 Open Access
 Total Downloads : 520
 Authors : Y. Siva Prasad, G. Sambasiva Rao , V. Balakrishna Murthy
 Paper ID : IJERTV1IS8121
 Volume & Issue : Volume 01, Issue 08 (October 2012)
 Published (First Online): 29102012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
ThermoElastic Analysis of AnglePly Laminates with Circular CutOut under Cylindrical Bending
Y. Siva Prasad, G. Sambasiva Rao and V. Balakrishna Murthy
Mechanical Engineering Department, V. R. Siddhartha Engineering College, Vijayawada, India.
Abstract
Fourlayered symmetric and antisymmetric laminates with circular cutout and subjected to transverse uniform pressure load under cylindrical bending are analyzed using threedimensional finite element analysis. The problem is modelled in ANSYS software. Transverse deflection and rectangular components of normal and shear stresses are evaluated and variation of these results with respect to fiber angle for both the sequences is discussed.
Keywords: FRP, FEM, Symmetry, AntiSymmetry, cut out, Interface.

Introduction
The increasing use of fiber reinforced laminates in space vehicles, aircrafts, automobiles, ships and chemical vessels has necessitated the rational analysis of structures for their mechanical response. In addition, the anisotropy and nonhomogeneity and larger ratio of longitudinal to transverse modulii of these new materials demand improvement in the existing analytical tools. As a result, the analysis of laminated composite structures has attracted many research workers, and has been considerably improved to achieve realistic results. In the threedimensional elasticity solution, each layer is modelled as a three dimensional solid. Usually, the anisotropy in laminated composite structures causes complicated responses under different loading conditions by creating complex couplings between extensions, bending, and shear deformation modes. To capture the full mechanical behaviour, it must be described by three dimensional elasticity theories.

Literature Review
In solving the threedimensional elasticity equations of rectangular plates, quite a number of solution approaches have been proposed. One would find the
earlier research work of Pagano, who studied the static bending of infinitely long and finite size composite laminates under sinusoidal lateral loading using an analytical method. The elasticity solutions were compared with the classical thin plate (CTP) theory solutions, and the limitations of the CTP theory were pointed out in his work.
Srinivas and Rao [1] and Srinivas et al. [2] presented a set of complete analytical analyses on bending, buckling and free vibration of plates with both isotropic and orthotropic materials. Based on the analysis of Srinivas and Rao [1] and Srinivas et al. [2], Wittrick [3] worked out a detailed analytical threedimensional elasticity solution of simply supported plates for Eigen value problems of buckling and free vibration and for static deflections under sinusoidal lateral loading. Pagano et al. [4] has given exact solutions for the deflections and stresses of a crossply laminated rectangular composite without holes using elasticity theory.
Paolo et al. [5] analyzed the behaviour of an arbitrary laminated composite plate by assuming a layer wise polynomial expansion along the thickness direction for displacements. In contrast with other proposed approaches and in order to take into account the transverse normal stress distribution, outofplane displacements are not assumed to be constant along the thickness. Based on the proposed Kinematic assumptions the continuity of the interlaminar stress components at the interface can also be achieved. A finite element procedure is established and plate models are derived in which the stress field is obtained directly from the constitutive relations and not by the integration of the threedimensional equilibrium equations.
Busby and Saidiwakar [6] modified the finite quasi prismatic (FQP) element to analyze anisotropic materials. The finite quasiprismatic element is a three dimensional finite element which uses conventional
interpolating functions in two directions and functions based on Chebyshev polynomials in the third direction. Kong and Cheung [7] proposed a displacementbased, threedimensional finite element scheme for analyzing thick laminated plates by treating the plate as a three dimensional inhomogeneous anisotropic elastic body.
Limited literature is available on bending of composite plates with a cutout. Hwang and Sun [8] presented a continuous mixed field iterative scheme based on a threedimensional finite element displacement method. This method is very powerful in the determination of stress distributions for problems with either material and/or geometric discontinuities. For laminated composite materials this method is reliable in stress evaluation at locations away from the optimal Gauss points such as free edges near a notch or a hole. It is also useful in the determination of interlaminar stresses at an interface of laminated composites.
Prasad and Shuart [9] presented a closed form solution for the moment distributions around holes in symmetric laminates subjected to bending moments. Delale et al. [10] considered the stress analysis of plate made up of two bonded dissimilar isotropic materials with a central circular hole subjected to axisymmetric bending.
Lo and Leissa [11] considered the bending of isotropic square plates with a circular hole subjected to uniform transverse load. Results were shown for simply supported and clamped boundary conditions. Shiau and George [12] developed an 18 degreeoffreedom higherorder triangular plane stress element to investigate the effect of variable fiber spacing on the stress concentration around a hole in a composite laminated plate subjected to inplane boundary loadings.
Wen and Chyanbin [13] employed an asymptotic analysis to separate the 3D problem of laminate with hole into two plane problems. One is an interior problem, the other is a boundary layer problem. The former is treated by classical lamination theory and is solved by a special boundary element; the latter is then solved by the finite element method developed for the generalized plane deformation problems. Ramesh Kumar et al. [14] presented an approximate solution in the form of a polynomial for the normal stress distribution adjacent to a class of optimum holes in symmetrically laminated infinite composite plates under uniaxial loading. Sambasiva Rao [15] has studied the prediction of static and thermoelastic behaviour of FRP composite crossply laminates with cut outs under cylindrical bending.
The present investigation is an extension of the work of Sambasiva Rao [15] for angleply laminates.

