7/23/2019 Laminated plates Theory http://slidepdf.com/reader/full/laminated-plates-theory 1/43 Finite Element Analysis of Composite Laminates Tejas M. Patil Institute of technology, Nirma university 14MCLC22 Guide : Dr. P. V. Patel 28 April 2015 Tejas M. Patil Finite Element Analysis of Composite Laminates 1/43
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The term composite originally arose in engineering when twoor more materials were combined in order to rectify some
shortcoming of a particularly useful component. For example,cannons that had barrels made of wood were bound withbrass because a hollow cylinder of wood bursts easily underinternal pressure.A composite material can be defined as a heterogeneousmixture of two or more homogeneous phases that have beenbonded together. The phases can be of essentially anymaterial class, including metal, polymer, ceramic, carbon, oreven a fluid or void space
Composite materials can be tailored for various properties byappropriately choosing their components, their proportions,their distributions, their morphologies, their degrees of crystallinity, their crystallographic textures, as well as thestructure and composition of the interface between
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One of the earliest uses of composite material was by theancient Mesopotamians around 3400 B.C., when they gluedwood strips at different angles to create plywood.
In the Mongolian arcs, the compressed parts are made of corn,and the stretched parts are made of wood and cow tendonsglued together.
Japanese swords or sabers have their blades made of steel and
soft iron: the steel part is stratified like a sheet of paste, withorientation of defects and impurities in the long direction
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In about 1200 AD, the Mongols invented the first compositebows made from a combination of wood, bamboo, bone,cattle tendons, horns, bamboo and silk bonded with naturalpine resin.
From the 1870’s through the 1890’s, a revolution wasoccurring in chemistry. Early synthetic resins includedcelluloid, melamine and Bakelite.
In the early 1900’s, plastics such as vinyl, polystyrene,phenolic and polyester were developed. As important as theseinnovations were, reinforcement was needed to provide thestrength and rigidity.Bakelite, an early innovative plastic, was developed in 1907.
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World War II brought the FRP industry from research into
actual production.By 1947 a fully composite body automobile had been madeand tested.In early 1950’s, manufacturing methods such includedpultrusion, vacuum bag molding, and large-scale filament
winding were developed.In 1961, first carbon fiber was patented, but it was severalyears before carbon fiber composites were commerciallyavailable.Fiber development in the late 1960’s led to fibers made fromultra high molecular weight polyethylene in the early 1970’s.Progress in advanced fibers led to breakthroughs in aerospacecomponents, structural and personal armor, sportingequipment, medical devices, and many other applications.
Development of the 787 Dreamliner, PVD and THERMTIAL...Tejas M. Patil Finite Element Analysis of Composite Laminates 6/43
A lamina, or ply is plane layer of unidirectional fibres or wovenfabric in a matrix.
Orthotropic material with principal material axes in thedirection of the fibers, normal to the fibres in plane of laminaand normal to the plane of lamina.
Laminate
A laminate is made up of two or more unidirectional laminaeor plies stacked together at various orientations.
Composite laminate may be made up of two or more types of
unidirectional laminae of different thicknesses.Examples of laminated composites are Bimetals, Clad metals,laminated glass, plastic-based laminates, and laminatedfibrous compos- ites
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Properties of composites such as low densities, high strengthand stiffness to weight ratio can be employed with manyadvantages in civil enginnering.
Composite materials have more environmental resistance than
traditional civil engineering materials.Composite materials are as stiff as steel, but weighapproximately 80 times less and have stiffness-to-weight ratiohigher (approx. 5 times) than that of steel and so lesssusceptible to be in resonance with the ground motion of anearthquake.
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S. P. Joshi 1 and N. G. R. Iyengar studied the effect of thickness ratio on transverse deflection and its dependenceupon the ratio of shear stiffness and bending stiffness.Nine-noded isoparametric plate finite element based on
Mindlin’s theory was developed to predict transversedeflection and first natural frequency of laminated plates. Theperformance and accuracy of derived finite elementformulation had been studied by comparing the results with
other solutions/previous experimental results.
