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An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation
We develop and analyze an ultraweak variational formulation of the Reissner–Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness t . We also prove weak convergence of the Reissn...
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| Published in: | Numerische Mathematik 2020-06, Vol.145 (2), p.313-344 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c319t-32c5394fdadf3956ed1619c1c0c8097a8d4a00a4a9660bda2f0a6eb62912c6853 |
| container_end_page | 344 |
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| container_title | Numerische Mathematik |
| container_volume | 145 |
| creator | Führer, Thomas Heuer, Norbert Sayas, Francisco-Javier |
| description | We develop and analyze an ultraweak variational formulation of the Reissner–Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness
t
. We also prove weak convergence of the Reissner–Mindlin solution to the solution of the corresponding Kirchhoff–Love model when
t
→
0
. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov–Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free. |
| doi_str_mv | 10.1007/s00211-020-01116-0 |
| format | article |
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t
. We also prove weak convergence of the Reissner–Mindlin solution to the solution of the corresponding Kirchhoff–Love model when
t
→
0
. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov–Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free.</description><identifier>ISSN: 0029-599X</identifier><identifier>EISSN: 0945-3245</identifier><identifier>DOI: 10.1007/s00211-020-01116-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Bending ; Convergence ; Galerkin method ; Locking ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Mindlin plates ; Numerical Analysis ; Numerical and Computational Physics ; Simulation ; Theoretical ; Well posed problems</subject><ispartof>Numerische Mathematik, 2020-06, Vol.145 (2), p.313-344</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020</rights><rights>Springer-Verlag GmbH Germany, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-32c5394fdadf3956ed1619c1c0c8097a8d4a00a4a9660bda2f0a6eb62912c6853</citedby><cites>FETCH-LOGICAL-c319t-32c5394fdadf3956ed1619c1c0c8097a8d4a00a4a9660bda2f0a6eb62912c6853</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Führer, Thomas</creatorcontrib><creatorcontrib>Heuer, Norbert</creatorcontrib><creatorcontrib>Sayas, Francisco-Javier</creatorcontrib><title>An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation</title><title>Numerische Mathematik</title><addtitle>Numer. Math</addtitle><description>We develop and analyze an ultraweak variational formulation of the Reissner–Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness
t
. We also prove weak convergence of the Reissner–Mindlin solution to the solution of the corresponding Kirchhoff–Love model when
t
→
0
. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov–Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free.</description><subject>Bending</subject><subject>Convergence</subject><subject>Galerkin method</subject><subject>Locking</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mindlin plates</subject><subject>Numerical Analysis</subject><subject>Numerical and Computational Physics</subject><subject>Simulation</subject><subject>Theoretical</subject><subject>Well posed problems</subject><issn>0029-599X</issn><issn>0945-3245</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kM9LwzAUx4MoOKf_gKeA5-p7aZouxzF1ChNFFDwIIWvS2dmlM2lRb_4P_of-JcZV8ObpvcP3Fx9CDhGOESA_CQAMMQEGCSCiSGCLDEDyLEkZz7bjD0wmmZQPu2QvhCUA5oLjgDyOHe3q1utXq59p2fhVV-u2ahxtSto-WXprqxCc9V8fn1eVM3Xl6DoqLJ1bZyq3oKvG2JpqZ-jpzZTq9do3b9Vqk7FPdkpdB3vwe4fk_vzsbnKRzK6nl5PxLClSlG2cWGSp5KXRpkxlJqxBgbLAAooRyFyPDNcAmmspBMyNZiVoYeeCSWSFGGXpkBz1ubH7pbOhVcum8y5WKsZBMuQZ5lHFelXhmxC8LdXax6H-XSGoH4qqp6giRbWhqCCa0t4UotgtrP-L_sf1DYo9dgA</recordid><startdate>20200601</startdate><enddate>20200601</enddate><creator>Führer, Thomas</creator><creator>Heuer, Norbert</creator><creator>Sayas, Francisco-Javier</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20200601</creationdate><title>An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation</title><author>Führer, Thomas ; Heuer, Norbert ; Sayas, Francisco-Javier</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-32c5394fdadf3956ed1619c1c0c8097a8d4a00a4a9660bda2f0a6eb62912c6853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Bending</topic><topic>Convergence</topic><topic>Galerkin method</topic><topic>Locking</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mindlin plates</topic><topic>Numerical Analysis</topic><topic>Numerical and Computational Physics</topic><topic>Simulation</topic><topic>Theoretical</topic><topic>Well posed problems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Führer, Thomas</creatorcontrib><creatorcontrib>Heuer, Norbert</creatorcontrib><creatorcontrib>Sayas, Francisco-Javier</creatorcontrib><collection>CrossRef</collection><jtitle>Numerische Mathematik</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Führer, Thomas</au><au>Heuer, Norbert</au><au>Sayas, Francisco-Javier</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation</atitle><jtitle>Numerische Mathematik</jtitle><stitle>Numer. Math</stitle><date>2020-06-01</date><risdate>2020</risdate><volume>145</volume><issue>2</issue><spage>313</spage><epage>344</epage><pages>313-344</pages><issn>0029-599X</issn><eissn>0945-3245</eissn><abstract>We develop and analyze an ultraweak variational formulation of the Reissner–Mindlin plate bending model both for the clamped and the soft simply supported cases. We prove well-posedness of the formulation, uniformly with respect to the plate thickness
t
. We also prove weak convergence of the Reissner–Mindlin solution to the solution of the corresponding Kirchhoff–Love model when
t
→
0
. Based on the ultraweak formulation, we introduce a discretization of the discontinuous Petrov–Galerkin type with optimal test functions (DPG) and prove its uniform quasi-optimal convergence. Our theory covers the case of non-convex polygonal plates. A numerical experiment for some smooth model solutions with fixed load confirms that our scheme is locking free.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00211-020-01116-0</doi><tpages>32</tpages></addata></record> |
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| ispartof | Numerische Mathematik, 2020-06, Vol.145 (2), p.313-344 |
| issn | 0029-599X 0945-3245 |
| language | eng |
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| subjects | Bending Convergence Galerkin method Locking Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mindlin plates Numerical Analysis Numerical and Computational Physics Simulation Theoretical Well posed problems |
| title | An ultraweak formulation of the Reissner–Mindlin plate bending model and DPG approximation |
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