Open Access

ARTICLE

A Refined Asymptotic Theory for the Nonlinear Analysis of Laminated Cylindrical Shells

Chih-Ping Wu¹, Yen-Wei Chi¹

1NCKU, Tainan, Taiwan, ROC

Computers, Materials & Continua 2004, 1(4), 337-352. https://doi.org/10.3970/cmc.2004.001.337

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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Keywords

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