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An iterative method for finite dimensional structural optimization problems with repeated eigenvalues
Author(s) -
Choi Kyung K.,
Haug Edward J.,
Seong Hwal G.
Publication year - 1983
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.1620190110
Subject(s) - eigenvalues and eigenvectors , mathematics , buckling , differentiable function , optimization problem , projection (relational algebra) , mathematical optimization , mathematical analysis , algorithm , structural engineering , engineering , physics , quantum mechanics
A numerical method for solving finite dimensional structural optimization problems with constraints on natural frequency and on buckling is formulated. The method treats nondifferentiable repeated eigenvalues that have been shown to systematically arise in structural optimization. Recent results on differentiability of eigenvalues are used to develop a generalized gradient projection method for structural optimization. The algorithm is shown to overcome technical difficulties associated with nondifferentiability of repeated eigenvalues. The method is used to solve buckling and vibration optimization problems in which repeated eigenvalues occur.