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| Description
| - 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.
- 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. (en)
- Článek uvažuje klasickou formulaci problému optimalizace topologie diskrétních nebo discretizovaných pružných těles. Cílem je maximalizovat nejmenší přirozené frekvence tělesa. Vyvíjíme neheuristické matematické modely věnující zvláštní pozornost situaci, kdy některé návrhové proměnné mají nulové hodnoty. Tyto modely zohledňují opakovaném zatížení, rovnováhu sil, omezení o konstantním objemu, a možné nestrukturální hmotnosti. Probíráme závažné překážky pro úspěšné numerické řešení této formulace jako nelipschitzovské chování a nespojitost cílového funkcionálu. Prezentujeme ekvivalentní formulaci jako bilineární semidefinitní program. Algoritmus je určen pro hledání přibližného globálně optimálního řešení. (cs)
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| Title
| - On the Maximization of the Fundamental Eigenvalue in Topology Optimization
- On the Maximization of the Fundamental Eigenvalue in Topology Optimization (en)
- O maximalizaci nejmenšího vlastního čísla v topologické optimalizaci (cs)
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| skos:prefLabel
| - On the Maximization of the Fundamental Eigenvalue in Topology Optimization
- On the Maximization of the Fundamental Eigenvalue in Topology Optimization (en)
- O maximalizaci nejmenšího vlastního čísla v topologické optimalizaci (cs)
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| skos:notation
| - RIV/67985556:_____/07:00323131!RIV09-AV0-67985556
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(IAA1075402), Z(AV0Z10750506)
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| http://linked.open...iv/cisloPeriodika
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/67985556:_____/07:00323131
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - Topology optimization; Vibration of structures; Optimization of Eigenvalues; Nonlinear semidefinite programming (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/nazevZdroje
| - Structural and Multidisciplinary Optimization
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| http://linked.open...in/vavai/riv/obor
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| http://linked.open...ichTvurcuVysledku
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| http://linked.open...cetTvurcuVysledku
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| http://linked.open...vavai/riv/projekt
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| http://linked.open...UplatneniVysledku
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| http://linked.open...v/svazekPeriodika
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| http://linked.open...iv/tvurceVysledku
| - Kočvara, Michal
- Achtziger, W.
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| http://linked.open...ain/vavai/riv/wos
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| http://linked.open...n/vavai/riv/zamer
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| issn
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| number of pages
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