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    Robust design optimisation of advance hybrid (fiber–metal) composite structures.pdf

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    Robust design optimisation of advance hybrid (fiber–metal) composite structures.pdf

    Robust design optimisation of advance hybridDongSeop Leea,c, Carlos Morillob,⇑, Sergio Ollera,b, GabrielaCentre Internacional de Metodes Numerics en Enginyeria CIMNE, Edificio C1, Gran Capitan,bUniversitat Politecnica de Catalunya, Barcelona Tech UPC, Edificio C1, Gran Capitan, s/n,cDeloitte Analytics, Deloitte Consulting LLC, Seoul, Republic of KoreaMulti-Objective Optimisationrobust design optimisationFinite Element AnalysisHCSspropertiessecond application considers a Robust Multi-Objective Design Optimisation RMDO to minimise totals tThe FRP core has higher stiffness-to-weight ratios than monolithicmetal that is less sensitive to fatigue effects. In addition, the com-posite can potentially outperform either of two constituent mate-rials in elevated temperature structural applications [4].From HCS literature reviews, it can be seen that most ofresearchers focused on experimental test of mechanical properties[3–12], and few studies deal with the optimisation of these hybridcomposites; Nam et al. [13] consider a single-objective optimisa-tion of HCS using GA to maximise the composite strength by alter-ing the ply orientation of the composite. Peng et al. [14] considerAluminium Bronze UNS C63000 metal structure; MS Ti-A, reference Titanium Grade12 Annealed metal structure; Mt, Metal thickness; Ni-A, Nickel Aluminium BronzeUNS C63000; NMD, normalised mean displacement; PDF, Probability DensityFunction; PM, Pareto member; PSO, Particle Swarm Optimisation; RDO, robustdesign optimisation; RMDO, Robust Multi-Objective Design Optimisation; RMOGA,Robust Multi-Objective Genetic Algorithm; RMOP, Robust Multi-objective Optimi-sation Platform; SDD, Standard Deviations of the Displacement; Ti-A, TitaniumGrade 12 Annealed; Ti–Gr, Titanium–Graphite.qhttp//www.cimne.com.⇑Corresponding author.E-mail addresses dsleecimne.upc.edu D. Lee, cmorillocimne.upc.eduC. Morillo, sergio.ollerupc.edu S. Oller, bugedacimne.upc.edu G. Bugeda,Composite Structures 99 2013 181–192Contents lists available atComposite Structuresjournal homepage www.elsevionatecimne.upc.edu E. Oate.properties and lower operating cost [1]. The definition of HybridComposite Structures HCSs is consisted of several thin metal al-were originally developed at Delft University of Technology atthe beginning of 1980 [2]. Recently, some new hybrid materialshave been developed like the newest metal laminates consistingof thin titanium plies sandwiched by layers of polymer matrixcomposites. Boeing Airplane Company refers to this class of mate-rials as Ti–Gr titanium–graphite, while others have referred tothem as Hybrid Titanium Composite Laminates HTCLs [3].InHCS, the metal protects the FRP core from environmental effectssuch as thermal degradation and moisture ingress while poten-tially providing higher impact resistance and bearing properties.Abbreviations Al-A, Aluminium 2024-T3; CAD, Computer Aided Design; CDF,Cumulative Distribution Function; CFD, Computation Fluid Dynamic; FEA, FiniteElement Analysis; FEM, Finite Element Method; FRP, Fiber-Reinforced Polymer; GA,Genetic Algorithm; HCSs, Hybrid Composite Structures; HTCL, Hybrid TitaniumComposite Laminate; Mo, Metal Orientation; MODO, Multi-Objective DesignOptimisation; MOGA, Multi-Objective Genetic Algorithm; MS, metal structure;MS Al-A, reference Aluminium 2024-T3 metal structure; MS Ni-A, reference Nickel1. IntroductionThe development of hybrid compositesfrom aerospace and marine industrie0263-8223/ - see front matter C211 2012 Elsevier Ltd. Allhttp//dx.doi.org/10.1016/j.compstruct.2012.11.033weight of HCS and to minimise both, the normalised mean displacement and the standard deviationsof displacement, considering critical load cases. For the optimisation process, a distributed/parallelMulti-Objective Genetic Algorithm in robust multi-objective optimisation platform is used and it is cou-pled to a Finite Element Analysis based composite structure analysis tool to find the optimal combinationof laminates sequences for HCSs. Numerical results show the advantages in mechanical properties of HCSover the metal structures, and also the use of RMDO methodology to obtain higher characteristics of HCSin terms of mechanical properties and its stability at the variability of load cases.C211 2012 Elsevier Ltd. All rights reserved.has been motivatedo improve mechanicalloy sheets and plies of continuous Fiber-Reinforced PolymerFRP materials. HCSs have both the advantages of metallic andcomposite materials, including good plasticity, impact resistance,processability, low weight and excellent fatigue properties. TheyKeywordsStacking sequenceHybrid fiber–metal composite structuresThe concept of robust design approach ensures that a structure will be tolerant to unexpected loadingand operating