A Bound Theorem In Eigenvalues and Its Practical Applications

Item

Title
A Bound Theorem In Eigenvalues and Its Practical Applications
Description
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.
Creator
Irons, Bruce M.
Treharne, Gabe
Abstract
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.
Corporate Author
University of Wales, Swansea
Ove Arup and Partners, London
Report Number
AFFDL TR 71-160 p. 245-254
Report Availability
Full text available
Publisher
Wright-Patterson Air Force Base, OH : Air Force Flight Dynamics Laboratory, Air Force Systems Command and Air Force Institute of Technology, Air University
Date
1973
Type
article
Date Issued
1973-12
Provenance
Bombardier/Aero
Distribution Classification
1
Distribution Conflict
No
DTIC Record Exists
No
Format
1 online resource (10 pages) : ill.
Extent
10
Identifier
AD0785968
Is Part Of
Proceedings of the Third Conference on Matrix Methods in Structural Mechanics: Proceedings of the Conference held at Wright-Patterson Air Force Base, Ohio 19-21 October 1971
Media
AFFDLTR71-160article08.pdf

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Items with "Has Part: A Bound Theorem In Eigenvalues and Its Practical Applications"
Title Class
Proceedings of the Third Conference on Matrix Methods in Structural Mechanics: Proceedings of the Conference held at Wright-Patterson Air Force Base, Ohio 19-21 October 1971