Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection
Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing...
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| Veröffentlicht in: | Mathematical problems in engineering 2013-01, Vol.2013 (2013), p.1-12 |
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| creator | Xu, S. P. Wang, C. M. Xu, Meirong |
| description | Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies. |
| doi_str_mv | 10.1155/2013/341232 |
| format | Article |
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P. ; Wang, C. M. ; Xu, Meirong</creator><contributor>Chou, Jyh Horng</contributor><creatorcontrib>Xu, S. P. ; Wang, C. M. ; Xu, Meirong ; Chou, Jyh Horng</creatorcontrib><description>Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2013/341232</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Applied mathematics ; Approximation ; Archives & records ; Carbon ; Columns (structural) ; Configurations ; Defects ; Deformation ; Differential equations ; Elasticity ; Engineering ; Exact solutions ; Mathematical analysis ; Mathematical models ; Mathematical problems ; Mechanics ; Nanotechnology ; Nonlinear differential equations ; Nonlocal elasticity ; Numerical methods ; Perturbation methods ; Postbuckling ; Size effects ; Stability analysis ; Studies</subject><ispartof>Mathematical problems in engineering, 2013-01, Vol.2013 (2013), p.1-12</ispartof><rights>Copyright © 2013 S. P. Xu et al.</rights><rights>Copyright © 2013 S. P. Xu et al.; This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c422t-89fb9ed9ef2cfdfe671843592b999c52934df3bcc98ce2777104d915f7f7e88e3</citedby><cites>FETCH-LOGICAL-c422t-89fb9ed9ef2cfdfe671843592b999c52934df3bcc98ce2777104d915f7f7e88e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><contributor>Chou, Jyh Horng</contributor><creatorcontrib>Xu, S. P.</creatorcontrib><creatorcontrib>Wang, C. M.</creatorcontrib><creatorcontrib>Xu, Meirong</creatorcontrib><title>Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection</title><title>Mathematical problems in engineering</title><description>Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.</description><subject>Applied mathematics</subject><subject>Approximation</subject><subject>Archives & records</subject><subject>Carbon</subject><subject>Columns (structural)</subject><subject>Configurations</subject><subject>Defects</subject><subject>Deformation</subject><subject>Differential equations</subject><subject>Elasticity</subject><subject>Engineering</subject><subject>Exact solutions</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematical problems</subject><subject>Mechanics</subject><subject>Nanotechnology</subject><subject>Nonlinear differential equations</subject><subject>Nonlocal elasticity</subject><subject>Numerical methods</subject><subject>Perturbation methods</subject><subject>Postbuckling</subject><subject>Size effects</subject><subject>Stability analysis</subject><subject>Studies</subject><issn>1024-123X</issn><issn>1563-5147</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>BENPR</sourceid><recordid>eNqN0c9LwzAUB_AiCs7pybsUvIhSl5cfTXIcY-pg6EEFbyVNE5aRNbNpGfvv7agH8aKn93jvwzu8b5JcAroHYGyCEZAJoYAJPkpGwHKSMaD8uO8Rplk__zhNzmJcI4SBgRglT6-tKp137T6d1srvo4tpsOlzqH3Qyqdzr2LrdDoLvtvUMd25dpUuate6frnYbE1jjW5dqM-TE6t8NBffdZy8P8zfZk_Z8uVxMZsuM00xbjMhbSlNJY3F2lbW5BwEJUziUkqpGZaEVpaUWkuhDeacA6KVBGa55UYIQ8bJzXB324TPzsS22LiojfeqNqGLBVAqOEGcsX9QLAXPGRzo9S-6Dl3TP6RXUmKOMUV5r-4GpZsQY2NssW3cRjX7AlBxCKA4BFAMAfT6dtArV1dq5_7AVwM2PTFW_cAEBFDyBWspjTw</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>Xu, S. 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P. ; Wang, C. M. ; Xu, Meirong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c422t-89fb9ed9ef2cfdfe671843592b999c52934df3bcc98ce2777104d915f7f7e88e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Applied mathematics</topic><topic>Approximation</topic><topic>Archives & records</topic><topic>Carbon</topic><topic>Columns (structural)</topic><topic>Configurations</topic><topic>Defects</topic><topic>Deformation</topic><topic>Differential equations</topic><topic>Elasticity</topic><topic>Engineering</topic><topic>Exact solutions</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematical problems</topic><topic>Mechanics</topic><topic>Nanotechnology</topic><topic>Nonlinear differential equations</topic><topic>Nonlocal elasticity</topic><topic>Numerical methods</topic><topic>Perturbation methods</topic><topic>Postbuckling</topic><topic>Size effects</topic><topic>Stability analysis</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xu, S. 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P.</au><au>Wang, C. M.</au><au>Xu, Meirong</au><au>Chou, Jyh Horng</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection</atitle><jtitle>Mathematical problems in engineering</jtitle><date>2013-01-01</date><risdate>2013</risdate><volume>2013</volume><issue>2013</issue><spage>1</spage><epage>12</epage><pages>1-12</pages><issn>1024-123X</issn><eissn>1563-5147</eissn><abstract>Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><doi>10.1155/2013/341232</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Applied mathematics Approximation Archives & records Carbon Columns (structural) Configurations Defects Deformation Differential equations Elasticity Engineering Exact solutions Mathematical analysis Mathematical models Mathematical problems Mechanics Nanotechnology Nonlinear differential equations Nonlocal elasticity Numerical methods Perturbation methods Postbuckling Size effects Stability analysis Studies |
| title | Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection |
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