CONVERGENCE OF THE CLASSICAL RAYLEIGH-RITZ METHOD AND THE FINITE-ELEMENT METHOD

The Rayleigh-Ritz method is a technique for approximating the eigensolution associated with a distributed structure. The method amounts to approximating the solution of a differential eigenvalue problem having no known closed-form solution by a finite series of trial functions, thus replacing the differential eigenvalue problem by an algebraic eigenvalue problem. The finite element method can be regarded as a Rayleigh-Ritz method, at least for structures. The main difference between the finite element method and the classical Rayleigh-Ritz method lies in the nature of the admissible functions. An important question in both the classical Rayleigh-Ritz method and the finite element method is the speed of convergence. It is demonstrated in this paper that convergence of the classical Rayleigh-Ritz method can be vastly improved by introducing a new class of admissible functions, called quasi-comparison functions. Factors affecting the convergence of the finite element method are also discussed. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.