New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework
In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of common...
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Veröffentlicht in: | Applied Mathematical Modelling 2021-10, Vol.98, p.398-415 |
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description | In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues. |
doi_str_mv | 10.1016/j.apm.2021.05.017 |
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However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues.</description><identifier>ISSN: 0307-904X</identifier><identifier>ISSN: 1088-8691</identifier><identifier>EISSN: 0307-904X</identifier><identifier>DOI: 10.1016/j.apm.2021.05.017</identifier><language>eng</language><publisher>New York: Elsevier Inc</publisher><subject>Analytic solution ; Boundary conditions ; Buckling ; Cylindrical panel ; Cylindrical shells ; Exact solutions ; Hamiltonian functions ; Hamiltonian system ; Panels ; Partial differential equations ; Radius of curvature ; Symplectic method</subject><ispartof>Applied Mathematical Modelling, 2021-10, Vol.98, p.398-415</ispartof><rights>2021 Elsevier Inc.</rights><rights>Copyright Elsevier BV Oct 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-d9739638c956d566314ca9d4ec5dfb8bfa34649c0bc3f32aba8fa1717b18e51f3</citedby><cites>FETCH-LOGICAL-c325t-d9739638c956d566314ca9d4ec5dfb8bfa34649c0bc3f32aba8fa1717b18e51f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.apm.2021.05.017$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Zheng, Xinran</creatorcontrib><creatorcontrib>Ni, Zhuofan</creatorcontrib><creatorcontrib>Xu, Dian</creatorcontrib><creatorcontrib>Wang, Zixuan</creatorcontrib><creatorcontrib>Liu, Mingfeng</creatorcontrib><creatorcontrib>Li, Yihao</creatorcontrib><creatorcontrib>Du, Jingyu</creatorcontrib><creatorcontrib>Li, Rui</creatorcontrib><title>New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework</title><title>Applied Mathematical Modelling</title><description>In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues.</description><subject>Analytic solution</subject><subject>Boundary conditions</subject><subject>Buckling</subject><subject>Cylindrical panel</subject><subject>Cylindrical shells</subject><subject>Exact solutions</subject><subject>Hamiltonian functions</subject><subject>Hamiltonian system</subject><subject>Panels</subject><subject>Partial differential equations</subject><subject>Radius of curvature</subject><subject>Symplectic method</subject><issn>0307-904X</issn><issn>1088-8691</issn><issn>0307-904X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKxDAYhYMoOI4-gLuA69akaXrBlQzeYNCNgruQ5uKk0yY16czQR_I5fDEzjAtXrv7zwzkHzgfAJUYpRri4blM-9GmGMpwimiJcHoEZIqhMapS_H__Rp-AshBYhROM3A_JZ7SC3vJtGI2CzEevO2A8YXLcZjbMBOg2ts8ny-2s7JeM0KCimaJHeCN7BgVvVBbgz48pYOK4UDFM_dErs27Tnvdo5vz4HJ5p3QV383jl4u797XTwmy5eHp8XtMhEko2Mi65LUBalETQtJi4LgXPBa5kpQqZuq0ZzkRV4L1AiiScYbXmmOS1w2uFIUazIHV4fewbvPjQoja93Gx3GBZbSoEMFlnUcXPriEdyF4pdngTc_9xDBie5isZREm28NkiLIIM2ZuDpm4Vm2N8iwIo6xQ0vg4lkln_kn_ALcMf4o</recordid><startdate>202110</startdate><enddate>202110</enddate><creator>Zheng, Xinran</creator><creator>Ni, Zhuofan</creator><creator>Xu, Dian</creator><creator>Wang, Zixuan</creator><creator>Liu, Mingfeng</creator><creator>Li, Yihao</creator><creator>Du, Jingyu</creator><creator>Li, Rui</creator><general>Elsevier Inc</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>202110</creationdate><title>New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework</title><author>Zheng, Xinran ; Ni, Zhuofan ; Xu, Dian ; Wang, Zixuan ; Liu, Mingfeng ; Li, Yihao ; Du, Jingyu ; Li, Rui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-d9739638c956d566314ca9d4ec5dfb8bfa34649c0bc3f32aba8fa1717b18e51f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Analytic solution</topic><topic>Boundary conditions</topic><topic>Buckling</topic><topic>Cylindrical panel</topic><topic>Cylindrical shells</topic><topic>Exact solutions</topic><topic>Hamiltonian functions</topic><topic>Hamiltonian system</topic><topic>Panels</topic><topic>Partial differential equations</topic><topic>Radius of curvature</topic><topic>Symplectic method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zheng, Xinran</creatorcontrib><creatorcontrib>Ni, Zhuofan</creatorcontrib><creatorcontrib>Xu, Dian</creatorcontrib><creatorcontrib>Wang, Zixuan</creatorcontrib><creatorcontrib>Liu, Mingfeng</creatorcontrib><creatorcontrib>Li, Yihao</creatorcontrib><creatorcontrib>Du, Jingyu</creatorcontrib><creatorcontrib>Li, Rui</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied Mathematical Modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zheng, Xinran</au><au>Ni, Zhuofan</au><au>Xu, Dian</au><au>Wang, Zixuan</au><au>Liu, Mingfeng</au><au>Li, Yihao</au><au>Du, Jingyu</au><au>Li, Rui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework</atitle><jtitle>Applied Mathematical Modelling</jtitle><date>2021-10</date><risdate>2021</risdate><volume>98</volume><spage>398</spage><epage>415</epage><pages>398-415</pages><issn>0307-904X</issn><issn>1088-8691</issn><eissn>0307-904X</eissn><abstract>In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues.</abstract><cop>New York</cop><pub>Elsevier Inc</pub><doi>10.1016/j.apm.2021.05.017</doi><tpages>18</tpages></addata></record> |
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subjects | Analytic solution Boundary conditions Buckling Cylindrical panel Cylindrical shells Exact solutions Hamiltonian functions Hamiltonian system Panels Partial differential equations Radius of curvature Symplectic method |
title | New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework |
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