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Derivatives of eigenvectors of locally modified structures
Author(s) -
Hirai Itio,
Kashiwaki Mitsuhiro
Publication year - 1977
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.1620111110
Subject(s) - eigenvalues and eigenvectors , truss , mathematics , mathematical analysis , structural engineering , engineering , physics , quantum mechanics
In this study a method for obtaining the derivatives of eigenvectors of a locally modified structure with respect to a design variable is presented. Eigensolution to the locally modified structure is expressed by equations consisting of the condensed matrices only which refer to the modified part. The analysis presented herein is developed in conjunction with eigensolution to the modified structure, and the derived fundamental equations are also represented by the same type of condensed matrices only. So, advantages are realized both in computational effort and in computer storage, if the modified part is small compared with the unmodified part. To find exact results, complete eigensolution to the unmodified structure needs to be given. Approximate results are obtained from a few lower eigenvectors and eigenvalues. A pin‐jointed truss is solved as a numerical example.