Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates
The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Kármán nonlinear strains. The equations of equilibrium of the nonlocal beam theories are derived, and virtual work statements in terms of the gen...
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| Veröffentlicht in: | International journal of engineering science 2010-11, Vol.48 (11), p.1507-1518 |
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| container_title | International journal of engineering science |
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| creator | Reddy, J.N. |
| description | The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Kármán nonlinear strains. The equations of equilibrium of the nonlocal beam theories are derived, and virtual work statements in terms of the generalized displacements are presented for use with the finite element model development. The governing equilibrium equations of the classical and first-order shear deformation theories of plates with the von Kármán nonlinearity are also formulated. The theoretical development presented herein should serve to obtain the finite element results and determine the effect of the geometric nonlinearity and nonlocal constitutive relations on bending response. |
| doi_str_mv | 10.1016/j.ijengsci.2010.09.020 |
| format | Article |
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The equations of equilibrium of the nonlocal beam theories are derived, and virtual work statements in terms of the generalized displacements are presented for use with the finite element model development. The governing equilibrium equations of the classical and first-order shear deformation theories of plates with the von Kármán nonlinearity are also formulated. The theoretical development presented herein should serve to obtain the finite element results and determine the effect of the geometric nonlinearity and nonlocal constitutive relations on bending response.</description><identifier>ISSN: 0020-7225</identifier><identifier>EISSN: 1879-2197</identifier><identifier>DOI: 10.1016/j.ijengsci.2010.09.020</identifier><identifier>CODEN: IJESAN</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Beams (structural) ; Bending ; Classical theories ; Constitutive relationships ; Exact sciences and technology ; Finite element method ; Fundamental areas of phenomenology (including applications) ; Mathematical analysis ; Mathematical models ; Nonlinearity ; Nonlocal elasticity ; Physics ; Plates ; Shear deformation ; Shear deformation theories ; Solid mechanics ; Static elasticity (thermoelasticity...) ; Structural and continuum mechanics ; Virtual work principles ; Von Kármán nonlinearity</subject><ispartof>International journal of engineering science, 2010-11, Vol.48 (11), p.1507-1518</ispartof><rights>2010 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c374t-cee36bbd75102e4b2bec95f00e26b4a6c3a2469f383ff1804c6c28679bf09bad3</citedby><cites>FETCH-LOGICAL-c374t-cee36bbd75102e4b2bec95f00e26b4a6c3a2469f383ff1804c6c28679bf09bad3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.ijengsci.2010.09.020$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>315,782,786,3554,27933,27934,46004</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23630368$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Reddy, J.N.</creatorcontrib><title>Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates</title><title>International journal of engineering science</title><description>The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Kármán nonlinear strains. 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The theoretical development presented herein should serve to obtain the finite element results and determine the effect of the geometric nonlinearity and nonlocal constitutive relations on bending response.</description><subject>Beams (structural)</subject><subject>Bending</subject><subject>Classical theories</subject><subject>Constitutive relationships</subject><subject>Exact sciences and technology</subject><subject>Finite element method</subject><subject>Fundamental areas of phenomenology (including applications)</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Nonlinearity</subject><subject>Nonlocal elasticity</subject><subject>Physics</subject><subject>Plates</subject><subject>Shear deformation</subject><subject>Shear deformation theories</subject><subject>Solid mechanics</subject><subject>Static elasticity (thermoelasticity...)</subject><subject>Structural and continuum mechanics</subject><subject>Virtual work principles</subject><subject>Von Kármán nonlinearity</subject><issn>0020-7225</issn><issn>1879-2197</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNqFkMFu1DAQhi0EEkvhFVAuiFO2Yztx4huooqVSRS_lbNnOuPWStRdPFom3x9ktXDnZHn3_P_LH2HsOWw5cXe62cYfpkXzcCqhD0FsQ8IJt-DjoVnA9vGQbqKN2EKJ_zd4Q7QCgl1pv2I9vOc3Z27lJ9RIT2tKEXPbH2S4xJ1ofjcM0xfTY5ND42RLFlbdpauhp5SdcEye-WZ4wl4i0sg7tnk7cobYhvWWvgp0J3z2fF-z79ZeHq6_t3f3N7dXnu9bLoVtajyiVc9PQcxDYOeHQ6z4AoFCus8pLKzqlgxxlCHyEzisvRjVoF0A7O8kL9vHceyj55xFpMftIHufZJsxHMqPivexU11VSnUlfMlHBYA4l7m35bTiYVa7Zmb9yzSrXgDbVZA1-eF5hqcoIxSYf6V9aSCVBqrFyn84c1v_-ilhMbcLkcYoF_WKmHP-36g_jKJWb</recordid><startdate>20101101</startdate><enddate>20101101</enddate><creator>Reddy, J.N.</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20101101</creationdate><title>Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates</title><author>Reddy, J.N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c374t-cee36bbd75102e4b2bec95f00e26b4a6c3a2469f383ff1804c6c28679bf09bad3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Beams (structural)</topic><topic>Bending</topic><topic>Classical theories</topic><topic>Constitutive relationships</topic><topic>Exact sciences and technology</topic><topic>Finite element method</topic><topic>Fundamental areas of phenomenology (including applications)</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Nonlinearity</topic><topic>Nonlocal elasticity</topic><topic>Physics</topic><topic>Plates</topic><topic>Shear deformation</topic><topic>Shear deformation theories</topic><topic>Solid mechanics</topic><topic>Static elasticity (thermoelasticity...)</topic><topic>Structural and continuum mechanics</topic><topic>Virtual work principles</topic><topic>Von Kármán nonlinearity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Reddy, J.N.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>International journal of engineering science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Reddy, J.N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates</atitle><jtitle>International journal of engineering science</jtitle><date>2010-11-01</date><risdate>2010</risdate><volume>48</volume><issue>11</issue><spage>1507</spage><epage>1518</epage><pages>1507-1518</pages><issn>0020-7225</issn><eissn>1879-2197</eissn><coden>IJESAN</coden><abstract>The classical and shear deformation beam and plate theories are reformulated using the nonlocal differential constitutive relations of Eringen and the von Kármán nonlinear strains. 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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Beams (structural) Bending Classical theories Constitutive relationships Exact sciences and technology Finite element method Fundamental areas of phenomenology (including applications) Mathematical analysis Mathematical models Nonlinearity Nonlocal elasticity Physics Plates Shear deformation Shear deformation theories Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics Virtual work principles Von Kármán nonlinearity |
| title | Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates |
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