A higher-order theory of moderately thick elastic shells is developed using Reissner’s variational principle with Legendre polynomial expansions representing variation through the thickness of all dependent variables. A truncation scheme is suggested to yield a finite set of governing differential equations. For symmetrically loaded shells of revolution, the equations are cast in first-order form suitable for numerical integration. Results are presented for pressurized cylinders and compared with exact 3-D elasticity solutions and with solutions obtained using the finite-element method. The developed approximate theory contains one level of extension and bending effects beyond what is usually contained in classical shell theory with shear deformation. Estimates are made of thickness-to-mean radius ratios and elastic moduli ratios for which the new theory yields valid results.

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