{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T02:31:51Z","timestamp":1777861911324,"version":"3.51.4"},"reference-count":39,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2015,12,29]],"date-time":"2015-12-29T00:00:00Z","timestamp":1451347200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Reinforced Plastics and Composites"],"published-print":{"date-parts":[[2016,4]]},"abstract":"<jats:p>A novel invariant-based approach to describe stiffness and strength of carbon-fiber-reinforced plastic composites has been recently proposed in the literature. In this work, a direct sizing method based on trace of the plane stress stiffness matrix and unit circle failure criterion is proposed. Strength-based profile of a panel is first determined for a baseline material based on the upper-bound value of the calculated failure index k-field from a boundary-value problem. The structural component can then be scaled linearly to meet the stiffness requirements that include deformation, deflection, natural frequency, and buckling. Material selection by scaling is the last step in this sizing method. The proposed approach is conceptually simple to implement, not material specific, and immediately applicable for automated tape laying. Although this is a 2D formulation of an orthotropic homogenized laminate, the 3D stiffness can be separated into two uncoupled in- and out-of-plane submatrices. Thus, the in-plane results of this method are independent of the out-of-plane behavior.<\/jats:p>","DOI":"10.1177\/0731684415624770","type":"journal-article","created":{"date-parts":[[2015,12,30]],"date-time":"2015-12-30T20:25:07Z","timestamp":1451507107000},"page":"589-600","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":24,"title":["A trace-based approach to design for manufacturing of composite laminates"],"prefix":"10.1177","volume":"35","author":[{"given":"Stephen W","family":"Tsai","sequence":"first","affiliation":[{"name":"Department of Aeronautics and Astronautics, Stanford University, CA USA"}]},{"given":"Albertino","family":"Arteiro","sequence":"additional","affiliation":[{"name":"Departamento de Engenharia Mec\u00e2nica, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal"}]},{"given":"Jose DD","family":"Melo","sequence":"additional","affiliation":[{"name":"Department of Materials Engineering, Federal University of Rio Grande do Norte, Natal, Brazil"}]}],"member":"179","published-online":{"date-parts":[[2015,12,29]]},"reference":[{"key":"bibr1-0731684415624770","unstructured":"Park WJ. An optimal design of simple symmetric laminates under the first ply failure criteria. Report no. AFWAL-TR-81-4175, Materials Laboratory, Air Force Wright Aeronautical Laboratories, Air Force Systems Command, Wright-Patterson Air Force Base, Dayton OH, 1982."},{"key":"bibr2-0731684415624770","unstructured":"Manne PM. Design optimization of composite plates. PhD Thesis, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, 1996."},{"key":"bibr3-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1177\/002199839703102301"},{"key":"bibr4-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1177\/002199839803200603"},{"key":"bibr5-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0263-8223(99)00052-5"},{"key":"bibr6-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0263-8223(00)00128-8"},{"key":"bibr7-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-004-0425-9"},{"key":"bibr8-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-30927-6_21"},{"key":"bibr9-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2006.06.001"},{"key":"bibr10-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2005.01.021"},{"key":"bibr11-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2011.04.007"},{"key":"bibr12-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2012.11.005"},{"key":"bibr13-0731684415624770","unstructured":"Khot NS. Computer program (OPTCOMP) for optimization of composite structures for minimum weight design. Technical Report AFFDL-TR-76-149, Air Force Flight Dynamics, Air Force Wright Aeronautical, Air Force Systems Command, Wright-Patterson Air Force Base, Ohio, 1977."},{"key":"bibr14-0731684415624770","unstructured":"Miravete A. Optimization of laminated composite plates. Report no. WRDC-TR-89-4107, Materials Laboratory, Air Force Wright Research and Development Center, Air Force Systems Command, Wright-Patterson Air Force Base, Dayton OH, 1989."},{"key":"bibr15-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2011.07.015"},{"key":"bibr16-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/0895-7177(94)90050-7"},{"key":"bibr17-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7949(95)00138-7"},{"key":"bibr18-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0263-8223(97)00120-7"},{"key":"bibr19-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0263-8223(99)00077-X"},{"key":"bibr20-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0263-8223(00)00170-7"},{"key":"bibr21-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-460X(03)00270-0"},{"key":"bibr22-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1259"},{"key":"bibr23-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compscitech.2009.01.011"},{"key":"bibr24-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.finel.2009.10.003"},{"key":"bibr25-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2010.04.003"},{"key":"bibr26-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1007\/s10409-011-0506-0"},{"key":"bibr27-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compositesb.2013.04.005"},{"key":"bibr28-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1007\/BF01743714"},{"key":"bibr29-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(99)90391-2"},{"key":"bibr30-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1299\/jsmea.44.490"},{"key":"bibr31-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0263-8223(03)00182-X"},{"key":"bibr32-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1177\/002199839803200603"},{"key":"bibr33-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/S0263-8223(01)00179-9"},{"key":"bibr34-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2009.01.006"},{"key":"bibr35-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2010.06.001"},{"key":"bibr36-0731684415624770","volume-title":"Composite materials design and testing","author":"Tsai SW","year":"2015"},{"key":"bibr37-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compscitech.2014.06.017"},{"key":"bibr38-0731684415624770","doi-asserted-by":"publisher","DOI":"10.1016\/j.compscitech.2015.08.003"},{"key":"bibr39-0731684415624770","unstructured":"Tsai SW and Melo JDD. A unit circle failure criterion for carbon fiber reinforced polymer composites.\n                      Compos Sci Technol\n                      (unpublished)."}],"container-title":["Journal of Reinforced Plastics and Composites"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0731684415624770","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0731684415624770","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0731684415624770","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T05:05:12Z","timestamp":1777525512000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0731684415624770"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,29]]},"references-count":39,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["10.1177\/0731684415624770"],"URL":"https:\/\/doi.org\/10.1177\/0731684415624770","relation":{},"ISSN":["0731-6844","1530-7964"],"issn-type":[{"value":"0731-6844","type":"print"},{"value":"1530-7964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12,29]]}}}