Structural topology optimization for frequency response problem using model reduction schemes

This study uses model reduction (MR) schemes such as the mode superposition (MS), Ritz vector (RV), and quasi-static Ritz vector (QSRV) methods, which reduce the size of the dynamic stiffness matrix of dynamic structures, to calculate dynamic responses and sensitivity values with adequate efficiency...

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Vydané v:	Computer methods in applied mechanics and engineering Ročník 199; číslo 25; s. 1744 - 1763
Hlavný autor:	Yoon, Gil Ho
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Kidlington Elsevier B.V 01.05.2010 Elsevier
Predmet:	Dynamic structural analysis Dynamics Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Mode superposition method Model reduction Model reduction method Physics Quasi-static Ritz vector method Recreational vehicles Reduction Ritz vector method Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Topology optimization Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...) Ritz vector method Topology optimization Mode superposition method Quasi-static Ritz vector method Model reduction method Geometrical shape Stiffness matrix Vibration Eigenmode Frequency domain method Quasi static theory Topology Vector method Modeling Dynamic method Optimization Truncation Finite element method Frequency response Reduced order systems Ritz method Reliability Structural analysis
ISSN:	0045-7825, 1879-2138
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Popis
Shrnutí:	This study uses model reduction (MR) schemes such as the mode superposition (MS), Ritz vector (RV), and quasi-static Ritz vector (QSRV) methods, which reduce the size of the dynamic stiffness matrix of dynamic structures, to calculate dynamic responses and sensitivity values with adequate efficiency and accuracy for topology optimization in the frequency domain. The calculation of structural responses to dynamic excitation using the framework of the finite element (FE) procedure usually requires a significant amount of computation time; that is mainly attributable to repeated inversions of dynamic stiffness matrices depending on time or frequency intervals, which hastens the dissemination of the MR schemes in the analysis. However, using well-established MR schemes in topology optimization has not been prevalent. Therefore, this study conducted a comprehensive investigation to highlight the drawbacks and advantages of these MR schemes for topology optimization. In the results, the MS method, which generates reduction bases by considering some of the lowest eigenmodes, can lose the accuracy in both approximated structural responses and sensitivity values due to locally vibrating eigenmodes and higher mode truncation in the solid isotropic material with penalization (SIMP) approach. In addition, the RV and QSRV methods, which generate reduction bases by considering the external force, mass, and stiffness matrices of a structure, can be used as alterative model reduction schemes for stable optimization. Through several analysis and design examples, the efficiency and reliability of the model reduction schemes for topology optimization are compared and validated.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0045-7825 1879-2138
DOI:	10.1016/j.cma.2010.02.002