Nonlinear analysis of anisotropic panels

Abstract

A computational procedure is presented for the efficient nonlinear analysis of symmetric anisotropic panels. The three key elements of the procedure are: 1) use of three-field mixed models having independent interpolation (shape) functions for stress resultants, strain components, and generalized displacements, with the stress resultants and strain components allowed to be discontinuous at interelement boundaries; 2) decomposition of the material stiffness matrix into the sum of an orthotropic and a nonorthotropic (anisotropic) part; and 3) 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 amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The global approximation vectors are taken to be various-order derivatives of the strain components, stress resultants, and generalized displacements with respect to an anisotropic tracing parameter and a load parameter; they are evaluated at zero values of the two parameters. The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed computational procedure is demonstrated by means of a numerical example, and its potential for solving quasi-symmetric nonlinear problems of composite structures is discussed.