DOI : 10.17577/IJERTV2IS111078
- Open Access
- Total Downloads : 353
- Authors : Shaik Mohammad Yasin, N. Suneel Kumar, Yogeswara Reddy Aramalla
- Paper ID : IJERTV2IS111078
- Volume & Issue : Volume 02, Issue 11 (November 2013)
- Published (First Online): 28-11-2013
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
An Investigation of Ply Behaviour in A Composite Laminate Plate Based on Failure Criterion
Shaik Mohammad Yasin1, N. Suneel Kumar2 , Yogeswara Reddy Aramalla3
1M.Tech(CAD/CAM), Nimra College of Engineering & Technology, Nimra Nagar, Ibrahimpatnam, Vijayawada, Andhra Pradesh, India.
2Assistant Professor, Dept of Mechanical Engineering, Nimra College of Engineering & Technology,
Nimra Nagar, Ibrahimpatnam, Vijayawada, Andhra Pradesh, India.
3Sr.CAE Engineer, Automotive Robotics Engineering Service (India) Pvt. Ltd., Andhra Pradesh, India.
Abstract
Fibre reinforced composites have become increasingly important over the past few years and are now the first choice for fabricating structures where low weight in combination with high strength and stiffness are required. The present work is aimed at gaining an initial understanding of the failure behaviour of fibre reinforced laminates with carbon, E-glass and Kevlar 149 fibres and epoxy resins by using Tsai-Wu failure criterion. The purpose of this investigation is to characterize the effect of ply angle sequence on the composite laminates subjected to various loadings and get the best ply design for the materials considered in this investigation. Finite element models are created with ABAQUS/CAE software. These models are used to simulate for different materials with different ply angles, as well as different loads. Graphs are plotted to compare the failure index of different materials, the best ply design for the composites investigated in this project.
Keywords: ABAQUS/CAE, FRP Composites, Tsai-Wu failure criterion.
-
Introduction
Fibre reinforced composites have become increasingly important over the past few years and are now the first choice for fabricating structures where low weight in combination with high strength and stiffness are required. Because of their low specific gravities, high strength to weight ratios and modulus to weight ratios, these composite materials are markedly superior to those of metallic materials. The fatigue strength- weight ratios as well as fatigue damage tolerances of many composite laminates are excellent. In fibrous composites, Fibre Reinforced Plastics (FRP) composites are in greatest commercial use. The
important factor about FRP is that, unlike metals, the material is made at the same time as the component. This gives an increased freedom to the design process.
These composites may have thermo-set polymers (resins) or thermo-plastic polymers as matrix. The matrix plays a minor role in the tensile- load- carrying capacity of a composite structure but has major influence to the inter laminar shear as well as in-plane shear properties of the composites. Resins such as epoxies and polyesters are widely used matrix materials. Glass fibres are the most common of all reinforcing fibres for plastic matrix composites. The principal advantages of glass fibres are low cost, high tensile strength, high chemical resistance and excellent insulating properties. E- Glass and S- Glass are two varieties of Glass fibres. Carbon/ Graphite fibres have high tensile- weight ratio as well as high tensile modulus- weight ratio, very low coefficient of thermal expansion and high fatigue strength. Boron and ceramic fibres are also in use. Till date, Metal or Ceramic matrix composites have very small market share because of their cost, high processing temperatures and fabrication complexities.
-
Literature review
J. Eskandari Jam and N. Garshasbi Nia [1] developed finite element analysis on the failure behavior of laminated composite plates subjected to impulsive loads were undertaken using ANSYS These studies include the effects of parameters like size of plates, boundary conditions and fiber orientation angles. Extensive studies on convergence and validity of results based on available data have been carried out prior to the presentation of salient results of this analysis. The normal mode superposition technique is used for the analytical solutions of dynamic response. The failure analysis of the plates was calculated based on the material failure of the facings predicted from Tsai-Wu theory.
Dr. Roberto Frias and camanho P [2] presented recent developments in the numerical simulation of damage and structural collapse of advanced composite structures. The constitutive models presented are developed in the framework of Continuum Damage Mechanics and Fracture Mechanics, and can predict the onset and propagation of the different damage mechanisms occurring in composite materials.
David W.Sleight [3] developed progressive failure analysis for predicting the failure of laminated composite structures under geometrically nonlinear deformations. The progressive failure analysis uses C shell elements based on classical lamination theory to calculate the in-plane stresses. Several failure criteria, including the maximum strain criterion, Hashins criterion, and Christensens criterion, are used to predict the failure mechanisms and several options are available to degrade the material properties after failures.
