Godunov-Conte Method for Solution of Eigenvalue Problems and Its Applications

[+] Author and Article Information
I. Elishakoff, M. Charmats

Department of Aeronautical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

J. Appl. Mech 44(4), 776-779 (Dec 01, 1977) (4 pages) doi:10.1115/1.3424177 History: Received February 01, 1977; Revised June 01, 1977; Online July 12, 2010


The method originally presented by Godunov and modified by Conte for solution of two-point boundary-value problems, is outlined here as applied to eigenvalue problems. The method (which avoids the loss of accuracy resulting from the numerical treatment, often associated with stability and vibration analysis of elastic bodies) consists of parallel integration of the set of k homogeneous equations under the Kronecker-delta initial conditions which are orthogonal (k being the number of “missing” conditions), after each step. Subject to Conte’s test, the set of solutions is reorthogonalized by the Gram-Schmidt procedure and integration continues. The procedure prevents flattening of the base solutions, which otherwise become numerically dependent. The method is applied to stability analysis of polar orthotropic plates, and as in the isotropic case (as shown by Yamaki), it is seen that assumption of symmetric buckling results in a stability overestimate for an annular plate.

Copyright © 1977 by ASME
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