{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T14:40:09Z","timestamp":1747665609076,"version":"3.40.5"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T00:00:00Z","timestamp":1746748800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T00:00:00Z","timestamp":1746748800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,7]]},"DOI":"10.1007\/s40314-025-03223-w","type":"journal-article","created":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T19:07:14Z","timestamp":1746817634000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Block-parametric approach for determining the geometric characteristics of elastic layered packages"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8401-4570","authenticated-orcid":false,"given":"Alexander Vladimirovich","family":"Trofimov","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,9]]},"reference":[{"key":"3223_CR1","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/5072676","author":"IV Andrianov","year":"2019","unstructured":"Andrianov IV, Ausheva NM, Olevska YB, Olevskyi VI (2019) Surfaces modelling using isotropic fractional-rational curves. J Appl Math. https:\/\/doi.org\/10.1155\/2019\/5072676","journal-title":"J Appl Math"},{"issue":"2","key":"3223_CR2","doi-asserted-by":"publisher","first-page":"R1","DOI":"10.1088\/0266-5611\/21\/2\/R01","volume":"21","author":"M Bonnet","year":"2005","unstructured":"Bonnet M (2005) Constantinescu, A. Inverse Probl Elast Inverse Probl 21(2):R1","journal-title":"Inverse Probl Elast Inverse Probl"},{"key":"3223_CR3","volume-title":"Structural identifiability of parametric models","author":"G Chavent","year":"1987","unstructured":"Chavent G (1987) Identifiability of parameters in the output least squares formulation. In: Walter E (ed) Structural identifiability of parametric models. Pergamon Press, Oxford"},{"key":"3223_CR4","volume-title":"Nonlinear least squares for inverse problems","author":"G Chavent","year":"2009","unstructured":"Chavent G (2009) Nonlinear least squares for inverse problems. Springer Science + Business Media B.V, Berlin"},{"key":"3223_CR5","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/BF01449027","volume":"1","author":"G Chavent","year":"1974","unstructured":"Chavent G, Lemonnier P (1974) Identification de la non-Linearite D\u2019Une equation parabolique quasilineare. Appl Math Optim 1:121\u2013162","journal-title":"Appl Math Optim"},{"key":"3223_CR6","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971200","volume-title":"Numerical methods for unconstrained optimization and nonlinear equations","author":"JE Dennis","year":"1996","unstructured":"Dennis JE, Schnabel RB (1996) Numerical methods for unconstrained optimization and nonlinear equations. SIAM, Philadelphia"},{"key":"3223_CR7","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/j.commatsci.2006.10.021","volume":"40","author":"P Egan","year":"2007","unstructured":"Egan P, Whelan MP, Lakestani F, Connelly MJ (2007) Small punch test: an approach to solve the inverse problem by deformation shape and finite element optimization. Comput Mater Sci 40:33\u201339","journal-title":"Comput Mater Sci"},{"issue":"5","key":"3223_CR8","doi-asserted-by":"publisher","first-page":"667","DOI":"10.1016\/j.ijnonlinmec.2011.02.011","volume":"46","author":"A Hasanov","year":"2011","unstructured":"Hasanov A (2011) Some new classes of inverse coefficient problems in non-linear mechanics and computational material science. Int J Non Linear Mech 46(5):667\u2013684. https:\/\/doi.org\/10.1016\/j.ijnonlinmec.2011.02.011","journal-title":"Int J Non Linear Mech"},{"issue":"2","key":"3223_CR9","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1080\/17415970903545157","volume":"18","author":"A Hasanov","year":"2010","unstructured":"Hasanov A, Tatar S (2010) Semi-analytic inversion method for the determination of elastoplastic properties of power hardening materials from limited torsional experiment. Inverse Probl Sci Eng 18(2):265\u2013278. https:\/\/doi.org\/10.1080\/17415970903545157","journal-title":"Inverse Probl Sci Eng"},{"key":"3223_CR10","first-page":"1","volume":"2014","author":"R Ji","year":"2014","unstructured":"Ji R, Siddiki N, Nantung T, Kim D (2014) Evaluation of resilient modulus of subgrade and base materials in Indiana and its implementation in MEPDG. Sci World J 2014:1\u201314","journal-title":"Sci World J"},{"issue":"3","key":"3223_CR11","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1016\/0021-8928(86)90133-4","volume":"50","author":"VI Kuz'menko","year":"1986","unstructured":"Kuz\u2019menko VI (1986) Inverse contact problems of the theory of plasticity. J Appl Math Mech 50(3):361\u2013367","journal-title":"J Appl Math Mech"},{"key":"3223_CR12","doi-asserted-by":"publisher","first-page":"57","DOI":"10.7546\/jgsp-50-2018-57-69","volume":"50","author":"V Olevskyi","year":"2018","unstructured":"Olevskyi V, Olevska Y (2018) Mathematical model of elastic closed flexible shells with nonlocal shape deviations. J Geom Symmetry Phys 50:57\u201369","journal-title":"J Geom Symmetry Phys"},{"issue":"4","key":"3223_CR13","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1515\/jiip.2000.8.4.421","volume":"8","author":"VG Romanov","year":"2000","unstructured":"Romanov VG, Weng C-I, Chen T-C (2000) An inverse problem related to layered elastic plate. J Inverse Ill Posed Probl 8(4):421\u2013447. https:\/\/doi.org\/10.1515\/jiip.2000.8.4.421","journal-title":"J Inverse Ill Posed Probl"},{"key":"3223_CR14","doi-asserted-by":"crossref","unstructured":"Saric A, Pozder M (2018) Artificial neural networks application in the back calculation process of flexible pavement layers elasticity modulus. In: Had\u017eikadi\u0107 M, Avdakovi\u0107 S (eds) Advanced