{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T13:31:13Z","timestamp":1790343073933,"version":"4.1.0"},"reference-count":19,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler\u2019s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.<\/jats:p>","DOI":"10.1155\/2015\/420649","type":"journal-article","created":{"date-parts":[[2015,9,13]],"date-time":"2015-09-13T07:25:16Z","timestamp":1442129116000},"page":"1-12","source":"Crossref","is-referenced-by-count":15,"title":["Solution of Contact Problems for Nonlinear Gao Beam and Obstacle"],"prefix":"10.1155","volume":"2015","author":[{"given":"J.","family":"Machalov\u00e1","sequence":"first","affiliation":[{"name":"Faculty of Science, Palack\u00fd University in Olomouc, 17. listopadu 1192\/12, 771 46 Olomouc, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"H.","family":"Netuka","sequence":"additional","affiliation":[{"name":"Faculty of Science, Palack\u00fd University in Olomouc, 17. listopadu 1192\/12, 771 46 Olomouc, Czech Republic"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"98","reference":[{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/0093-6413(95)00071-2"},{"key":"6","year":"1981"},{"key":"8","year":"1988"},{"key":"17","first-page":"127","volume":"2","year":"2009","journal-title":"Bulletin of the Transilvania University of Bra\u015fov, Series III, Mathematics, Informatics, Physics"},{"key":"16","year":"2004"},{"key":"19","series-title":"Lecture Note Series 398","year":"2012"},{"issue":"1","key":"18","first-page":"99","volume":"2","year":"2010","journal-title":"Annals of the Academy of Romanian Scientists. Series on Mathematics and its Applications"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1002\/zamm.201000161"},{"key":"10","series-title":"Springer Monographs in Mathematics","year":"2006"},{"key":"9","year":"1971"},{"key":"20","year":"2010"},{"key":"7","series-title":"Springer Series in Applied Mathematical Sciences","volume":"66","year":"1988"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1063\/1.3636963"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2014.09.012"},{"key":"12","first-page":"45","volume":"5","year":"2011","journal-title":"Applied and Computational Mechanics"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7462(98)00091-2"},{"key":"2","year":"1999"},{"key":"15","year":"2006"},{"key":"14","year":"2006"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/420649.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/420649.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/420649.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T17:40:39Z","timestamp":1471542039000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/420649\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":19,"alternative-id":["420649","420649"],"URL":"https:\/\/doi.org\/10.1155\/2015\/420649","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}