{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:18:04Z","timestamp":1760145484779,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,3]],"date-time":"2024-08-03T00:00:00Z","timestamp":1722643200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The Reissner\u2013Mindlin (RM) hypothesis is considered for the investigation of the mechanical performance of a 3D cylindrical shell pipe without and with preformed hole problems under concentrated and compression loading in the linear elastic behavior for trimmed and untrimmed surfaces in structural engineering problems. B\u00e9zier extraction from T-Splines is integrated for an isogeometric analysis (IGA) approach. The numerical results obtained, particularly for the displacement and von Mises stress, are compared with and validated against the literature results, particularly with those for Non-Uniform Rational B-Spline (NURBS) IGA and the finite element method (FEM) Abaqus methods. The obtained results show that the computation time of the IGA based on the T-Spline method is shorter than that of the IGA NURBS and FEM Abaqus\/CAE (computer-aided engineering) methods. Furthermore, the highlighted results confirm that the IGA approach based on the T-Spline method shows more success than numerical reference methods. We observed that the NURBS IGA method is very limited for studying trimmed surfaces. The T-Spline method shows its power and capability in computing trimmed and untrimmed surfaces.<\/jats:p>","DOI":"10.3390\/axioms13080529","type":"journal-article","created":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T13:57:28Z","timestamp":1722866248000},"page":"529","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Numerical Analysis of the Cylindrical Shell Pipe with Preformed Holes Subjected to a Compressive Load Using Non-Uniform Rational B-Splines and T-Splines for an Isogeometric Analysis Approach"],"prefix":"10.3390","volume":"13","author":[{"given":"Said","family":"EL Fakkoussi","sequence":"first","affiliation":[{"name":"Mechanical Engineering Laboratory, Faculty of Sciences and Techniques, Sidi Mohamed Ben Abdellah University of Fez, Fez 30000, Morocco"}]},{"given":"Ouadie","family":"Koubaiti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, MSISI, Laboratory, Faculty of Sciences and Techniques of Errachidia, Moulay Ismail University of Meknes, B.P 509 Boutalamine, Errachidia 52000, Morocco"}]},{"given":"Ahmed","family":"Elkhalfi","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Laboratory, Faculty of Sciences and Techniques, Sidi Mohamed Ben Abdellah University of Fez, Fez 30000, Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8679-2579","authenticated-orcid":false,"given":"Sorin","family":"Vlase","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Faculty of Mechanical Engineering, Transylvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania"},{"name":"Technical Sciences Academy of Romania, 030167 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1552-3763","authenticated-orcid":false,"given":"Marin","family":"Marin","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Mathematics and Informatics, Transylvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania"},{"name":"Academy of Romanian Scientist, Ilfov Street, No. 3, 050045 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.cma.2009.02.036","article-title":"Isogeometric analysis using T-splines","volume":"199","author":"Bazilevs","year":"2010","journal-title":"Comput. 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