{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T01:32:55Z","timestamp":1769909575264,"version":"3.49.0"},"reference-count":22,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T00:00:00Z","timestamp":1675900800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ningbo natural science foundation","award":["202003N4169"],"award-info":[{"award-number":["202003N4169"]}]},{"name":"Ningbo natural science foundation","award":["LGF22E080021"],"award-info":[{"award-number":["LGF22E080021"]}]},{"name":"Ningbo natural science foundation","award":["52008215"],"award-info":[{"award-number":["52008215"]}]},{"name":"Ningbo natural science foundation","award":["LQ20E080013"],"award-info":[{"award-number":["LQ20E080013"]}]},{"name":"Ningbo natural science foundation","award":["2019B10076"],"award-info":[{"award-number":["2019B10076"]}]},{"name":"Zhejiang public welfare project","award":["202003N4169"],"award-info":[{"award-number":["202003N4169"]}]},{"name":"Zhejiang public welfare project","award":["LGF22E080021"],"award-info":[{"award-number":["LGF22E080021"]}]},{"name":"Zhejiang public welfare project","award":["52008215"],"award-info":[{"award-number":["52008215"]}]},{"name":"Zhejiang public welfare project","award":["LQ20E080013"],"award-info":[{"award-number":["LQ20E080013"]}]},{"name":"Zhejiang public welfare project","award":["2019B10076"],"award-info":[{"award-number":["2019B10076"]}]},{"name":"Natural Science Foundation of China","award":["202003N4169"],"award-info":[{"award-number":["202003N4169"]}]},{"name":"Natural Science Foundation of China","award":["LGF22E080021"],"award-info":[{"award-number":["LGF22E080021"]}]},{"name":"Natural Science Foundation of China","award":["52008215"],"award-info":[{"award-number":["52008215"]}]},{"name":"Natural Science Foundation of China","award":["LQ20E080013"],"award-info":[{"award-number":["LQ20E080013"]}]},{"name":"Natural Science Foundation of China","award":["2019B10076"],"award-info":[{"award-number":["2019B10076"]}]},{"name":"Zhejiang Province Natural Science Foundation","award":["202003N4169"],"award-info":[{"award-number":["202003N4169"]}]},{"name":"Zhejiang Province Natural Science Foundation","award":["LGF22E080021"],"award-info":[{"award-number":["LGF22E080021"]}]},{"name":"Zhejiang Province Natural Science Foundation","award":["52008215"],"award-info":[{"award-number":["52008215"]}]},{"name":"Zhejiang Province Natural Science Foundation","award":["LQ20E080013"],"award-info":[{"award-number":["LQ20E080013"]}]},{"name":"Zhejiang Province Natural Science Foundation","award":["2019B10076"],"award-info":[{"award-number":["2019B10076"]}]},{"name":"the project of Ningbo science and technology innovation 2025","award":["202003N4169"],"award-info":[{"award-number":["202003N4169"]}]},{"name":"the project of Ningbo science and technology innovation 2025","award":["LGF22E080021"],"award-info":[{"award-number":["LGF22E080021"]}]},{"name":"the project of Ningbo science and technology innovation 2025","award":["52008215"],"award-info":[{"award-number":["52008215"]}]},{"name":"the project of Ningbo science and technology innovation 2025","award":["LQ20E080013"],"award-info":[{"award-number":["LQ20E080013"]}]},{"name":"the project of Ningbo science and technology innovation 2025","award":["2019B10076"],"award-info":[{"award-number":["2019B10076"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The sensitivity reanalysis technique is an important tool for selecting the search direction in structural optimization design. Based on the decomposition perturbation of the flexibility matrix, a fast and exact structural displacement sensitivity reanalysis method is proposed in this work. For this purpose, the direct formulas for computing the first-order and second-order sensitivities of structural displacements are derived. The algorithm can be applied to a variety of the modifications in optimal design, including the low-rank modifications, high-rank modifications, small modifications and large modifications. Two numerical examples are given to verify the effectiveness of the proposed approach. The results show that the presented algorithm is exact and effective. Compared with the existing two reanalysis methods, this method has obvious advantages in calculation accuracy and efficiency. This new algorithm is very useful for calculating displacement sensitivity in engineering problems such as structure optimization, model correction and defect detection.<\/jats:p>","DOI":"10.3390\/axioms12020179","type":"journal-article","created":{"date-parts":[[2023,2,9]],"date-time":"2023-02-09T02:55:54Z","timestamp":1675911354000},"page":"179","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Fast Calculation Method for Sensitivity Analysis Using Matrix Decomposition Technique"],"prefix":"10.3390","volume":"12","author":[{"given":"Qiuwei","family":"Yang","sequence":"first","affiliation":[{"name":"School of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, China"},{"name":"Engineering Research Center of Industrial Construction in Civil Engineering of Zhejiang, Ningbo University of Technology, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xi","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, China"},{"name":"Engineering Research Center of Industrial Construction in Civil Engineering of Zhejiang, Ningbo University of Technology, Ningbo 315211, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106536","DOI":"10.1016\/j.ymssp.2019.106536","article-title":"A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives","volume":"138","author":"Lin","year":"2020","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Yang, Q., and Peng, X. (2020). An Exact Method for Calculating the Eigenvector Sensitivities. Appl. Sci., 10.","DOI":"10.3390\/app10072577"},{"key":"ref_3","unstructured":"Kirsch, U. (2008). Reanalysis of Structures, Springer."