A reanalysis method for local modification and the application in large-scale problems
A novel reanalysis method, named independent coefficients (IC) method is suggested in this study. This method is proposed to reanalyze structures with local modification which leads to a low-rank change in the stiffness matrix. IC method requires only initial solution as input, and can determine the...
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| Published in | Structural and multidisciplinary optimization Vol. 49; no. 6; pp. 915 - 930 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.06.2014
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1615-147X 1615-1488 |
| DOI | 10.1007/s00158-013-1022-6 |
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| Abstract | A novel reanalysis method, named independent coefficients (IC) method is suggested in this study. This method is proposed to reanalyze structures with local modification which leads to a low-rank change in the stiffness matrix. IC method requires only initial solution as input, and can determine the independent coefficients for each degree of freedoms (DOFs) influenced by structural modifications. Since any extra operations such as decomposition of the initial stiffness matrix is not involved in computation procedure, the IC is a “cheap” algorithm and can be an alternative choice for reanalysis. In order to verify the performance of IC method, several large scale numerical examples are tested. The results demonstrate that the IC method has high accuracy as well as efficiency when the modification is local. The cases involving beyond 1,500,000 DOFs and 3,000,000 DOFs show that IC method has low demands on computer storage, and large scale problems can be easily reanalyzed by this method. |
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| AbstractList | A novel reanalysis method, named independent coefficients (IC) method is suggested in this study. This method is proposed to reanalyze structures with local modification which leads to a low-rank change in the stiffness matrix. IC method requires only initial solution as input, and can determine the independent coefficients for each degree of freedoms (DOFs) influenced by structural modifications. Since any extra operations such as decomposition of the initial stiffness matrix is not involved in computation procedure, the IC is a “cheap” algorithm and can be an alternative choice for reanalysis. In order to verify the performance of IC method, several large scale numerical examples are tested. The results demonstrate that the IC method has high accuracy as well as efficiency when the modification is local. The cases involving beyond 1,500,000 DOFs and 3,000,000 DOFs show that IC method has low demands on computer storage, and large scale problems can be easily reanalyzed by this method. |
| Author | Li, Guangyao Huang, Guanxin Wang, Hu |
| Author_xml | – sequence: 1 givenname: Guanxin surname: Huang fullname: Huang, Guanxin organization: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University – sequence: 2 givenname: Hu surname: Wang fullname: Wang, Hu email: wanghu@hnu.edu.cn organization: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University – sequence: 3 givenname: Guangyao surname: Li fullname: Li, Guangyao organization: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University |
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| Cites_doi | 10.1002/nme.2778 10.1007/s00158-010-0610-y 10.1016/j.finel.2007.09.003 10.3901/JME.2011.18.086 10.1108/02644409810244129 10.1007/s00158-009-0369-1 10.1016/S0141-0296(98)00111-4 10.1016/j.cma.2005.09.013 10.1002/nme.2536 10.1007/s001580100112 10.1016/S0045-7825(03)00201-9 10.1007/s001580050141 10.1002/nme.1084 |
