{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T17:52:13Z","timestamp":1792000333153,"version":"4.4.0"},"reference-count":41,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,3,21]],"date-time":"2025-03-21T00:00:00Z","timestamp":1742515200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2020R1I1A3061349"],"award-info":[{"award-number":["NRF-2020R1I1A3061349"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Cylindrical shells are extensively employed in fluid transport, pressure vessels, and aerospace structures, where they endure mechanical and environmental stresses. However, under high pressure or external loading, circumferential cracks may develop, threatening structural integrity. Composite patch reinforcement is an effective method to mitigate crack propagation and restore structural performance. This study presents a finite element model using p-refinement techniques to analyze cylindrical shells with circumferential cracks reinforced by composite patches. The approach integrates equivalent single-layer (ESL) and layer-wise (LW) theories within a unified single-element mesh, significantly reducing the degrees of freedom compared to conventional LW models. Fracture analysis is conducted using the virtual crack closure technique (VCCT) to evaluate stress intensity factors. The model\u2019s accuracy and efficiency are verified through benchmark and patch reinforcement simulations. Additionally, a parametric study examines how patch material, thickness, and adhesive properties affect reinforcement efficiency across varying crack angles. This study provides an effective methodology for analyzing composite-reinforced thin-walled cylindrical shells, offering valuable insights for aerospace, marine, and pipeline engineering.<\/jats:p>","DOI":"10.3390\/ma18071404","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T04:48:18Z","timestamp":1742791698000},"page":"1404","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Computationally Efficient p-Version Finite Element Analysis of Composite-Reinforced Thin-Walled Cylindrical Shells with Circumferential Cracks"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2756-4298","authenticated-orcid":false,"given":"Jae S.","family":"Ahn","sequence":"first","affiliation":[{"name":"School of General Education, Yeungnam University, Gyeongsan 38541, Republic of Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Fracture of Pipelines and Cylinders Containing a Circumferential Crack","volume":"288","author":"Erdogan","year":"1983","journal-title":"Weld. 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