A refined asymptotic theory for the nonlinear analysis of laminated cylindrical shells

Chih-Ping Wu, Yen Wei Chi

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Within the framework of the three-dimensional (3D) nonlinear elasticity, a refined asymptotic theory is developed for the nonlinear analysis of laminated circular cylindrical shells. In the present formulation, the basic equations including 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. After using proper nondimensionalization, asymptotic expansion, successive integration and then bringing the effects of transverse shear deformation into the leading-order level, we obtain recursive sets of the governing equations for various orders. It is shown that the von Karman-type first-order shear deformation theory (FSDT) is derived as a first-order approximation to the 3D nonlinear theory. The differential operators in the linear terms of governing equations for the leading order problem remain identical to those for the higher-order problems. 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. It is also illustrated that the nonlinear analysis of laminated circular cylindrical shells can be made in a hierarchic and consistent way.

Original language English 337-352 16 Computers, Materials and Continua 1 4 Published - 2004 Dec 1

Fingerprint

Cylindrical Shell
Nonlinear analysis
Asymptotic Theory
Nonlinear Analysis
Shear deformation
Shear Deformation
Elasticity
Governing equation
Term
Hooke's law
First-order
Finite Strain
Nonlinear Elasticity
Deformation Theory
Elastic Material
Asymptotic Expansion
Differential operator
Transverse
Higher Order
Unknown

All Science Journal Classification (ASJC) codes

• Biomaterials
• Modelling and Simulation
• Mechanics of Materials
• Computer Science Applications
• Electrical and Electronic Engineering

Cite this

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title = "A refined asymptotic theory for the nonlinear analysis of laminated cylindrical shells",
abstract = "Within the framework of the three-dimensional (3D) nonlinear elasticity, a refined asymptotic theory is developed for the nonlinear analysis of laminated circular cylindrical shells. In the present formulation, the basic equations including 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. After using proper nondimensionalization, asymptotic expansion, successive integration and then bringing the effects of transverse shear deformation into the leading-order level, we obtain recursive sets of the governing equations for various orders. It is shown that the von Karman-type first-order shear deformation theory (FSDT) is derived as a first-order approximation to the 3D nonlinear theory. The differential operators in the linear terms of governing equations for the leading order problem remain identical to those for the higher-order problems. 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. It is also illustrated that the nonlinear analysis of laminated circular cylindrical shells can be made in a hierarchic and consistent way.",
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In: Computers, Materials and Continua, Vol. 1, No. 4, 01.12.2004, p. 337-352.

Research output: Contribution to journalArticle

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AU - Wu, Chih-Ping

AU - Chi, Yen Wei

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N2 - Within the framework of the three-dimensional (3D) nonlinear elasticity, a refined asymptotic theory is developed for the nonlinear analysis of laminated circular cylindrical shells. In the present formulation, the basic equations including 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. After using proper nondimensionalization, asymptotic expansion, successive integration and then bringing the effects of transverse shear deformation into the leading-order level, we obtain recursive sets of the governing equations for various orders. It is shown that the von Karman-type first-order shear deformation theory (FSDT) is derived as a first-order approximation to the 3D nonlinear theory. The differential operators in the linear terms of governing equations for the leading order problem remain identical to those for the higher-order problems. 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. It is also illustrated that the nonlinear analysis of laminated circular cylindrical shells can be made in a hierarchic and consistent way.

AB - Within the framework of the three-dimensional (3D) nonlinear elasticity, a refined asymptotic theory is developed for the nonlinear analysis of laminated circular cylindrical shells. In the present formulation, the basic equations including 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. After using proper nondimensionalization, asymptotic expansion, successive integration and then bringing the effects of transverse shear deformation into the leading-order level, we obtain recursive sets of the governing equations for various orders. It is shown that the von Karman-type first-order shear deformation theory (FSDT) is derived as a first-order approximation to the 3D nonlinear theory. The differential operators in the linear terms of governing equations for the leading order problem remain identical to those for the higher-order problems. 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. It is also illustrated that the nonlinear analysis of laminated circular cylindrical shells can be made in a hierarchic and consistent way.

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