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A new approach to 2‐D eigenvalue shape design
Author(s) -
Melnikov Y. U. A.,
Titarenko S. A.
Publication year - 1993
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.1620361205
Subject(s) - eigenvalues and eigenvectors , computation , boundary value problem , mathematics , vibration , shape optimization , material derivative , mathematical optimization , mathematical analysis , computer science , algorithm , structural engineering , finite element method , engineering , physics , quantum mechanics
Abstract A new approach to solve problems in the optimal shape design of eigenvalues is presented. The idea behind the approach is based on a combination of the known material derivative method 4,7 and a specially adapted Green's functions formulation. 14 In the current study, numerical testing has been limited to two‐dimensional shape optimization. The two test cases involve the first eigenvalues of boundary value problems which model (i) free vibrations of a fixed membrane and (ii) natural frequencies of clamped thin plates. The basic algorithm can easily be adapted to serve other types of boundary value problems dealing with the highest eigenvalues that occur in applied mechanics. Computational aspects of the proposed approach, such as accuracy of the obtained sensitivities, cost of computation and so on are discussed in References 16 (in preparation).