-
Problem description
A Composite material is a material brought about by combining materials differing in composition or form on a macro scale for the purpose of obtaining specific characteristics and properties. To identify the failure mechanism and to trace the path of the failure propagation, failure criteria are used. The failure modes such as fibre breakage and matrix damage are predicted using different failure theories.
The problem is to characterize the effect of the ply sequences, material properties & type of loading on the performance of composite laminates plates. This subject is a crucial design question that appears frequently in the design of new composite products. This investigation attempts to provide initial insight behaviour of composite laminated plate by applying different loads with finite element models and predicted the behaviour of the laminates under different loading situations. Further research is needed to evaluate the effects of damage on specific applications.
-
Methodology
-
Abaqus
Abaqus is a suite of powerful engineering simulation programs, based on the finite element method, which can solve problems ranging from relatively simple linear analyses to the most challenging nonlinear simulations. Abaqus offers a wide range of capabilities for simulation of linear and nonlinear applications. Problems with multiple components are modeled by associating the geometry defining each component with the appropriate material
models and specifying component interactions. In a nonlinear analysis Abaqus automatically chooses appropriate load increments and convergence tolerances and continually adjusts them during the analysis to ensure that an accurate solution is obtained efficiently.
-
Shell element
Shell elements are used to model structures in which one dimension (the thickness) is significantly smaller than the other dimensions and the stresses in the thickness direction are negligible. Shell element names in Abaqus begin with the letter S. Two types of shell elements are available in Abaqus: conventional shell elements and continuum shell elements. Conventional shell elements discretize a reference surface by defining the element's planar dimensions, its surface normal, and its initial curvature. Continuum shell elements, on the other hand, resemble three-dimensional solid elements in that they discretize an entire three-dimensional body yet are formulated so that their kinematic and constitutive ehaviour is similar to conventional shell elements.
-
Material Properties
In the present analyses, the material properties for the various composite laminated plates are shown in the below table.
Table 1. Composite material properties of Carbon epoxy
E1
134.75GPa
Xt
1500MPa
E2
8.24GPa
Xc
1200MPa
G12=G23=G31
7.0GPa
Yt
50MPa
J12
0.325
Yc
250MPa
Ply Thickness:
0.0025m
S
70MPa
Table 2. Composite material properties of E-Glass epoxy
E1
39GPa
Xt
1080MPa
E2
8.6GPa
Xc
620MPa
G12=G23=G31
3.8GPa
Yt
39MPa
J12
0.28
Yc
128MPa
Ply Thickness:
0.0025m
S
89MPa
Table 3. Composite material properties of Kevlar 149 epoxy
E1
87GPa
Xt
1280MPa
E2
5.5GPa
Xc
335MPa
G12=G23=G31
2.2GPa
Yt
30MPa
J12
0.34
Yc
158MPa
Ply Thickness:
0.0025m
S
49MPa
The lay-up sequences used for the investigation are 1. [45/-45/45/0/90]s
2. [0/90/0/90/0]s
-
Failure theory used
Failure modes in laminated composites are strongly dependent on geometry, loading direction, and ply orientation. Typically, one distinguishes in-plane failure modes and transverse failure modes (associated with interlaminar shear or peel stress). Since this composite is loaded in-plane, only in-plane failure modes need to be considered, which can be done for each ply individually. The failure strength in laminates also depends on the ply layup. The effective failure strength of the layup is at a maximum if neighboring plies are orthogonal to each other. The effective strength decreases as the angle between plies decreases and is at a minimum if plies have the same direction.
The preceding biaxial strength theories suffer from various inadequacies in their description of experimental data. One obvious way to improve the correlation between theory and experiment is to increase the number of terms in the prediction equation. This increase in curve fitting ability plus the added feature of representing the various strengths in tensor form was used by Tsai and Wu. In this process, several new strength definitions are required, mainly having to do interaction between stresses in two directions.
The equation proposed by Tsai & Wu is given below
Where the Tsai-Wu coefficients are defined as
,
, ,
In ABAQUS the additional parameter F12 is specified by f* or .
If is given
Otherwise
Where -1.0 f* 1.0 and the default value of f* is zero.
Proper value of F12 can provide slightly more accurate results compared to experimental data, although the difference usually is not large.
-
-
Finite element analysis
Finite element analysis is used to gain information about the behaviour of the composite laminates subjected to various loading conditions. Simple models are analyzed. FEA is used to predict the stresses and failure index induced in the laminate. These stresses and failure index can later be used to predict the life
span of the composite under various loading conditions. ABAQUS finite element codes are used for the simulations.
