Laminated plates Theory

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Finite Element Analysis of Composite Laminates

Tejas M. PatilInstitute of technology,

Nirma university14MCLC22

Guide : Dr. P. V. Patel28 April 2015

Tejas M. Patil Finite Element Analysis of Composite Laminates 1/43



Outline

Composite Materials : IntroductionComposite Materials : History

Composite Materials : Classification

Laminated Composites

Composites : Structural ApplicationsObjective, Scope

Literature Review

Mechanics of Composite plates

Static Analysis of composite platesResults and Discussions

References




Composite Materials : Introduction

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

components.Tejas M. Patil Finite Element Analysis of Composite Laminates 3/43



Composite Materials : History

Ancient Times -

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





1200’s to 1900’s-

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.





1940’s to 2000’s

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




Composite materials are commonly classified at following twodistinct levels:With respect to the matrix constituent

Polymer-Matrix CompositesMetal-Matrix Composites

Carbon-Matrix Composites

Ceramic-Matrix Composites





With respect to reinforcement form,-

Fibrous Composites

Particulate Composites



C




Lamina

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 composites


L i L i



Laminae-Laminate


L i L i



Laminae-Laminate


C it St t l A li ti



Composites : Structural Applications

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.


C it St t l A li ti



Composites : Structural Applications

Prefabricated bridge decks for either new bridges orrehabilitation of old bridges.

Seismic retrofitting of conventional concrete-steel bridgecolumns.

Suitable for Construction of Tall Buildings, Highway Bridges,Power Transmission towers, Silos, Office/Residential Buildings


C sit s St t l A li ti s E l s



Composites : Structural Applications Examples

Dome structure in Benghazi in 1968.

The first USA advanced composite vehicular bridgesuperstructure was dedicated into service on December 4,1996 in Russell, Kansas.

Suitable for Construction of Tall Buildings, Highway Bridges,Power Transmission towers, Silos, Office/Residential Buildings

Dubai Airport built in 1972.

American Express Building in Brighton, England.

Radome structure - 30.5 m high GFRP towers inserted intosteel tower at the Chicago McCook Illinois.


Radome structure



Radome structure


Dubai Airport



Dubai Airport


American Express Building in Brighton England



American Express Building in Brighton, England.


Objective



Objective

To study and incorporate different shear deformation theoriesfor analysis of laminated composite plates.

To derive the formulation of finite element for analysis of Laminated Composite Plates.

To study effect of various parameters on response of laminated composite plates.


Scope



Scope

Formulation of finite element for analysis of Laminated

Composite Plates.Static analysis of Laminated composite plates.


Literature Review



Literature Review

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.


Literature Review



Literature Review

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.


Literature Review



Literature Review

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.


Literature Review



Literature Review

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.


Literature Review



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.


Mechanics of Composite Laminates



p

For an orthotropic lamina in a 3-D state, the strain-stressrelationship at a point in each of the three orthogonal planesis given by,





p

The stress-strain constitutive relations can be obtained byinversion of strain-stress relations and are written in followingmatrix form.





p





The principal material axes of a lamina may not coincide withthe reference axes for the laminated plate. It is therefore

necessary to transform the constitutive relation from thelamina principal axes (1,2,3) to the reference axes of thelaminate (x, y, z).






Static Analysis of Laminates



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.





Displacement field Model:





stress-strain relationships





We consider a quadrilateral element, defined by four nodes innatural coordinates (ζ ,η). The coordinates are interpolated as





Stiffness K and load vector can be obtained using gaussquadrature method


Flow Chart for Static Analysis Program




Static Analysis of Laminates : Example



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


Static Analysis of Laminates: Results and Conclusions



In above example convergence of results is studied by

descretizing plate in different scheme of meshing.

Results

As from study it can be concluded that at 6 x 6 meshingscheme, the convergence is obtained.


Static Analysis of Laminates: Results and Conclusions



For 20x20 mesh size,-


References



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.


References



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.


Thank you

Laminated plates Theory

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