Topology optimization of plate structures subject to initial excitations for minimum dynamic performance index
This paper studies optimal topology design of damped vibrating plate structures subject to initial excitations. The design objective is to minimize an integrated square performance measure. The artificial density of the plate element is the topology design variable and the material volume is given....
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| Published in | Structural and multidisciplinary optimization Vol. 53; no. 3; pp. 623 - 633 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2016
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1615-147X 1615-1488 |
| DOI | 10.1007/s00158-015-1350-9 |
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| Abstract | This paper studies optimal topology design of damped vibrating plate structures subject to initial excitations. The design objective is to minimize an integrated square performance measure. The artificial density of the plate element is the topology design variable and the material volume is given. The Lyapunov’s second method is applied to reduce the calculation of performance measure to the solution of the Lyapunov equation. An adjoint sensitivity analysis method is used, which only needs to solve the Lyapunov equation twice. However, when the problem has a large number of degrees of freedom, the solution process of Lyapunov equation is computational costly. Thus, the full model is transformed to a reduced space by mode reduction method. To further reduce the scale of reduced model, we propose a mode screen method to decrease the number of eigenmodes. Numerical examples of optimum topology design of bending plates are presented for illustrating validity and efficiency of our new algorithm. |
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| AbstractList | This paper studies optimal topology design of damped vibrating plate structures subject to initial excitations. The design objective is to minimize an integrated square performance measure. The artificial density of the plate element is the topology design variable and the material volume is given. The Lyapunov’s second method is applied to reduce the calculation of performance measure to the solution of the Lyapunov equation. An adjoint sensitivity analysis method is used, which only needs to solve the Lyapunov equation twice. However, when the problem has a large number of degrees of freedom, the solution process of Lyapunov equation is computational costly. Thus, the full model is transformed to a reduced space by mode reduction method. To further reduce the scale of reduced model, we propose a mode screen method to decrease the number of eigenmodes. Numerical examples of optimum topology design of bending plates are presented for illustrating validity and efficiency of our new algorithm. |
| Author | Wang, Bo Ping Yan, Kun Cheng, Gengdong |
| Author_xml | – sequence: 1 givenname: Kun surname: Yan fullname: Yan, Kun email: yankun@mail.dlut.edu.cn organization: State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology – sequence: 2 givenname: Gengdong surname: Cheng fullname: Cheng, Gengdong organization: State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology – sequence: 3 givenname: Bo Ping surname: Wang fullname: Wang, Bo Ping organization: Department of Mechanical and Aerospace Engineering, University of Texas at Arlington |
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| CitedBy_id | crossref_primary_10_1007_s00158_017_1886_y crossref_primary_10_1007_s00158_019_02282_y crossref_primary_10_1016_j_compstruc_2017_05_002 crossref_primary_10_1016_j_cma_2024_116787 crossref_primary_10_1016_j_tws_2022_108901 crossref_primary_10_1016_j_jsv_2017_12_015 crossref_primary_10_1016_j_finel_2017_12_003 crossref_primary_10_1299_transjsme_18_00343 crossref_primary_10_1007_s00158_024_03815_w crossref_primary_10_1016_j_compstruc_2018_09_004 crossref_primary_10_1016_j_cma_2019_01_004 crossref_primary_10_1016_j_engstruct_2023_116433 crossref_primary_10_1007_s00158_017_1765_6 crossref_primary_10_1007_s00158_017_1769_2 crossref_primary_10_1016_j_cma_2018_09_022 crossref_primary_10_1016_j_compstruc_2019_07_008 crossref_primary_10_1016_j_jsv_2018_06_003 crossref_primary_10_1016_j_jsv_2020_115442 crossref_primary_10_1007_s00158_019_02451_z crossref_primary_10_1016_j_ijheatmasstransfer_2024_125815 |
| Cites_doi | 10.1007/s00158-013-1024-4 10.1016/S0045-7825(02)00559-5 10.1002/nme.1620350707 10.1016/j.jsv.2013.01.029 10.1061/(ASCE)0733-9399(2006)132:1(46) 10.1016/j.jsv.2007.08.024 10.1016/0045-7825(91)90046-9 10.1080/0305215X.2012.709513 10.1016/j.jsv.2012.09.006 10.1016/j.finel.2007.06.006 10.1016/j.compstruc.2009.11.011 10.1007/s00158-005-0575-4 10.1016/j.jsv.2010.05.015 10.1016/j.jsv.2008.06.023 10.1080/0305215X.2013.832235 10.1115/1.2948373 10.1007/s001580050176 10.2514/3.3027 10.1016/0022-460X(84)90637-0 10.1007/s00158-012-0829-x 10.1007/BF01650949 10.2514/3.2874 10.1016/j.ijsolstr.2007.04.012 10.1016/j.cma.2005.02.002 10.1002/nme.1620240207 10.1155/2011/830793 10.1007/s00158-011-0746-4 10.1115/96-DETC/DAC-1477 10.1007/978-3-662-05086-6 10.1007/s00158-015-1323-z |
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| Keywords | Lyapunov’s second method Topology optimization Adjoint method Mode screen method |
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| Snippet | This paper studies optimal topology design of damped vibrating plate structures subject to initial excitations. The design objective is to minimize an... |
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| SubjectTerms | Algorithms Computational Mathematics and Numerical Analysis Engineering Engineering Design Excitation Mathematical analysis Performance indices Plates (structural members) Research Paper Sensitivity analysis Theoretical and Applied Mechanics Topology optimization |
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| Title | Topology optimization of plate structures subject to initial excitations for minimum dynamic performance index |
| URI | https://link.springer.com/article/10.1007/s00158-015-1350-9 https://www.proquest.com/docview/2262592549 |
| Volume | 53 |
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