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 language English 329-342 14 International Journal of Nonlinear Sciences and Numerical Simulation 2 4 https://doi.org/10.1515/IJNSNS.2001.2.4.329 Published - 2001 Jan 1

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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

title = "An Asymptotic Theory for the Nonlinear Analysis of Laminated Cylindrical Shells",
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.",
author = "Chih-Ping Wu and Liu, {Chi Chuan}",
year = "2001",
month = "1",
day = "1",
doi = "10.1515/IJNSNS.2001.2.4.329",
language = "English",
volume = "2",
pages = "329--342",
journal = "International Journal of Nonlinear Sciences and Numerical Simulation",
issn = "1565-1339",
publisher = "Walter de Gruyter GmbH & Co. KG",
number = "4",

}

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

Research output: Contribution to journalArticle

TY - JOUR

T1 - An Asymptotic Theory for the Nonlinear Analysis of Laminated Cylindrical Shells

AU - Wu, Chih-Ping

AU - Liu, Chi Chuan

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

AB - 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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U2 - 10.1515/IJNSNS.2001.2.4.329

DO - 10.1515/IJNSNS.2001.2.4.329

M3 - Article

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EP - 342

JO - International Journal of Nonlinear Sciences and Numerical Simulation

JF - International Journal of Nonlinear Sciences and Numerical Simulation

SN - 1565-1339

IS - 4

ER -