technologies, systems, and applications II. IAT 2017. Lecture notes in networks and systems, 28","DOI":"10.1007\/978-3-319-71321-2_49"},{"key":"3223_CR15","unstructured":"Sokhatsky AV, Trofimov AV et al (2022) Modelling in Transportation Technologies Part 1. Chapter 3. Dnipro: UMSF, 76\u2013122, ISBN 978-966-328-191-9"},{"key":"3223_CR16","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717921","volume-title":"Inverse problem theory and methods for model parameter estimation","author":"A Tarantola","year":"2005","unstructured":"Tarantola A (2005) Inverse problem theory and methods for model parameter estimation. SIAM, Society for Industrial and Applied Mathematics, Philadelphia"},{"key":"3223_CR17","volume-title":"Handbook of grid generation","author":"JF Thompson","year":"1999","unstructured":"Thompson JF, Soni B, Weatherill N (1999) Handbook of grid generation. CRC Press, New York"},{"key":"3223_CR18","volume-title":"Solutions of ill-posed problems","author":"AN Tikhonov","year":"1977","unstructured":"Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Wiley, New York+"},{"issue":"1","key":"3223_CR19","first-page":"140","volume":"53","author":"AV Trofimov","year":"2015","unstructured":"Trofimov AV (2015) Local Fourier analysis for constructing multigrid methods for layered elastic and elasto-plastic bases problems. Dnipro Syst Technol 53(1):140\u2013155","journal-title":"Dnipro Syst Technol"},{"issue":"1","key":"3223_CR20","first-page":"119","volume":"55","author":"AV Trofimov","year":"2016","unstructured":"Trofimov AV (2016) Multigrid iterative algorithms for layered elastic and elasto-plastic foundations with curvilinear boundaries\u2019 boundary-value problems. Dnipro Syst Technol 55(1):119\u2013137","journal-title":"Dnipro Syst Technol"},{"key":"3223_CR21","doi-asserted-by":"publisher","first-page":"1773","DOI":"10.1007\/s00419-020-01854-5","volume":"91","author":"AV Trofimov","year":"2021","unstructured":"Trofimov AV (2021) Inverse problem analysis for nondestructive evaluation of structural characteristics of multilayered foundations. Arch Appl Mech 91:1773\u20131792. https:\/\/doi.org\/10.1007\/s00419-020-01854-5","journal-title":"Arch Appl Mech"},{"key":"3223_CR22","doi-asserted-by":"publisher","first-page":"04003","DOI":"10.1051\/matecconf\/202439004003","volume":"390","author":"AV Trofimov","year":"2024","unstructured":"Trofimov AV (2024) Block-parametric approach to non-destructive control data analysis of railroad layered foundations. MATEC Web Conf 390:04003. https:\/\/doi.org\/10.1051\/matecconf\/202439004003","journal-title":"MATEC Web Conf"},{"issue":"2","key":"3223_CR23","first-page":"69","volume":"54","author":"AV Trofimov","year":"2015","unstructured":"Trofimov AV, Petrova YV (2015) Multigrid iterative grid generation algorithms for layered elastic and elasto-plastic foundations\u2019 problems. Dnipro Syst Technol 54(2):69\u201380","journal-title":"Dnipro Syst Technol"},{"key":"3223_CR24","doi-asserted-by":"publisher","first-page":"03012","DOI":"10.1051\/matecconf\/201929403012","volume":"294","author":"AV Trofimov","year":"2019","unstructured":"Trofimov AV et al (2019) Non-destructive control data analysis of railroad foundation constructions. MATEC Web Conf 294:03012. https:\/\/doi.org\/10.1051\/matecconf\/201929403012","journal-title":"MATEC Web Conf"},{"key":"3223_CR25","volume-title":"Multigrid","author":"U Trottenberg","year":"2001","unstructured":"Trottenberg U, Oosterlee CW, Schuller A (2001) Multigrid. Academic Press, New York"},{"issue":"3","key":"3223_CR26","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/BF02467848","volume":"38","author":"I Tsvelodub","year":"1997","unstructured":"Tsvelodub I (1997) Inverse problems of deformation of nonlinear viscoelastic bodies. J Appl Mech Tech Phys 38(3):453\u2013463","journal-title":"J Appl Mech Tech Phys"},{"key":"3223_CR27","volume-title":"Inverse problems in deformable solid body mechanics","author":"A Vatulian","year":"2007","unstructured":"Vatulian A (2007) Inverse problems in deformable solid body mechanics. Fizmatlit, Moscow"},{"key":"3223_CR28","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/976837","author":"F Yaman","year":"2013","unstructured":"Yaman F, Yakhno VG, Potthast R (2013) A survey on inverse problems for applied sciences. Math Probl Eng. https:\/\/doi.org\/10.1155\/2013\/976837","journal-title":"Math Probl Eng"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03223-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03223-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03223-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T14:11:30Z","timestamp":1747663890000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03223-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,9]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["3223"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03223-w","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2025,5,9]]},"assertion":[{"value":"23 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 March 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 April 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 May 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"There is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Approve all ethics norms and agree to participate.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Input and output data of considered inverse problems for multilayered elastic packet with curvilinear boundaries can be shared. Because of the potential commercial value of the program C++ code, availability to readers would be a matter for negotiations.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Replication of results"}}],"article-number":"273"}}