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A simple penalty finite element formulation is presented for the largerotation and postbuckling analyses of curved beams. The analytical formulation is based on a form of Reissner's largedeformation theory with the transverse shear deformation and the extensibility of the center line constrained through the use of the penalty method. Reduced integration is used in evaluating the elemental arrays, and a procedure is outlined for determining the critical points in the solution path. Numerical results are presented to demonstrate the effectiveness of the finite elements developed.

A predictor‐corrector approach is presented for calculating the composite shear correction factors and analyzing multilayered composite cylinders. In the predictor phase a two‐dimensional first‐order shear deformation theory is used to predict the gross response characteristics of the cylinder (vibration frequencies, average through‐the‐thickness displacements, rotations, and transverse shear strain energy per unit area) as well as the in‐plane strains and stresses in the thickness direction. The three‐dimensional equilibrium equations and constitutive relations are then used to compute the transverse stresses and strains as well as the transverse shear factors, and they are also used to correct the predicted response quantities of the cylinder. For simply supported multilayered cylinders the response quantities obtained by using the proposed approach are shown to be in close agreement with three‐dimensional elasticity solutions for a wide range of lamination and geometric parameters. Also, the potential of the proposed approach for use in conjunction with large‐scale finite element models of composite cylinders is outlined.

An efficient computational procedure is presented for the analysis of laminated anisotropic shells of revolution and assessing the sensitivity of their response to anisotropic (nonorthotropic) material coefficients. The analytical formulation is based on a form of the Sanders‐Budiansky shell theory, including the effects of both the transverse shear deformation and the laminated anisotropic material response. Each of the shell variables is expanded in a Fourier series in the circumferential coordinate, and a two‐field mixed finite element model is used for the discretization in the meridional direction. The three key elements of the procedure are: (1) use of mixed finite element models in the meridional direction with discontinuous stress resultants at the element interfaces; (2) operator splitting, or decomposition of the material compliance matrix of the shell into the sum of an orthotropic and nonorthotropic (anisotropic) part; and (3) application of a reduction method through the successive use of the finite element method and the classical Rayleigh‐Ritz technique. The finite element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh‐Ritz technique. The potential of the proposed procedure is discussed and numerical results are presented to demonstrate its effectiveness.