Re‐analysis procedure based on the mixed formulation

Abstract

A simple and efficient re‐analysis procedure is presented for large‐scale structural systems. The procedure is based on using a mixed formulation with the fundamental unknowns consisting of both stress and displacement parameters. The other key elements of the procedure are: (a) lumping of the large number of design variables into a single tracing parameter; (b) operator splitting or additive decomposition of the different arrays in the finite element equations of the modified structure into the corresponding arrays of the original structure plus correction terms; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov‐Galerkin technique. The finite element method is first used to generate a few approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Bubnov—Galerkin technique. The re‐analysis procedure is applied to the linear static and free vibration problems of plate and shell structures. Changes in both the sizing and shape (configuration) design variables are considered. The high accuracy of the proposed technique, for sizable changes in the design variables, is demonstrated by means of numerical examples of composite plates and shells.

Citation

Noor, A.K. and Peters, J.M. (1987), "Re‐analysis procedure based on the mixed formulation", Engineering Computations, Vol. 4 No. 4, pp. 289-299. https://doi.org/10.1108/eb023707