An Asymptotic Theory for the Nonlinear Analysis of Laminated Cylindrical Shells

Chih-Ping Wu, Chi Chuan Liu

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

On the basis of three-dimensional (3D) nonlinear elasticity, an asymptotic theory is developed for the analysis of multilayered anisotropic circular cylindrical shells. The nonlinear relations between the finite strains (Green strains) and displacements, the nonlinear equilibrium equations in terms of the Kirchhoff stress components, and the generalized Hooke's law for a monoclinic elastic material are considered in the present formulation without making a priori static or kinematic assumptions. By means of proper nondimensionalization, asymptotic expansion and successive integration, recursive sets of the governing equations for various orders are obtained. It is shown that the von Karman nonlinear theory is derived as a first-order approximation to the 3D nonlinear theory. The differential operators in the linear terms of governing equations for various orders remain identical, the nonlinear terms related to the unknowns of the current order appear in a regular pattern, and the other nonhomogeneous terms can be calculated by the lower-order solutions. With the sets of appropriate edge conditions, the nonlinear analysis of laminated cylindrical shells can be made in a hierarchic and consistent way.

Original languageEnglish
Pages (from-to)329-342
Number of pages14
JournalInternational Journal of Nonlinear Sciences and Numerical Simulation
Volume2
Issue number4
DOIs
Publication statusPublished - 2001 Jan 1

Fingerprint

cylindrical shells
Cylindrical Shell
Nonlinear analysis
Asymptotic Theory
Nonlinear Analysis
circular shells
equilibrium equations
differential operators
Elasticity
Kinematics
kinematics
elastic properties
Governing equation
formulations
Term
expansion
Hooke's law
approximation
Finite Strain
Nonlinear Elasticity

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Computational Mechanics
  • Modelling and Simulation
  • Engineering (miscellaneous)
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Applied Mathematics

Cite this

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abstract = "On the basis of three-dimensional (3D) nonlinear elasticity, an asymptotic theory is developed for the analysis of multilayered anisotropic circular cylindrical shells. The nonlinear relations between the finite strains (Green strains) and displacements, the nonlinear equilibrium equations in terms of the Kirchhoff stress components, and the generalized Hooke's law for a monoclinic elastic material are considered in the present formulation without making a priori static or kinematic assumptions. By means of proper nondimensionalization, asymptotic expansion and successive integration, recursive sets of the governing equations for various orders are obtained. It is shown that the von Karman nonlinear theory is derived as a first-order approximation to the 3D nonlinear theory. The differential operators in the linear terms of governing equations for various orders remain identical, the nonlinear terms related to the unknowns of the current order appear in a regular pattern, and the other nonhomogeneous terms can be calculated by the lower-order solutions. With the sets of appropriate edge conditions, the nonlinear analysis of laminated cylindrical shells can be made in a hierarchic and consistent way.",
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An Asymptotic Theory for the Nonlinear Analysis of Laminated Cylindrical Shells. / Wu, Chih-Ping; Liu, Chi Chuan.

In: International Journal of Nonlinear Sciences and Numerical Simulation, Vol. 2, No. 4, 01.01.2001, p. 329-342.

Research output: Contribution to journalArticle

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