{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,2]],"date-time":"2025-10-02T06:15:46Z","timestamp":1759385746071,"version":"3.41.2"},"reference-count":20,"publisher":"Emerald","issue":"3","license":[{"start":{"date-parts":[[2016,10,10]],"date-time":"2016-10-10T00:00:00Z","timestamp":1476057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MMMS"],"published-print":{"date-parts":[[2016,10,10]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/mmms-12-2015-0081","type":"journal-article","created":{"date-parts":[[2016,10,7]],"date-time":"2016-10-07T19:35:45Z","timestamp":1475868945000},"page":"558-576","source":"Crossref","is-referenced-by-count":0,"title":["Design variation of thin-walled composite beam cross-section properties"],"prefix":"10.1108","volume":"12","author":[{"given":"An\u00edbal J.J.","family":"Valido","sequence":"first","affiliation":[]},{"given":"Jo\u00e3o Barradas","family":"Cardoso","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"issue":"2","key":"key2020121200594184600_ref001","doi-asserted-by":"crossref","first-page":"538","DOI":"10.2514\/3.10949","article-title":"A variational principle for shape design sensitivity analysis","volume":"30","year":"1992","journal-title":"AIAA Journal"},{"issue":"3","key":"key2020121200594184600_ref002","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0020-7683(84)90039-8","article-title":"A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections","volume":"20","year":"1984","journal-title":"International Journal Solids and Structures"},{"issue":"9","key":"key2020121200594184600_ref003","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1016\/0020-7225(94)00118-4","article-title":"A geometrically non-linear theory for laminated anisotropic thin-walled beams","volume":"33","year":"1995","journal-title":"International Journal of Engineering Science"},{"year":"2001","key":"key2020121200594184600_ref005","article-title":"Design variation of thin-walled beam cross-section properties by adjoint warping"},{"year":"1979","key":"key2020121200594184600_ref006","article-title":"Finite element structural analysis based on the Vlasov beam theory"},{"issue":"11-12","key":"key2020121200594184600_ref007","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1016\/j.compstruc.2010.12.009","article-title":"Cross-section optimal design of composite laminated thin-walled beams","volume":"89","year":"2011","journal-title":"Computers and Structures"},{"issue":"11","key":"key2020121200594184600_ref004","doi-asserted-by":"crossref","first-page":"1363","DOI":"10.1016\/j.tws.2009.03.002","article-title":"Finite element analysis of thin-walled composite laminated beams with geometrically nonlinear behavior including warping deformation","volume":"47","year":"2009","journal-title":"Thin-Walled Structures"},{"issue":"2","key":"key2020121200594184600_ref008","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0045-7949(98)00154-0","article-title":"Computational approach for analysis and optimal design of FRP beams","volume":"70","year":"1999","journal-title":"Computers and Structures"},{"volume-title":"The Theory of Thin-walled Beams","year":"1981","key":"key2020121200594184600_ref009"},{"issue":"1","key":"key2020121200594184600_ref010","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/S1359-8368(97)00022-X","article-title":"Optimal fiber orientation in lateral stability of laminated channel section beams","volume":"29","year":"1998","journal-title":"Composites: Part B"},{"key":"key2020121200594184600_ref011","doi-asserted-by":"crossref","unstructured":"Lee, J. and Lee, S. (2004), \u201cFlexural-torsional behavior of thin-walled composite beams\u201d, Thin-Walled Structures, Vol. 42 No. 9, pp. 1293-1305.","DOI":"10.1016\/j.tws.2004.03.015"},{"issue":"November","key":"key2020121200594184600_ref012","first-page":"1065","article-title":"Optimum design of thin-walled composite beams for flexural-torsional buckling problem","volume":"132","year":"2015","journal-title":"Composite Structures"},{"issue":"7","key":"key2020121200594184600_ref013","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1002\/nme.155.abs","article-title":"Effects of approximations in analyses of beams of open thin-walled cross-section \u2013 part I: flexural-torsional stability","volume":"51","year":"2001","journal-title":"International Journal for Numerical Methods in Engineering"},{"issue":"7","key":"key2020121200594184600_ref014","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1002\/nme.156.abs","article-title":"Effects of approximations in analyses of beams of open thin-walled cross-section \u2013 part II: 3-D non-linear behavior","volume":"51","year":"2001","journal-title":"International Journal for Numerical Methods in Engineering"},{"issue":"2","key":"key2020121200594184600_ref015","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.compstruct.2004.08.027","article-title":"Optimal laminate sequence of non-prismatic thin-walled composite spatial members of generic section","volume":"70","year":"2005","journal-title":"Composite Structures"},{"volume-title":"Theory of Composites Design","year":"1992","key":"key2020121200594184600_ref016"},{"issue":"5","key":"key2020121200594184600_ref017","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1080\/03052150310001604784","article-title":"Geometrically nonlinear composite beam structures: design sensitivity analysis","volume":"35","year":"2003","journal-title":"Engineering Optimization"},{"issue":"5","key":"key2020121200594184600_ref018","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1080\/03052150310001604793","article-title":"Geometrically nonlinear composite beam structures: optimal design","volume":"35","year":"2003","journal-title":"Engineering Optimization"},{"volume-title":"Thin-walled Elastic Beams","year":"1961","key":"key2020121200594184600_ref019"},{"issue":"24","key":"key2020121200594184600_ref020","doi-asserted-by":"crossref","first-page":"1843","DOI":"10.1016\/S0045-7949(02)00223-7","article-title":"A displacement method for the analysis of flexural shear stresses in thin-walled isotropic composite beams","volume":"80","year":"2002","journal-title":"Computers and Structures"}],"container-title":["Multidiscipline Modeling in Materials and Structures"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/MMMS-12-2015-0081","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/MMMS-12-2015-0081\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/MMMS-12-2015-0081\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T21:44:01Z","timestamp":1753393441000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/mmms\/article\/12\/3\/558-576\/454337"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10,10]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,10,10]]}},"alternative-id":["10.1108\/MMMS-12-2015-0081"],"URL":"https:\/\/doi.org\/10.1108\/mmms-12-2015-0081","relation":{},"ISSN":["1573-6105"],"issn-type":[{"type":"print","value":"1573-6105"}],"subject":[],"published":{"date-parts":[[2016,10,10]]}}}