-
Modeling
A 3D deformable planar shell of length 400mm and width 200mm and thickness of each layer is 2.5mm, created to represent as a composite laminated plate in ABAQUS.
Figure 1. Shell model
-
Meshing
The finite element model is developed by meshing the model with S4 element type of element edge length 10mm.
Figure 2. Finite element model of composite
plate
-
Loading
The analysis is carried out by fixing one end of the composite plate as a cantilever and applying various types of loads such as tension, shear & transverse at the other end. The loaded model is shown in below figure.
When a steady load is applied gradually on this laminate, failure initiation occurs at 4300N approximately.
Figure 3. Composite plate with various boundary conditions
5.3. Analysis
Now the finite element model is ready to solve. The model is solved in three different cases such as tension
loading, transverse loading & shear loading with
1.5
1.4
1.3
1.2
1.1
Failure Index
Failure Index
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
3000 4000 5000 6000 7000 8000 9000
load(N)
varying the material properties and ply sequence. All cases are solved in static analysis. The results from this analysis were discussed in detail in the following chapter.
Figure 5. Failure index for carbon-epoxy [0/90/0/90/0]s laminate for tensile load
When a steady load is applied gradually on this laminate, failure initiation occurs at 4500N approximately.
-
-
Results & discussion
The finite element analysis is done for different FRP materials, with different arrangement of lay-up
layer 1
layer 2
layer 3
1.8 layer 4
layer 5
1.6 layer 6
1.4 layer 7
sequences, material properties and loads applied to the simulation model discussed in the previous chapter. These simulations are repeated for different loadings. The results for the simulations are extracted with the post processing tools ABAQUS/CAE. Three cases are solved by using the FEA model.
-
Tension load
1.2
Failure Index
Failure Index
1.0
0.8
0.6
0.4
0.2
0.0
500 1000 1500 2000 2500
Load(N)
layer 8
layer 9
layer 10
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
Here we took case I as tension load. These loads are applied by changing the material properties and changing the ply sequence. When this type of loads is applied on plates, the debonding between the fibres and matrix occurs and material breaks. Load vs. failure index graphs are plotted for each material and ply sequence as shown below
1.7
1.6
1.5
1.4
1.3
Failure Index
Failure Index
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500
Load(N)
Figure 4. Failure index for carbon-epoxy [45/- 45/45/0/90]s laminate for tensile load
Figure 6. Failure index for E glass-epoxy [45/- 45/45/0/90]s laminate for tensile load
layer 1
layer 2
layer3
layer 4
layer 5
layer 6
layer 7 layer8 layer 9
layer 10
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7 layer8 layer 9
layer 10
When a steady load is applied gradually on this laminate, failure initiation occurs at 1300N approximately.
1.8
1.6
1.4
Failure Index
Failure Index
1.2
1.0
0.8
0.6
0.4
0.2
500 1000 1500 2000 2500
Load(N)
Figure 7. Failure index for E glass-epoxy [0/90/0/90/0]s laminate for tensile load
When a steady load is applied gradually on this laminate, failure initiation occurs at 700N approximately.
1.6
1.4
1.2
Failure Index
Failure Index
1.0
0.8
0.6
0.4
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
-
Transverse load
In the case II we take the same material properties and same ply angles as in the above case. Since it is a transverse loading with a minimum loading the material tends to fail. When these types of loads are applied on the composite plates maximum damage occurs to the matrix and fails quickly. Load vs. failure index graphs are plotted for each material and ply sequence as shown below
layer 1
layer 2
0.2
1000 2000 3000 4000 5000
Load(N)
2.2
2.0
1.8
1.6
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
Figure 8. Failure index for Kevlar 149-epoxy [45/- 45/45/0/90]s laminate for tensile load
When a steady load is applied gradually on this laminate, failure initiation occurs at 2200N approximately.
layer 1
layer 2
1.4
failure index
failure index
1.2
1.0
0.8
0.6
0.4
layer 9
layer 10
0.75
0.70
0.65
0.60
0.55
Failure Index
Failure Index
0.50
0.45
0.40
0.35
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
0.2
0.0
40 50 60 70 80 90 100
Load(N)
0.30
0.25
0.20
0.15
0.10
0.05
1000 2000 3000 4000 5000
Load(N)
Figure 10. Failure index for carbon-epoxy [45/- 45/45/0/90]s laminate for transverse load
When a steady load is applied gradually on this laminate, failure initiation occurs at 55N approximately.
layer 1
layer 2
layer 3
Figure 9. Failure index for Kevlar 149-epoxy [0/90/0/90/0]s laminate for tensile load
When a steady load is applied gradually on this laminate, failure initiation occurs at 6500N approximately
S.
