Model‐Size Reduction for Buckling and Vibration Analyses of Anisotropic Panels

An efficient computational procedure is presented for the buckling and vibration analyses of symmetric anisotropic panels. In the proposed procedure, the size of the analysis model of the anisotropic panel is reduced to that of the corresponding orthotropic panel. The two key elements of the procedure are: (1) application of operator splitting technique through the decomposition of the material stiffness matrix of the panel into the sum of orthotropic and nonorthotropic (anisotropic) parts; and (2) use of a reduction method through successive application 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 classical Rayleigh‐Ritz technique is used to substantially reduce the size of the eigenvalue problem. The global approximation vectors are selected to be a few of the eigenvectors corresponding to zero nonorthotropic matrix, and their various‐order derivatives with respect to an anisotropic tracing parameter, identifying all the nonorthotropic material coefficients. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic panel. The effectiveness of the proposed procedure is demonstrated by means of numerical examples.