conditions. In this paper, two applications are considered; the first is to maximise the stiff-ness of the HCS while minimising its total weight through a Multi-Objective Design Optimisation. Thearticle infoArticle historyAvailable online 20 December 2012abstractHybrid Composite Structuresmetal sheets. Mechanicalusing an innovative methodologyrights reserved.fiber–metal composite structuresqBugedaa,b, Eugenio Oatea,bs/n, 08034 Barcelona, Spain08034 Barcelona, Spainare consisting of alternating layers of Fiber-Reinforced Polymer andand responses for off-design conditions of HCSs can be improvedcoupling Multi-Objective Genetic Algorithm and robust design method.SciVerse ScienceDirecter.com/locate/compstructoptimal strength design for FRP and HCS using Particle SwarmOptimisation PSO to minimise the failure by optimising fiber ori-entation angles. However, in practical situations, it is desirable tofind a structural design that optimises various performancessimultaneously at off-design conditions. Although the need forconsidering the multiple structural behaviours simultaneously asa set of objective functions is thus apparent, these previous studiesare limited to the case of a single objective function.Robust design optimisation RDO proposed by Taguchi [15] canbe an emerging design method in composite structures whereprincipal objective is to improve product quality by controllingthe uncertainty effect. In engineering, the RDO cannot be ignoredsince the variations of manufacturing process parameters, environ-mental aspect and loads life conditions can affect the solutionquality in terms of mean performance and its sensitivity [16,17].Some researchers have considered such variances or tolerancesapplying uncertain design conditions in fiber laminated compos-ites. Walter and Hamilton [18] described a procedure to designlaminatedplates for a maximisationof buckingload with manufac-turing uncertainty in the ply orientation angle. Adali et al. [19]present an optimal design of composite laminates subjected tobiaxial compressive loads belonging to a given uncertainty domainunder the worst possible case of biaxial compressive loading. Liaoand Chiou [20] proposed a method based on anti-optimisationtechnique by adding extra sensitivity terms in design constraintsthat is used for the robust optimum design of fiber reinforced com-posites with manufacturing uncertainties. Antonio and Hoffbauer[21] develop a mixed formulation of reliability-based design opti-misation and robust design optimisation for reinforced composites,considering the ply angle, load factor, the elastic and strengthmaterials properties as design variables. Lee et al. [22] set the dif-ferences between the damage tolerant design and robust designanalysing composite panels. They studied the effect of laminatestacking sequence on the robustness and present a methodologyto quantify it using FiniteElement Analysis. Literature reviews con-sidering the concept of robust design optimisation in compositestructures show that only manufacturing uncertainties have beenconsidered whereas uncertainties in loading conditions have not.In this paper, a robust multi-objective optimisation methodol-ogy is developed for a hybrid fiber–metal composite structureHCS design considering a set of uncertain critical load casesbending, shear and torsion and also treating manufacturing pro-cess parameters as design variables. The paper investigates the ro-bust multi-objective stacking sequence design optimisation forHCSs using a distributed/parallel Genetic Algorithm GA in RobustMulti-objective Optimisation Platform RMOP developed atCIMNE coupled with a Finite Element Analysis FEA based com-posite structure analysis tool named Compack [23–25]. Two HCSapplications are addressed; the first application in a multi-objec-tive manner is to improve mechanical properties both weightand stiffness of HCS, which is modelled as a simply two oppositesides supported quadrangular plate. The second application con-siders a robust design optimisation of HCS that is formulated tominimise its total weight while maximising HCS stiffness qualityin terms of mean and standard deviation of displacement. In thesecond application, the boundary condition is set as one side rigidrectangular hybrid composite plate. For HCS manufacturing designvariables, 32 design parameters are considered in total six types offiber aramid, glass, boron, and carbon fibers, eleven fiber thick-nesses, twelve fiber orientation angles, and also three differenthigh performed metals allows Aluminium 2024-T3 Al-A, Tita-nium Grade 12 Annealed Ti-A and Nickel Aluminium BronzeUNS C63000 Ni-A.182 D. Lee et al./Composite StructuresThe rest of this paper is organised as follows; Section 2 de-scribes a methodology for HCS design optimisation. Section 3 pre-sents a composite structure analysis tool. Section 4 considers tworeal-world HCS design optimisations. Section 5 concludes overallnumerical results and present future research avenues.2. Methodology2.1. Multi-Objective Design OptimisationOften, engineering