Nonlinear multiple-scale solution of a cylindrical shell
Authors:
James R. Stafford and Adolf T. Hsu
Journal:
Quart. Appl. Math. 30 (1973), 491-499
DOI:
https://doi.org/10.1090/qam/99718
MathSciNet review:
QAM99718
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Abstract: A multiple-scale perturbation technique is used with a two-parameter expansion to study the asymptotic solution of Reissner’s axisymmetric finite-deformation equations for a circular cylindrical shell with an edge-bending moment load. Beyond the assumptions of Reissner’s differential equations, it is assumed that (1) the rotations of a shell element are finite but not excessively large, (2) thickness variations in the differential equations are of order one and (3) the boundary-layer behavior is of the linear bending type to a first approximation. An asymptotic solution is then found which is uniformly valid in that it contains boundary-layer effects and corrections for extending the analysis into the shell’s interior. Upon considering certain limits, it is observed that the solution contains well-established linear and nonlinear approximations to the solution.
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M. Van Dyke, Perturbation methods in fluid dynamics, 1st edition, Academic Press, New York, 1969
J. A. Cochran, Problems in singular perturbation theory, Tech. Rep. No. 1, Applied Mathematics and Statistics Lab., Stanford University, 1962
J. R. Stafford, A multiple scale solution for circular cylindrical shells, Int. J. Solids Structures 5, 855–861 (1969)
E. Reissner, On axisymmetrical deformations of thin shells of revolution, Proc. Symp. Appl. Math. 3, 27–52 (1949), McGraw-Hill
J. D. Cole and J. Kevorkian, Uniformly valid asymptotic approximations for certain nonlinear differential equations, in Nonlinear differential equations and nonlinear mechanics, J. P. LaSalle and S. Lefchetz, eds., pp. 113–120, Academic Press, New York, 1963
F. B. Hildebrand, On asymptotic integration in shell theory, Proc. Symp. Appl. Math. 3, 53–66 (1949), McGraw-Hill
T. J. Lardner, Symmetric deformation of a circular cylindrical shell of variable thickness, Zeit. Ange. Math. Phys. 19, 270–277 (1968)
E. Reissner and J. H. Weinitschke, Finite pure bending of circular cylindrical tubes, Quart. Appl. Math. 20, 305–319 (1963)
E. Reissner, On influence coefficients and nonlinearity for thin shells of revolution, J. Appl. Mech. 26, 69–72 (1959)
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Article copyright:
© Copyright 1973
American Mathematical Society