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1002\/nme.7129","article-title":"A highly efficient method for structural model reduction","volume":"124","author":"Yang","year":"2023","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1016\/S0307-904X(02)00046-X","article-title":"Static reanalysis of discrete elastic structures with reflexive inverse","volume":"26","author":"Cheikh","year":"2002","journal-title":"Appl. Math. Model."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"673","DOI":"10.1002\/nme.1084","article-title":"A universal method for structural static reanalysis of topological modifications","volume":"61","author":"Chen","year":"2004","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1002\/cnm.812","article-title":"Static reanalysis of structures with added degrees of freedom","volume":"22","author":"Wu","year":"2006","journal-title":"Commun. Numer. Methods Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s00158-012-0758-8","article-title":"A hybrid Fox and Kirsch\u2019s reduced basis method for structural static reanalysis","volume":"46","author":"Zuo","year":"2012","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"823","DOI":"10.2514\/3.48671","article-title":"Sensitivity analysis of discrete structural systems","volume":"24","author":"Adelman","year":"1986","journal-title":"AIAA J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-009-0369-1","article-title":"Reanalysis and sensitivity reanalysis by combined approximations","volume":"40","author":"Kirsch","year":"2009","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s00366-007-0062-1","article-title":"Efficient structural optimization using reanalysis and sensitivity reanalysis","volume":"23","author":"Kirsch","year":"2007","journal-title":"Eng. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1399","DOI":"10.1007\/s00158-016-1586-z","article-title":"Sensitivity reanalysis of vibration problem using combined approximations method","volume":"55","author":"Zuo","year":"2017","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1504\/IJVD.2014.064546","article-title":"Component sensitivity analysis of conceptual vehicle body for lightweight design under static and dynamic stiffness demands","volume":"66","author":"Chen","year":"2014","journal-title":"Int. J. Veh. Des."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s00158-002-0170-x","article-title":"Issues of commercial optimization software development","volume":"23","author":"Thomas","year":"2002","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/j.advengsoft.2018.02.009","article-title":"Fast sensitivity reanalysis methods assisted by Independent Coefficients and Indirect Factorization Updating strategies","volume":"119","author":"Liu","year":"2018","journal-title":"Adv. Eng. Softw."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1007\/s00158-015-1368-z","article-title":"Sensitivity reanalysis of static displacement using Taylor series expansion and combined approximate method","volume":"53","author":"Zuo","year":"2016","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1177\/1077546309360052","article-title":"A new damage identification method based on structural flexibility disassembly","volume":"17","author":"Yang","year":"2011","journal-title":"J. Vib. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1177\/1475921710379517","article-title":"Structural damage localization and quantification using static test data","volume":"10","author":"Yang","year":"2011","journal-title":"Struct. Health Monit."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3599","DOI":"10.2514\/1.J057832","article-title":"Fast and Exact Algorithm for Structural Static Reanalysis Based on Flexibility Disassembly Perturbation","volume":"57","author":"Yang","year":"2019","journal-title":"AIAA J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.engstruct.2006.05.019","article-title":"Eigen-parameter decomposition of element matrices for structural damage detection","volume":"29","author":"Di","year":"2007","journal-title":"Eng. Struct."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1002\/nme.87","article-title":"Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas","volume":"50","author":"Garcelon","year":"2001","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_22","first-page":"8212730","article-title":"Structural Reanalysis Based on FRFs Using Sherman\u2013Morrison\u2013Woodbury Formula","volume":"3","author":"Ren","year":"2020","journal-title":"Shock Vib."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/179\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:28:05Z","timestamp":1760120885000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/12\/2\/179"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,9]]},"references-count":22,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,2]]}},"alternative-id":["axioms12020179"],"URL":"https:\/\/doi.org\/10.3390\/axioms12020179","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,9]]}}}