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Optimal shape of an elastic structure
Author(s) -
Sakawa Yoshiyuki,
Ukai Hiroyuki
Publication year - 1980
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660010407
Subject(s) - mathematics , eigenfunction , eigenvalues and eigenvectors , piecewise , hermite interpolation , interpolation (computer graphics) , hermite polynomials , rayleigh–ritz method , mathematical analysis , numerical analysis , mathematical optimization , computer science , boundary value problem , physics , animation , computer graphics (images) , quantum mechanics
This paper treats an optimal design problem of an elastic upright structure which can be regarded as a column. The optimal shape of the structure, which makes the lowest natural frequency as large as possible, is determined under several equality and inequality constraints. A necessary condition for optimality is derived, and a numerical procedure for obtaining the optimal shape is discussed. The piecewise Hermite interpolation technique and the Rayleigh‐Ritz method are employed for computing the smallest eigenvalue and the corresponding eigenfunction. Several numerical results are presented.