Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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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DOI: https://doi.org/10.1090/qam/99718
Article copyright: © Copyright 1973 American Mathematical Society

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