A Bound Theorem In Eigenvalues and Its Practical Applications

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Report Number: AFFDL TR 71-160 p. 245-254
Author(s): Irons, Bruce M., Treharne, Gabe
Corporate Author(s): University of Wales, Swansea, Ove Arup and Partners, London
Date of Publication: 1973-12
Pages: 10
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Identifier: This paper is part of a conference proceedings. See AD0785968

A familiar but undervalued theorem is presented, with applications. The theorem is that for positive-definite systems, the eigenvalues are bounded by the extreme element eigenvalues, and also by the extreme eigenvalues of infinitesimal elements. Familiar applications are to the relative stiffnesses of different formulations of the same element, to a roundoff criterion, and to the stability of elastoplastic solutions. Less familiar applications are to the noise dissipation and possible instability of first order marching solutions, and to the instability of creep solutions.

Provenance: Bombardier/Aero

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