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C. Chin et al, used finite element method using thin-plateelements to predict the buckling capacity of arbitrarily shapedthin walled structural members. They used principle of minimum total potential energy to derive linear and geometricstiffness matrices for thin-plate element. They presented an
efficient and versatile finite element method using six-node30-dof thin-plate element capable of predicting the local,distortional, and flexural-torsional bucklirtg capacities of arbitrarily shaped thin-walled structural members under anyloading and boundary conditions. The proposed finite element
formulation had been applied to a wide range of exampleproblems. It was demonstrated that in all cases, the methodwas able to predict the buckling loads and modes accurately.
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J.N. Reddy et al, presented a mixed finite element model forthe static analysis of laminated composite plates. finiteelement model considered the first-order shear deformationtheory with generalized displacements and stress resultants asindependent variables. Specifically, the mixed model isdeveloped using equal-order C 0 Lagrange interpolationfunctions of high p-levels along with full integration. Thepredictive capability of the proposed model was demonstratedby numerical examples of the static analysis of four laminated
composite plates, with different boundary conditions andvarious side-to-thickness ratios.
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K. Baskar et al, dealt with finite-element modeling andnonlinear analysis of steelconcrete composite plate girdersunder negative bending and shear loading. Athree-dimensional FE model, using a general purposefinite-element software, has been used to carry out thenonlinear analysis. Results obtained from the FE analysis werecompared with the corresponding experimental results. It wasobserved from the comparison that the proposed nonlinear FEmodel was capable of predicting the ultimate load behavior of
steelconcrete composite plate girders to an acceptableaccuracy.
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S.M. Shiyekar , Tarun Kant presented the study on Higherorder shear deformation effects on analysis of laminates withpiezoelectric fibre reinforced composites. A higher order shearand normal deformation theory (HOSNT12) is used to analyzesuch hybrid or smart laminates subjected to electromechanicalloading.
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The fist order shear deformation theory is based ondisplacement field, where the three components of thedisplacement vector are expanded in power series of thethickness coordinate and unknown functions. It is also knowncommonly as The Mindlin Plate Theory. The first order shear
deformation theory yields a constant value of transverse shearstrain through the thickness of plate by introducing shearcorrection factors.
The plane normal to the midplane before deformation will not
remain normal any longer after the deformation. In this theorytransverse shear deformation is accounted.
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A simple supported and a clamped square plate under uniformtransverse pressure is considered. The following is the data used inthe code.Youngs Modulus, E = 10920 Nm/Kg2
Plate thickness, t = 0.1 mPoissons ratio, = 0.3Length of the plate, a = 1 mBreadth of the plate, b = 1mPressure = 1 unit
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Static Analysis of Laminates: Results and Conclusions
Daniel I.M. and Ishai O., ”Engineering Mechanics of Composite Materials”, Oxford University Press, New York,
2007.Reddy J.N. and Ochoa O.O., ”Finite Element Analysis of Composite Laminates”, Kluwer Academic Publishers, London,1992.
Logan D. L., ”A First Course in the Finite Element Method”,Thomson Canada Limited, 2007.
Reddy J.N. and Chao W.C., ”A comparison of closed-formand finite element solutions of thick laminated anisotropicrectangular plates”, Nuclear Engineering and Design 1981,
Vol. 64, pp. 153-167.
Mukhopadhyay M., ”Mechanics of composite materials andstructures”, Universities Press Private Limited, Hyderabad,India, 2004.
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Shiyekar S.M. and Kant T., ”Higher order shear deformationeffects on analysis of laminates with piezoelectric fibrereinforced composite actuators”, Composite Structures 2011,Vol. 93, pp. 3252-3261.
S. P. Joshi and N. G. R. Iyengar. ”Analysis of hybridlaminated composite plates” , Journal of Solid Mechanics2010, Vol.2, No. 1, pp.79-90.
J. N. Reddy et al. ”Mixed least-squares finite element modelfor the static analysis of laminated composite
plates”,Composite Structures 2002, Vol. 56, pp. 329-344.
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