%0 Journal Article
%T Wkb and Numerical Compound Matrix Methods for Solving the Problem of Everted Neo-hookean Spherical Shell
%A Sanjaranipour, Morteza
%A Komeyli, Hamed
%J Journal of Mathematics and Computer Science
%D 2014
%V 11
%N 3
%@ ISSN 2008-949X
%F Sanjaranipour2014
%X The present paper deals with an eigenvalue problem which describes an everted neo-hookean spherical shell which its outer surface is deformed in compression under hydrostatic pressure. Our approach is based on mathematical modeling using a differential equation of order four and boundary conditions including two differential equations of order two and three. We solve the above mentioned problem using two different expansions of WKB method. We also investigate how to apply the numerical compound matrix on the problem and show the application of Runge-Kutta-Fehlberg and Newton-Raphson numerical algorithm. Finally, by comparing the data obtained from these two methods (numerical and WKB), we not only learn about the turning point, we also find out that the reason of the difference between the results of the two methods is this turning point.
%9 journal article
%R 10.22436/jmcs.011.03.02
%U http://dx.doi.org/10.22436/jmcs.011.03.02
%P 177-190
%0 Journal Article
%T A Numerical Method for Linear Two-point Boundary-value Problems Using Compound Matrices
%A B. S. Ng
%A W. H. Reid
%J Journal of Computational Physics
%D 1979
%V 30
%F Ng1979
%0 Journal Article
%T An Initial Value Matrix Method for Eigen-value Problems Using Compound Matrices
%A B. S. Ng
%A W. H. Reid
%J Journal of Computational Physics
%D 1979
%V 30
%F Ng1979
%0 Journal Article
%T The Compound Matrix Method for Ordinary Differential Systems
%A B. S. Ng
%A W. H. Reid
%J Journal of Computational Physics
%D 1985
%V 58
%F Ng1985
%0 Journal Article
%T On the Existence of Elastic Cylinders
%A Yi-Chao Chen
%A D. M. Haughton
%J Elasticity
%D 1997
%V 49
%F Chen1997
%0 Book
%T WKB Method with Repeated Roots and its Application to the Buckling Analysis of an Everted Cylindrical Tube
%A Y. B. Fu
%A M. Sanjaranipour
%D 2002
%I SIAM Journal of Applied Mathematics
%C 1856–1871
%F Fu2002
%0 Journal Article
%T Some Asymptotic Results Concern the Buckling of Arbitrary Thickness
%A Y. B. Fu
%J int. J. Non –linear Mech.
%D 1978
%V 33
%F Fu 1978
%0 Journal Article
%T On the Eversion of Incompressible Elastic Spherical Shells
%A D. M. Houghton
%A Yi-Chao Chen
%J ZAMP
%D 1999
%V 50
%F Houghton1999
%0 Journal Article
%T Asymptotic Bifurcation for the Eversion of Elastic Shells
%A D. M. Haughton
%A Yi-Chao Chen
%J ZAMP
%D 2003
%V 54
%F Haughton2003
%0 Journal Article
%T WKB Analysis of the Buckling of a Neo-hookean Cylindrical Shell of Arbitrary Thickness Subjected to an External Pressure
%A M. Sanjaranipour
%J International Journal of Applied Mathematics
%D 2010
%V
%F Sanjaranipour 2010
%0 Book
%T Application of WKB Method to Some of the Buckling Problems in Finite Elasticity
%A M. Sanjaranipour
%D 2001
%I Ph. D. thesis Keele
%C
%F Sanjaranipour 2001
%0 Book
%T A WKB Analysis of the Buckling of an Everted Neo-Hookean Cylindrical Tube
%A Y.B. Fu
%A Y. P. Lin
%D 2002
%I Department of Mathematics, Kunming Institute of Science and Technology, Kunming
%C China
%F Fu2002
%0 Book
%T Numerical Analysis
%A Richard L. Borden
%A J. Douglas Faires
%A Albert C. Reynolds
%D 2000
%I Qoqnoos Publication
%C Tehran
%F Borden2000
%0 Book
%T Protection for Engineers and Scientists
%A A. W. Bush
%D 1992
%I School of Computing and Mathematics Teesside, Polytechnic Middleborough
%C U. k
%F Bush 1992
%0 Book
%T Introduction to Perturbation Technique
%A Alihassan Nyfeh
%D 1980
%I University Distinguished Professor Virginia Polytechnic and University of Blackbury Virginia and Yamourk University Irbid Jordan
%C
%F Nyfeh1980
%0 Book
%T Advanced Mathematical Methods for Scientists and Engineers
%A Carl M. Bender
%D 1978
%I copy- right by McGraw-Hill Inc.
%C
%F Bender1978
%0 Book
%T Continuum Mechanics
%A P. Chadwick
%D 1976
%I Gorge Allen and Unwin
%C L.td.
%F Chadwick 1976