Refined Theories for Nonhomogeneous Anisotropic Cylindrical Shells: Part I-Derivation

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Abstract
First approximation thin shell and higher order thick shell correction theories are derived for nonhomogeneous anisotropic cylindrical elastic shells by use of the method of asymptotic expansion in terms of a small parameter along with Reissner's variational principle. The advantages of employing the asymptotic method, in addition to its systematic nature, are that no a priori kinematic or static assumptions need be made or both, that trasverse stresses develop naturally (even in the thin shell analysis) and that thick shell theories follow automatically. Use of the combined method generates various theories based upon different combinations of axial and circumferential length scales introduced in the nondimensionalization of the coordinates. The first approximation theories derived herein for anisotropic materials have their counterparts for isotropic materials. They are: (1)Simplified Donnell theory; (2)simple bending theory; (3)semimembrane theory; and (4)complete Donnell theory.

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