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On the Maximization of the Fundamental Eigenvalue in Topology Optimization
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SYSNO ASEP 0323131 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the Maximization of the Fundamental Eigenvalue in Topology Optimization Title O maximalizaci nejmenšího vlastního čísla v topologické optimalizaci Author(s) Achtziger, W. (DE)
Kočvara, Michal (UTIA-B) RID, ORCIDSource Title Structural and Multidisciplinary Optimization - ISSN 1615-147X
Roč. 34, č. 3 (2007), s. 181-195Number of pages 15 s. Language eng - English Country US - United States Keywords Topology optimization ; Vibration of structures ; Optimization of Eigenvalues ; Nonlinear semidefinite programming 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 000248587300001 DOI 10.1007/s00158-007-0117-3 Annotation The paper considers a classic formulation of the topology optimization problem of discrete or discretized structures. The objective function to be maximized is the smallest natural frequency of the structure. We develop non-heuristic mathematical models paying special attention to the situation when some design variables take zero values. These models take into account multiple load conditions, equilibrium of forces, constraints on compliance and volume, and the effect of possible non-structural mass. We discuss serious obstacles for a successful numerical treatment of this formulation such as non-Lipschitzean behavior and even discontinuity of the objective function. As a cure we present an equivalent reformulation as a bilinear semidefinite programming problem without the pitfalls of the original problem. An algorithm is presented for finding an approximation of a globally optimal solution up to a user-defined accuracy. 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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