{"title":"Application of GA Optimization in Analysis of Variable Stiffness Composites","authors":"Nasim Fallahi, Erasmo Carrera, Alfonso Pagani","volume":170,"journal":"International Journal of Materials and Metallurgical Engineering","pagesStart":65,"pagesEnd":71,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10011872","abstract":"Variable angle tow describes the fibres which are<br \/>\r\ncurvilinearly steered in a composite lamina. Significantly, stiffness<br \/>\r\ntailoring freedom of VAT composite laminate can be enlarged and<br \/>\r\nenabled. Composite structures with curvilinear fibres have been<br \/>\r\nshown to improve the buckling load carrying capability in contrast<br \/>\r\nwith the straight laminate composites. However, the optimal design<br \/>\r\nand analysis of VAT are faced with high computational efforts<br \/>\r\ndue to the increasing number of variables. In this article, an<br \/>\r\nefficient optimum solution has been used in combination with 1D<br \/>\r\nCarrera&rsquo;s Unified Formulation (CUF) to investigate the optimum fibre<br \/>\r\norientation angles for buckling analysis. The particular emphasis is<br \/>\r\non the LE-based CUF models, which provide a Lagrange Expansions<br \/>\r\nto address a layerwise description of the problem unknowns.<br \/>\r\nThe first critical buckling load has been considered under simply<br \/>\r\nsupported boundary conditions. Special attention is lead to the<br \/>\r\nsensitivity of buckling load corresponding to the fibre orientation<br \/>\r\nangle in comparison with the results which obtain through the<br \/>\r\nGenetic Algorithm (GA) optimization frame and then Artificial<br \/>\r\nNeural Network (ANN) is applied to investigate the accuracy of<br \/>\r\nthe optimized model. As a result, numerical CUF approach with<br \/>\r\nan optimal solution demonstrates the robustness and computational<br \/>\r\nefficiency of proposed optimum methodology.","references":"[1] R. Olmedo and Z. G\u00a8urdal. Buckling response of lamiates with\r\nspatially varying fiber orientations. Structural Dynamics and Materials\r\nConference, Structures, 1993.\r\n[2] Z. Gurdal, B.F. Tatting, and C.K. Wu. Variable stiffness composite\r\npanels: Effects of stiffness variation on the in-plane and buckling\r\nresponse. Composites Part A: Applied Science and Manufacturing,\r\n39(5):911 \u2013 922, 2008.\r\n[3] Zhangming Wu, Paul M. Weaver, Gangadharan Raju, and Byung Chul\r\nKim. Buckling analysis and optimisation of variable angle tow\r\ncomposite plates. Thin-Walled Structures, 60:163 \u2013 172, 2012.\r\n[4] A.W. Leissa and A.F. Martin. Vibration and buckling of rectangular\r\ncomposite plates with variable fiber spacing. Composite Structure,\r\n14(4):339\u2013357, 1990.\r\n[5] B Tatting and Z G\u00a8urdal. Analysis and design of tow-steered variable\r\nstiffness composite laminates. In American Helicopter Society Hampton\r\nRoads Chapter, Structure Specialists Meeting, Williamsburg, VA, 2001.\r\n[6] Paul M Weaver, Zhang Ming Wu, and Gangadharan Raju. Optimisation\r\nof variable stiffness plates. In Applied Mechanics and Materials, volume\r\n828, pages 27\u201348. Trans Tech Publ, 2016.\r\n[7] Mark W. Bloomfield, J. Enrique Herencia, and Paul M. Weaver.\r\nEnhanced two-level optimization of anisotropic laminated composite\r\nplates with strength and buckling constraints. Thin-Walled Structures,\r\n47(11):1161 \u2013 1167, 2009.\r\n[8] Zhangming Wu, Gangadharan Raju, and Paul M Weaver. Optimization\r\nof postbuckling behaviour of variable thickness composite panels with\r\nvariable angle tows: Towards buckle-free design concept. International\r\nJournal of Solids and Structures, 132:66\u201379, 2018.\r\n[9] Hossein Ghiasi, Kazem Fayazbakhsh, Damiano Pasini, and Larry\r\nLessard. Optimum stacking sequence design of composite materials\r\npart ii: Variable stiffness design. Composite Structures, 93(1):1 \u2013 13,\r\n2010.\r\n[10] E Carrera. Layer-wise mixed models for accurate vibrations analysis of\r\nmultilayered plates. 1998.\r\n[11] E. Carrera. Evaluation of layerwise mixed theories for laminated plates\r\nanalysis. AIAA Journal, 36(5):830\u2013839, 1998.