Godunov-conte method for solution of eigenvalue problems and its applications

Author Type

Faculty

Co-Author Type 1

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Journal of Applied Mechanics Transactions ASME

Publication Status

Version of Record

Abstract

The method originally presented by Godunou 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. © 1977 by ASME.

First Page

776

Last Page

779

DOI

10.1115/1.3424177

Publication Date

1-1-1977

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