Problem Modelling

Geometrical Modelling
Figure1 shows the inplane dimensions of laminate considered for the present analysis. The dimensions for b and l are taken as 2,000 mm and 4,000 mm respectively. The thickness of the laminate is taken as 200 mm and four layers of equal thickness are stacked in +///+ in symmetrical arrangement and +/ /+/ in antisymmetrical stacking sequence.
Figure 1: Composite Laminated with Circular cut out
The diameter of the hole is taken as per the ratio d/l =
0.1. Fiber angle varies from 00 to 900 with 150 intervals.

Finite Element Model
The finite element mesh is generated using a three dimensional brick element (SOLID 95) in ANSYS software. The element is defined by 20 nodes having three degrees of freedom per node: translations in the nodal x, y, and z directions. The FE mesh on the structure is shown in figure 2.

Boundary Conditions
The longer edges of the laminate are clamped. i.e. all the degrees of freedom of nodes along this faces are contrained.
At x = +1000 mm and x = 1000 mm Ux = 0; Uy = 0; Uz = 0.
Figure 2: FE mesh on Laminate
Sambasiva Rao [15] has validated by comparing FE results with the exact elasticity results given by Pagano
[4] for a crossply laminate under cylindrical bending subjected to transverse pressure loading with s =10 (Figure 3). Later he extended the analysis for laminates with cut outs due to pressure and thermal loads. The present analysis is extended for angleply laminates with cut outs under cylindrical bending subjected to transverse pressure load.FEM
80
Elasticity
Theory
60
40
20
0.1
0.2
0.3
0.4
0.
.5
0.4
0.3
0.2
0.1 20 0
40
60
80
100
12 =0.257, 23= 0.363, 31 = 0.257
G12= 4.13 GPa, G23= 3.75 GPa, G13= 4.13 GPa


Discussion of Results
Variations of inplane stresses with respect to fiber angle are shown in figures 4 to 6. x increases up to 300 of fiber angle and there after decreases for both laminates, the stresses in symmetric angleply condition are more when compared to that of the anti symmetric ply condition and maximum difference is found at =300 (Figure 4).
Figure 4 : Variation of x with respect to fiber angle [d/l=0.1, s=10]
It is observed that in both cases y increases up to 600 fiber angle and there after decreases, the stresses in symmetric angleply condition are more when compared to that of the antisymmetric ply condition and maximum difference is found at =600 (Figure 5).
0
0 5
100
Figure 3: Validation of FE results with analytical results of Pagano [4]
3.4 Material Properties
The properties evaluated by Sambasiva Rao [15] from micrmechanical numerical approach for T300 Epoxy composite for 60% volume fraction are used for the present analysis.
Figure 5: Variation of y with respect to fiber angle [d/l=0.1 s=10]
xy for both symmetric and anti symmetric conditions is observed to be increasing up to about 520 of fiber angle and there after decreases, the stresses in symmetric angleply condition are more when compared to that of the antisymmetric ply condition
E1 = 134.48 GPa, E2
= 9.92 GPa, E3= 9.92 GPa
and maximum difference is found at =520 (Figure 6).
Figure 6: Variation of xy with respect to fiber angle [d/l=0.1 s=10]
z for both symmetric and anti symmetric conditions is observed to be increasing up to 750 of fiber angle and there after decreases, the stresses in symmetric angle ply condition are more when compared to that of the antisymmetric ply condition and maximum difference is found at =450 (Figure 7).
.
Figure 7: Variation of z with respect to fiber angle [d/l=0.1 s=10]
yz for both symmetric and anti symmetric conditions is observed to be increasing up to 750 of fiber angle and there after decreases, the stresses in symmetric angle ply condition are more when compared to that of the antisymmetric ply condition and maximum difference is found at =750 (Figure 8).
Figure 8 : Variation of yz with respect to fiber angle [d/l=0.1 s=10]
zx for both symmetric and anti symmetric conditions is observed to be increasing up to 450 of fiber angle and there after decreases, the stresses in symmetric angle ply condition are more when compared to that of the antisymmetric ply condition and maximum difference is found at =450 (Figure 9).
Figure 9: Variation of zx with respect to fiber angle [d/l=0.1 s=10]
Uz for both symmetric and anti symmetric conditions is observed to be increasing up to 750 of fiber angle and there after decreases, the deflection in symmetric and antisymmetric laminates are almost equal (Figure 10).
Figure10: Variation of Uz with respect to fiber angle [d/l=0.1 s=10]
In a cylindrically loaded isotropic plate, inplane normal stress in xdirection is known to be significant. In the present case, other two inplane stresses are also observed to be significant. This is mainly due to the interaction of layers in a laminate leading to anisotropic behavior of total laminate where any kind of load produces extension, shear and bending responses of the laminate and this tendency depends on the arrangement of fibers in laminate. The resultant stiffness in a particular direction of the laminate varies with respect to fiber angle and hence all the stresses are varying with .

Conclusions
Stress analysis of a fourlayered angleply laminate is carried out using threedimensional finite element method. Variation of all the six components of stresses and transverse deflection with respect to fiber angle for both symmetric and antisymmetric laminates is discussed for a rectangular laminate with cut out subjected to transverse pressure load under cylindrical bending. The following conclusions are drawn.
All the stresses and deflection are sensitive towards change in fiber angle.
Stresses in symmetric laminates are higher than corresponding antisymmetric laminates.
Deflection is same for both the laminates.
10. References

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G Sambasiva Rao The prediction of static and thermo elastic behaviour of FRP composite laminates under cylindrical bending PhD Thesis, Andhra University, India, 2010.