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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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 199; H. 25; S. 1744 - 1763
1. Verfasser: Yoon, Gil Ho
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kidlington Elsevier B.V 01.05.2010
Elsevier
Schlagworte:
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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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2010.02.002