Analysis of Laminated Anisotropic Shells of Revolution

Abstract

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.