design problems require a simultaneousoptimisation of conflicting objectives and an associated numberof constraints. Unlike single objective optimisation problems, thesolution is a set of points known as Pareto optimal set. Solutionsare compared to other solutions using the concept of Pareto dom-inance. A multi-criteria optimisation problem can be formulated asMaximise/minimise the functionsfixii 1;...;N 1Subject to constraintsgjx0 j 1;...;MhkxC200 k 1;...;M2where fi, gj, hkare, respectively, the objective functions, the equalityand the inequality constraints. N is the number of objective func-tions and x is an n – dimensional vector where its arguments arethe decision variables. For a minimisation problem, a vector x1issaid partially less than vector x2if8ifix1C20fix2 and 9ifix1 fix23In this case the solution x1dominates the solution x2.As Genetic Algorithms GAs evaluate multiple populations ofpoints, they are capable of finding a numberof solutions in a Paretoset. Paretoselection ranks the populationand selects the non-dom-inated individuals for the Pareto fronts. A Genetic Algorithm thathas capabilities for multi-objective optimisation is termed Multi-Objective Genetic Algorithms MOGAs. Theory and applicationsof MOGAs can be found in Refs. [26–28].2.2. Robust design optimisationA robust design method, also called the Taguchi Method uncer-tainty, pioneered by Taguchi [15], improves the quality of engi-neering productivity. An optimisation problem can be define asMaximization/minimizationf fy1;...;yn;yn1;...;Ym4where y1;...;ynrepresent design parameters and yn1;...;ymrepre-sentuncertaintyparameters.Therangeofuncertaintydesignparam-eterscanbedefinedbyusingtwostatisticalfunctions;meanlxandvariance dx rx2 as part of the Probability Density FunctionPDF. The Taguchi optimization method minimises the variabilityof the performance under uncertain operating conditions. Thereforein order to perform an optimisation with uncertainties, the fitnessfunctions should be associated with two statistical formulas themean value lf and its variance df or standard deviation rf ffiffiffiffiffidfp.lf 1KXki1fi5df 1K C01XKi1fiC0lf26where K denotes the number of subintervals of variation conditions.The values obtained by the mean lf and the variance dforstandard deviation rf represent the reliability of model in terms99 2013 181–192of the magnitude of performance and stability/sensitivity at a set ofuncertain design conditions.2.3. Robust Multi-objective Optimisation PlatformRMOPisacomputationalintelligenceframeworkwhichisacollec-tionofpopulationbasedalgorithmsincludingMulti-ObjectiveGeneticAlgorithmMOGAandParticleSwarmOptimisationPSO[26,28,29].RMOP is easily coupled to any analysis tools such as ComputationFluid Dynamic CFD, Finite Element Analysis FEA and/or ComputerAided Design CAD systems. In addition, it is capable to solve anyengineeringdesignapplications.Inthispaper,aGAsearchingmethodin RMOP is used denoted as RMOGA under the parallel/distributedoptimisation system. RMOGA uses a Pareto tournament selectionoperator which ensures that the new individual is not dominated byany other solutions in the tournament. Fig. 1 shows the overall algo-rithm for robust design optimisation problems using RMOGA.3. Composite structure analysis toolsCompack is an analysis kit designed by Quantech and CIMNEable to use the necessary tools for the generation of a finite ele-ment model to perform structural simulations of composite mate-rial structures see references [30–32]. Compack is able todetermine the structural properties such as elastic behaviour, ulti-mate tensile, compression strength, and damage level of a compos-ite material. One of the principal benefits of Compack is thecapability of working with the constitutive model of the compositematerial in detail. To do so, it takes into account all mechanical andphysical properties, amount and orientation of each of its formingfibre and matrix materials, and follows a FEM procedure to solvethe structural problem.D. Lee et al./Composite Structures 99 2013 181–192 183Fig. 1. Overall algorithm for robust design optimisation problems using RMOGA.4. Advance hybrid fiber–metal composite structure designoptimisationThis section considers two applications of advanced hybrid fi-ber–metal composite structure HCS using RMOGA coupled toCompack; the first problem considers a Multi-Objective DesignOptimisation MODO design of HCS. The second problem is a Ro-bust Multi-Objective Design Optimisation RMDO of HCS consid-ering three different critical load conditions bending, shear andtorsion. Numerical results compare mechanical properties andmechanical behaviours of optimal HSCs, and three metal structurescomposed with Aluminium 2024-T3 denoted as MS Al-A, Tita-nium Grade 12 Annealed denoted as MS Ti-A and Nickel Alumin-4.1.3. Numerical resultsThe optimisation has run 20 h of computer time 2040 functionevaluations using ten CPUs in Dell PowerEdge 6850 IntelRXeonTM CPU 16 C2 3.20 GHz and 32 GB RAM ma

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