No.
Composite Material
Lay-up Sequence
Load (N)
1
Carbon Epoxy
[45/-45/45/0/90]s 4300
2
Carbon Epoxy
[0/90/0/90/0]s 4500
3
E glass Epoxy
[45/-45/45/0/90]s 1300
4
E glass Epoxy
[0/90/0/90/0]s 700
5
Kevlar149 Epoxy
[45/-45/45/0/90]s 2200
6
Kevlar149 Epoxy
[0/90/0/90/0]s 6500
S.
No.
Composite Material
Lay-up Sequence
Load (N)
1
Carbon Epoxy
[45/-45/45/0/90]s 4300
2
Carbon Epoxy
[0/90/0/90/0]s 4500
3
E glass Epoxy
[45/-45/45/0/90]s 1300
4
E glass Epoxy
[0/90/0/90/0]s 700
5
Kevlar149 Epoxy
[45/-45/45/0/90]s 2200
6
Kevlar149 Epoxy
[0/90/0/90/0]s 6500
Table 4. Load values at Failure index > 1 for Tensile load
2.4
2.2
2.0
1.8
failure index
failure index
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
300 350 400 450 500
Load(N)
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
From the above investigation we can say that Kevlar 149 epoxy with layup sequence of [0/90/0/90/0]s has high strength than the remaining layup sequence.
Figure 11. Failure index for carbon-epoxy [0/90/0/90/0]s laminate for transverse load
When a steady load is applied gradually on this laminate, failure initiation occurs at 250N approximately.
1.6
1.5
1.4
1.3
1.2
1.1
Failure index
Failure index
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
Load(N)
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
1.3
1.2
1.1
1.0
0.9
failure index
failure index
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
10 15 20 25 30
Load(N)
Figure 12. Failure index for E glass-epoxy [45/- 45/45/0/90]s laminate for transverse load
When a steady load is applied gradually on this laminate, failure initiation occurs at 30N approximately.
layer 1
Figure 14. Failure index for Kevlar 149-epoxy [45/- 45/45/0/90]s laminate for transverse load
When a steady load is applied gradually on this laminate, failure initiation occurs at 15N approximately.
1.6
1.4
1.2
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
1.4
1.2
failure index
failure index
1.0 layer 9
layer 10
1.0
0.8
0.6
0.4
0.2
0.0
40 60 80 100 120 140 160 180
Load(N)
0.8
failure index
failure index
0.6
0.4
0.2
0.0
50 100 150 200 250
load(N)
Figure 13. Failure index for E glass-epoxy [0/90/0/90/0]s laminate for transverse load
When a steady load is applied gradually on this laminate, failure initiation occurs at 40N approximately.
Figure 15. Failure index for Kevlar 149-epoxy [0/90/0/90/0]s laminate for transverse load
When a steady load is applied gradually on this laminate, failure initiation occurs at 75N approximately.
Table 5. Load values at Failure index > 1 for Transverse load
S.
No.
Composite Material
Lay-up Sequence
Load (N)
1
Carbon Epoxy
[45/-45/45/0/90]s 55
2
Carbon Epoxy
[0/90/0/90/0]s 250
/tr>
3
E glass Epoxy
[45/-45/45/0/90]s 30
4
E glass Epoxy
[0/90/0/90/0]s 40
5
Kevlar149 Epoxy
[45/-45/45/0/90]s 15
6
Kevlar149 Epoxy
[0/90/0/90/0]s 75
S.
No.
Composite Material
Lay-up Sequence
Load (N)
1
Carbon Epoxy
[45/-45/45/0/90]s 55
2
Carbon Epoxy
[0/90/0/90/0]s 250
3
E glass Epoxy
[45/-45/45/0/90]s 30
4
E glass Epoxy
[0/90/0/90/0]s 40
5
Kevlar149 Epoxy
[45/-45/45/0/90]s 15
6
Kevlar149 Epoxy
[0/90/0/90/0]s 75
From the above investigation we can say that the best ply sequence design for transverse loading is carbon epoxy with ply sequence [0/90/0/90/0]s.
-
Shear load
We will repeat the same procedure as done in the above two cases. But here we will apply the shear load. When this type of load is applied in composite plate delamination occurs, strength of the laminate decreases.
