibration of pre- stressed compressible elastic plates. International Journal of Engineering Science, 32(3):427-454, 1994.

[10] T.J.Vandyke,A.S.Wineman, Small amplitude sinusoidal disturbances superimposed on finite circular shear of a compressible, non-linearly elastic material, Int. J. Ing. Sci.,34 (1996) 1197-1210

[11] J.E.Adkins, Some generalizations of the shear problem for isotropic incompressible materials, Proc. Cambridg Philos. Soc. 50, 334-345 (1954).

[12] M.Zidi,Finite torsion and shearing of a compressible and anisotropic tube, Int. Journal of Non linear Mechanics, 35:1115-1126 (2000).

[13] E.Diouf,M.Zidi, Finite azimuthal shear motions of a transversely isotropic compressible elastic And pretressed tube, Int. J. Ing. Sci., 43 :262-274 (2005).

[14] Jouve F.,Modélisation de l’oeil en élasticité non linèaire, Masson, Paris, 1993.

[15] Zhi-Qiang Feng, B. Magnain, J. Cros, Solution of large deformation impact problems with friction between Blatz-Ko hyperelastic bodies. Int. J. Ing. Sci. 44 (2006) 113-126.

[16] P.G. Ciarlet,Elasticité tridimensionnelle, Masson, Collection, RMA, 1985.

[17] M. Destrade,G.Saccomandi,On finite amplitude elastic waves propagating in compressible solids.(2005)Physical Review E.

[18] M.Destrade,Finite-Amplitude inhomogeneous plane waves in a deformed Blatz-Ko Materal,CanCNSM, Victoria, June 16-20, 1999.

[19] A.D. Polignone, C.O. Horgan, Axisymmetric finite antiplane shear of compressible nonlinealy elastic circular tubes.Quarterly of applied mathematics, Vol.L, N.2, june 1992, Pages 323-341.

[20] C.Truesdell, W.Noll, The non-linear field theories of mechanics, Handbuch der Physik, III/3(S.Flugge, ed.), Springer-Verlag, Berlin, 1965

[21] F.Laroche,Promenade Mathématiques, Fonctions de Bessel, promenadesmaths.free.fr, 2004.

[22] C. Deschamps, A. Warusfel,Mathématiques Tout-en-un. 2ième année MP, 2ième edition Dunod, 2004.

[23] A.M. Stuart, A.R.Humphries,Dynamical systems and numerical analysis,Cambridge University Press, 1998.

[24] E.Hebey,Nonlinear elliptic equations of critical Sobolev growth from a dynamical viewpoint Noncompact problems at the inter-section of geometry, analysis, and topology, Contemp. Math., vol. 350, Amer. Math.Soc., Providence, RI, 2004,p.115-125.

[25] O.Druet, E.Hebey, J. Vétois, Boundary stability for strongly coupled critical elliptic systems below the geometyric threshold of the conformal Laplacien,J. Funct. Anal. 258 (2010), No.3,p. 999-1059.

[26] T.Kato, Pertubation theory for linear operator,Classic in Mathematics, Springer-Verlag,Berlin, 1995, Reprint of the 1980 edition.

[27] A.M.S., A.R.Humphries, Dynamical systems and numerical analysis. Camb ridge University Press, 1998.

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