\r\n[12] Yang Yan, Alfonso Pagani, and Erasmo Carrera. Exact solutions for\r\nfree vibration analysis of laminated, box and sandwich beams by refined\r\nlayer-wise theory. Composite Structures, 175:28 \u2013 45, 2017.\r\n[13] Masoud Tahani. Analysis of laminated composite beams using layerwise\r\ndisplacement theories. Composite Structures, 79(4):535 \u2013 547, 2007.\r\n[14] A. Viglietti, E. Zappino, and E. Carrera. Free vibration analysis of\r\nvariable angle-tow composite wing structures. Aerospace Science and\r\nTechnology, 92:114 \u2013 125, 2019.\r\n[15] A. Viglietti, E. Zappino, and E. Carrera. Analysis of variable angle tow\r\ncomposites structures using variable kinematic models. Composites Part\r\nB: Engineering, 171:272 \u2013 283, 2019.\r\n[16] Hossein Ghiasi, Damiano Pasini, and Larry Lessard. Optimum stacking\r\nsequence design of composite materials part i: Constant stiffness design.\r\nComposite Structures, 90(1):1 \u2013 11, 2009.\r\n[17] John Henry Holland et al. Adaptation in natural and artificial systems:\r\nan introductory analysis with applications to biology, control, and\r\nartificial intelligence. MIT press, 1992.\r\n[18] Mahdi Arian Nik, Kazem Fayazbakhsh, Damiano Pasini, and Larry\r\nLessard. Surrogate-based multi-objective optimization of a composite\r\nlaminate with curvilinear fibers. Composite Structures, 94(8):2306 \u2013\r\n2313, 2012.\r\n[19] Farhad Alinejad and Daniele Botto. Innovative adaptive penalty in\r\nsurrogate-assisted robust optimization of blade attachments. Acta\r\nMechanica, 230(8):2735\u20132750, Aug 2019.\r\n[20] Peng Hao, Xiaojie Yuan, Hongliang Liu, Bo Wang, Chen Liu, Dixiong\r\nYang, and Shuangxi Zhan. Isogeometric buckling analysis of composite\r\nvariable-stiffness panels. Composite Structures, 165:192 \u2013 208, 2017.\r\n[21] Zafer G\u00a8urdal; Reynaldo Olmedo. In-plane response of laminates with\r\nspatially varying fiber orientations - variable stiffness concept. AIAA\r\nJournal, 31(4):751\u2013758, 1993.\r\n[22] E. Carrera, M. Cinefra, M. Petrolo, and E. Zappino. Finite Element\r\nAnalysis of Structures Through Unified Formulation. John Wiley &\r\nSons, 2014.\r\n[23] E Carrera, A Pagani, PH Cabral, A Prado, and G Silva. Component-wise\r\nmodels for the accurate dynamic and buckling analysis of composite\r\nwing structures. In ASME 2016 International Mechanical Engineering\r\nCongress and Exposition. American Society of Mechanical Engineers\r\nDigital Collection, 2017. [24] Erasmo Carrera and Marco Petrolo. Refined beam elements with\r\nonly displacement variables and plate\/shell capabilities. Meccanica,\r\n47(3):537\u2013556, Mar 2012.\r\n[25] J.N. Reddy. An evaluation of equivalent-single-layer and layerwise\r\ntheories of composite laminates. Composite Structures, 25(1):21 \u2013 35,\r\n1993.\r\n[26] Ren\u00b4e De Borst, Mike A Crisfield, Joris JC Remmers, and Clemens V\r\nVerhoosel. Nonlinear finite element analysis of solids and structures.\r\nJohn Wiley & Sons, 2012.\r\n[27] Nasim Fallahi, Andrea Viglietti, Erasmo Carrera, Alfonso Pagani, and\r\nEnrico Zappino. Effect of fiber orientation path on the buckling, free\r\nvibration, and static analyses of variable angle tow panels. Facta\r\nUniversitatis, Series: Mechanical Engineering, 18(2):165\u2013188, 2020.\r\n[28] Fan Ye, Hu Wang, and Guangyao Li. Variable stiffness composite\r\nmaterial design by using support vector regression assisted efficient\r\nglobal optimization method. Structural and Multidisciplinary\r\nOptimization, 56(1):203\u2013219, 2017.\r\n[29] Chun-Teh Chen and Grace X Gu. Machine learning for composite\r\nmaterials. MRS Communications, 9(2):556\u2013566, 2019.\r\n[30] Monika Arora, Farhan Ashraf, Vipul Saxena, Garima Mahendru, Monica\r\nKaushik, and Pritish Shubham. A neural network-based comparative\r\nanalysis of br, lm, and scg algorithms for the detection of particulate\r\nmatter. In Advances in Interdisciplinary Engineering, pages 619\u2013634.\r\nSpringer, 2019.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 170, 2021"}