Load vs. failure index graphs are plotted for each
1.4
1.2
Failure Index
Failure Index
1.0
0.8
0.6
0.4
0.2
200 400 600 800 1000
Load(N)
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
material and ply sequence as shown below
1.5
1.4
1.3
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
Figure 17. Failure index for carbon-epoxy [0/90/0/90/0]s laminate for shear load
When a steady load is applied gradually on this laminate, failure initiation occurs at 650N approximately.
layer 1
layer 2
1.2
Failure Index
Failure Index
1.1
1.0
0.9
0.8
0.7
layer 8
layer 9
layer 10
1.4
1.2
Failure Index
Failure Index
1.0
0.8
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
0.6 0.6
0.5
0.4
300 350 400 450 500 550 600
Load(N)
0.4
0.2
0.0
50 100 150 200 250
Figure 16. Failure index for carbon-epoxy [45/- 45/45/0/90]s laminate for shear load
When a steady load is applied gradually on this laminate, failure initiation occurs at 400N approximately.
Load(N)
Figure 18. Failure index for E glass-epoxy [45/- 45/45/0/90]s laminate for shear load
When a steady load is applied gradually on this laminate, failure initiation occurs at 110N approximately.
1.4
1.2
1.0
Failure Index
Failure Index
0.8
0.6
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
1.4
1.2
Failure Index
Failure Index
1.0
0.8
0.6
layer 1
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
0.4
0.4
0.2
100 150 200 250 300
Load(N)
0.2
100 150 200 250 300 350 400
Load(N)
Figure 19. Failure index for E glass-epoxy [0/90/0/90/0]s laminate for shear load
When a steady load is applied gradually on this laminate, failure initiation occurs at 170N approximately.
layer 1
layer 2
Figure 21. Failure index for Kevlar 149-epoxy [0/90/0/90/0]s laminate for shear load
When a steady load is applied gradually on this laminate, failure initiation occurs at 250N approximately.
So from the above graphs we can observe that all the laminates with ply sequence [45/-45/45/0/90]s are behaving similarly and with ply sequence [0/90/0/90/0]s are behaving similarly. Since the loading
is shear plies with 90° angle are stronger and 0° plies
1.5
1.4
1.3
1.2
1.1
1.0
Failure Index
Failure Index
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
100 150 200 250 300 350 400
Load(N)
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
layer 9
layer 10
are failing soon.
Table 5. Load values at Failure index > 1 for Shear load
S.
No.
Composite Material
Lay-up Sequence
Load (N)
1
Carbon Epoxy
[45/-45/45/0/90]s 400
2
Carbon Epoxy
[0/90/0/90/0]s 650
3
E glass Epoxy
[45/-45/45/0/90]s 110
4
E glass Epoxy
[0/90/0/90/0]s 170
5
Kevlar149 Epoxy
[45/-45/45/0/90]s 200
6
Kevlar149 Epoxy
[0/90/0/90/0]s 250
Form the above investigation for shear loading we can observe that for carbon epoxy with [0/90/0/90/0]s has high strength compared to remaining laminates.
-
-
Conclusions
The present work is aimed at gaining an initial
Figure 20. Failure index for Kevlar 149-epoxy [45/- 45/45/0/90]s laminate for shear load
When a steady load is applied gradually on this laminate, failure initiation occurs at 200N approximately.
understanding of the ply behaviour of fiber reinforced laminates with carbon, E-glass and Kevlar fibers and epoxy resins. From the results of this work the following conclusions can be drawn.
-
The behavior of the composite changes with the application of the different loading conditions
-
The ply angle sequence of a composite material greatly affects on its failure behaviour.
-
Carbon epoxy with [0/90/0/90/0]s has best performance under shear loading and transverse loadings
-
Kevlar 149 epoxy with [0/90/0/90/0]s has best performance under tension loading.
-
-
References
-
J. ESKANDARI JAM & N. GARSHASBI NIA Dynamic failure analysis of laminated composite plates Association of metallurgical engineers of Serbia, AMES.
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Dr. ROBERTO FRIAS & CAMANHO P.P Advances in the simulation of damage and fracture of composite strictures
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DAVID W.SLEIGHT Progressive failure analysis methodology for laminated composite structures Langley research center, Hampton, Virginia, 1999.
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R.ZAHARI & A El ZAFRANY progressive damage analysis of composite layered plates using a mesh redution method International journal of engineering and technology, Vol 3, 2006, pp 21-36.
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J N REDDY Mechanics of laminated composite plates theory & analysis CRP Press 1997.
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Scripta book company, Washington, D.C. [11]ABAQUS 6.9 EF reference manual.