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Topology optimization for free vibrations using combined approximations
Author(s) -
Bogomolny M.
Publication year - 2009
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.2778
Subject(s) - eigenvalues and eigenvectors , topology optimization , sensitivity (control systems) , vibration , topology (electrical circuits) , mathematics , series (stratigraphy) , factorization , matrix (chemical analysis) , mathematical optimization , basis (linear algebra) , computer science , finite element method , algorithm , engineering , geometry , structural engineering , physics , electronic engineering , paleontology , materials science , quantum mechanics , combinatorics , composite material , biology
This study shows how the Combined Approximations (CA) can be used for reducing the computational effort in Topology Optimization for free vibrations. The previously developed approach is based on the integration of several concepts and methods, including matrix factorization, series expansion, and reduced basis. In this paper the CA method is used for repeated eigenvalue analysis. Adjoint sensitivity analysis is developed such that the inaccuracies of the approximation are taken into consideration. Several 2‐D and 3‐D numerical examples show how optimal topology designs can be achieved by the reduced computational effort compared with the exact eigenvalue analysis. Copyright © 2009 John Wiley & Sons, Ltd.