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| References_xml | – reference: KirschUBogomolniMSheinmanINonlinear dynamic reanalysis of structures by combined approximationsComput Methods Appl Mech Eng20061954420443210.1016/j.cma.2005.09.0131119.74020 – reference: ZuoWJXuTZhangHXuTSFast structural optimization with frequency constraints by genetic algorithm using adaptive eigenvalue reanalysis methodsStruct Multididc Optim20114379981010.1007/s00158-010-0610-y – reference: KirschUCombined approximation – a general reanalysis approach for structural optimizationStruct Multidisc Optim2000209710610.1007/s001580050141 – reference: HelfensteinRKokoJParallel preconditioned conjugate gradient algorithm on GPUJ Comput Appl Math2011101016 – reference: KirschUReanalysis and sensitivity reanalysis by combined approximationStruct Multidisc Optim20104011510.1007/s00158-009-0369-11274.742752565053 – reference: AmirOBendsøeMPSigmundOApproximate reanalysis in topology optimizationInt J Numer Meth Eng2009781474149110.1002/nme.25361183.74216 – reference: KirschUPapalambrosPYStructural reanalysis for topological modifications – a unified approachStruct Multidisc Optim20012133334410.1007/s001580100112 – reference: QuerinOMStevenGPXieYMEvolutionary structural optimization (ESO) using a bidirectional algorithmEng Comput1998151031104810.1108/026444098102441290938.74056 – reference: BogomolnyMTopology optimization for free vibrations using combined approximationsInt J Numer Meth Eng2010826176361188.74046 – reference: HuangCChenSLiuZStructural modal reanalysis for topological modifications of finite element systemsEng Struct20002230431010.1016/S0141-0296(98)00111-4 – reference: HeJJJiangJSXuBModal reanalysis methods for structural large topological modifications with added degrees of freedom and non-classical dampingFinite Elem Anal Des200744758510.1016/j.finel.2007.09.003 – reference: WuBSLiZGLiSHThe implementation of a vector-valued rational approximate method in structural reanalysis problemsComput Methods Appl Eng20031921773178410.1016/S0045-7825(03)00201-91044.74053 – reference: Wu JP, Wang ZH, Li XM (2004) Efficient solution the parallel computing of sparse linear system. Hunan Science and Technology Press, pp 23–41, pp 273–280 – reference: ChenSHYangZJA universal method for structural static reanalysis of topological modificationsInt J Numer Meth Eng20046167368610.1002/nme.10841075.74610 – reference: HuangGWangHGaoGLiGModified combined approximations and the application in reanalysis of vehicle frame stiffnessJ Mech Eng201147869210.3901/JME.2011.18.086 – reference: YangZJChenSHWuXMAn iterative combined approximation approach for structural static reanalysis of topological modificationsActa Mech Sinica200436611616 – reference: KirschUDesign-oriented analysis of structures2002LondonKluwer Academic Publisher1091191011.74003 – volume: 82 start-page: 617 year: 2010 ident: 1022_CR12 publication-title: Int J Numer Meth Eng doi: 10.1002/nme.2778 – volume: 10 start-page: 10 year: 2011 ident: 1022_CR16 publication-title: J Comput Appl Math – volume: 43 start-page: 799 year: 2011 ident: 1022_CR14 publication-title: Struct Multididc Optim doi: 10.1007/s00158-010-0610-y – volume: 44 start-page: 75 year: 2007 ident: 1022_CR10 publication-title: Finite Elem Anal Des doi: 10.1016/j.finel.2007.09.003 – ident: 1022_CR15 – volume: 47 start-page: 86 year: 2011 ident: 1022_CR6 publication-title: J Mech Eng doi: 10.3901/JME.2011.18.086 – volume: 15 start-page: 1031 year: 1998 ident: 1022_CR17 publication-title: Eng Comput doi: 10.1108/02644409810244129 – volume: 40 start-page: 1 year: 2010 ident: 1022_CR2 publication-title: Struct Multidisc Optim doi: 10.1007/s00158-009-0369-1 – volume: 22 start-page: 304 year: 2000 ident: 1022_CR9 publication-title: Eng Struct doi: 10.1016/S0141-0296(98)00111-4 – volume: 195 start-page: 4420 year: 2006 ident: 1022_CR11 publication-title: Comput Methods Appl Mech Eng doi: 10.1016/j.cma.2005.09.013 – volume: 78 start-page: 1474 year: 2009 ident: 1022_CR13 publication-title: Int J Numer Meth Eng doi: 10.1002/nme.2536 – volume: 36 start-page: 611 year: 2004 ident: 1022_CR5 publication-title: Acta Mech Sinica – volume: 21 start-page: 333 year: 2001 ident: 1022_CR3 publication-title: Struct Multidisc Optim doi: 10.1007/s001580100112 – volume: 192 start-page: 1773 year: 2003 ident: 1022_CR7 publication-title: Comput Methods Appl Eng doi: 10.1016/S0045-7825(03)00201-9 – start-page: 109 volume-title: Design-oriented analysis of structures year: 2002 ident: 1022_CR1 – volume: 20 start-page: 97 year: 2000 ident: 1022_CR8 publication-title: Struct Multidisc Optim doi: 10.1007/s001580050141 – volume: 61 start-page: 673 year: 2004 ident: 1022_CR4 publication-title: Int J Numer Meth Eng doi: 10.1002/nme.1084 |
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