Model‐size reduction technique for the analysis of symmetric anisotropic structures

Abstract

A two‐step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (a) decomposition of the stiffness matrix into the sum of an orthotropic and non‐orthotropic (anisotropic) parts; and (b) successive application of the finite element method and the classical Rayleigh—Ritz technique. The finite element method is first used to generate 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 selected to be the solution corresponding to zero non‐orthotropic matrix and its various‐order derivatives with respect to an anisotropic tracing parameter (identifying the non‐orthotropic material coefficients). 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 technique is demonstrated by means of numerical examples and its potential for solving other quasi‐symmetric problems is discussed.