WKB method with repeated roots and its application to the buckling analysis of an everted cylindrical tube

SIAM Journal on Applied Mathematics

Volumn 62, Issue 6, 2002, Pages 1856-1871

  Fu, Y B ^a   Sanjarani Pour, M ^a  

^a KEELE UNIVERSITY   (United Kingdom)

Author keywords

Eversion of tubes; Finite elasticity; Singular perturbation; WKB method

Indexed keywords

BOUNDARY VALUE PROBLEMS; BUCKLING; EIGENVALUES AND EIGENFUNCTIONS; PERTURBATION TECHNIQUES;

STRAIN ENERGY FUNCTION;

TUBES (COMPONENTS);

EID: 0036665195     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139901389641     Document Type: Article

References (12)

1. S. A. ADELEKE (1983), On the problems of eversion for incompressible elastic materials, J. Elasticity, 13, pp. 63-69.
2. C. M. BENDER AND S. A. ORSZAG (1978), Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York.
3. P. CHADWICK (1972), The existence and uniqueness of solutions of two problems in the Mooney-Rivlin theory for rubber, J. Elasticity, 2, pp. 123-128.
4. P. CHADWICK AND E. W. HADDON (1972), Inflation-extension and eversion of a tube of incompressible isotropic elastic material, J. Inst. Math. Appl., 10, pp. 258-278.
5. M. A. DOWAIKH AND R. W. OGDEN (1990), On surface waves and deformations in a pre-stressed incompressible elastic solid, IMA J. Appl. Math., 44, pp. 261-284.
6. Y. B. FU (1998), Some asymptotic results concerning the buckling of a spherical shell of arbitrary thickness, Internat. J. Non-Linear Mech., 33, pp. 1111-1122.
7. Y. B. FU (2001), Perturbation methods and nonlinear stability analysis, in Nonlinear Elasticity: Theory and Applications, Y. B. Fu and R. W. Ogden, eds., Cambridge University Press, Cambridge, UK, pp. 345-391.
8. D. M. HAUGHTON AND A. ORR (1995), On the eversion of incompressible elastic cylinders, Internat. J. Non-Linear Mech., 30, pp. 81-95.
9. R. S. RIVLIN (1949), Large elastic deformations of isotropic materials. VI. Further results in the theory of torsion, shear and flexure, Phil. Trans. Roy. Soc. Lond. Ser A, 242, pp. 173-195.
10. C. R. STEELE (1976), Application of the WKB method in solid mechanics, Mechanics Today, 3, pp. 243-295.
11. O. H. VARGA (1966), Stress-Strain Behaviour of Elastic Materials, Interscience, New York.
12. S. WOLFRAM (1988), Mathematica: A System for Doing Mathematics by Computer, Addison-Wesley, Reading, MA.