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A successive bounding method to find the exact eigenvalues of transcendental stiffness matrix formulations
Author(s) -
Ye Jianqiao,
Williams F. W.
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620380612
Subject(s) - eigenvalues and eigenvectors , mathematics , transcendental equation , stiffness matrix , bounding overwatch , matrix (chemical analysis) , mathematical analysis , stiffness , quadratic equation , buckling , numerical analysis , geometry , structural engineering , computer science , engineering , physics , materials science , quantum mechanics , artificial intelligence , composite material
An alternative algorithm for finding exact natural frequencies or buckling loads from the transcendental, e.g. dynamic, stiffness matrix method is presented in this paper and evaluated by using the plate assembly testbed program VICONOPT. The method is based on the bounding properties of the eigenvalues provided by either linear or quadratic matrix pencils on the exact solutions of the transcendental eigenvalue problem. The procedure presented has five stages, including two accuracy checking stages which prevent unnecessary calculations. Numerical tests on buckling of general anisotropic plate assemblies show that significant time savings can be achieved compared with an earlier multiple determinant parabolic interpolation method.