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Structural Topology Optimization with Eigenvalues
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SYSNO ASEP 0323133 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Structural Topology Optimization with Eigenvalues Title Strukturální topologická optimalizace s vlastními čísly Author(s) Achtziger, W. (DE)
Kočvara, Michal (UTIA-B) RID, ORCIDSource Title SIAM Journal on Optimization. - : SIAM Society for Industrial and Applied Mathematics - ISSN 1052-6234
Roč. 18, č. 4 (2007), s. 1129-1164Number of pages 36 s. Language eng - English Country US - United States Keywords Topology optimization ; Vibration of structures ; Optimization of Eigenvalues Subject RIV BA - General Mathematics R&D Projects IAA1075402 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10750506 - UTIA-B (2005-2011) UT WOS 000207940400001 DOI https://doi.org/10.1137/060651446 Annotation The paper considers different problem formulations of topology optimization of discrete or discretized structures with eigenvalues as constraints or as objective functions. We study multiple load case formulations of minimum volume or weight, minimum compliance problems and of the problem of maximizing the minimal eigenvalue of the structure including the effect of non-structural mass. The paper discusses interrelations of the problems and, in particular, shows how solutions of one problem can be derived from solutions of the other ones. This allows for the calculation of guaranteed global optimizers of the original problems by the use of modern solution techniques of semidefinite programming. For the problem of maximization of the minimum eigenvalue we show how to verify the global optimality and present an algorithm for finding a tight approximation of a globally optimal solution. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2009
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