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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017

ANALYSIS OF COMPOSITE LAMINATED PLATE USING FEM NETHRAVATHI C1 AND SREENIVASA M B2 1 2

PG SCHOLAR,STRUCTURAL ENGINEERING DEPARTMENT,V.T.U PG STUDIES,MYSURU,INDIA.

ASSISTANT PROFESSOR OF STRUCTURAL ENGINEERING DEPARTMENT,V.T.U PG STUDIES,MYSURU,INDIA.

Abstract: A numerical analysis using finite element method(FEM) has been carried out to study the buckling behavior of graphite/epoxy laminated composite plates subjected to inplane uniaxial and biaxial compression loadings .In the present study, the effect of aspect ratio, number of plies and fibre orientation on buckling behavior graphite/epoxy. The results shows that the buckling loads of a composite laminated plate subjected to inplane uniaxial compressive loading decreases by increasing the plate aspect ratio (β).It is seen that the number of plies,inplane loads and aspect ratio (β) have a substantial influence on buckling strength of composite laminated plate. Key words : buckling analysis,aspect ratio,boundary condition,number of plies,symmetrically laminated composite plate,uniaxial and biaxial compression loading.

principal structural materials used in early days .Thus Euler’s theory was not much used due to the bulkiness of the structural elements. Buckling property of many engineering structural elements under compressive loading has always been an important field of research.

1.INTRODUCTION The rapid development of technology in the field of “material science” has made structural components slender with less weight, superior specific strength and stiffness compared to conventional materials.These materials are widely used in many engineering applications like aerospace, spacecraft nuclear structures, offshore and marine structures. Many studies have showed that such structures fail not due to high stress but due to insufficient elastic stability of slender or thin walled members. This results made to focus more on the static stability and buckling characteristics of beam, column plate and shell type of structures. The ability of the structure to retain its equilibrium configuration under loading is termed as stability and when loading produces an abrupt change in shape of member it is termed as instability. About 200 years ago L. Euler a German scientist studied the first problem of elastic instability concerned to lateral buckling of compressed members. Wood and stone where the IDL - International Digital Library

Improvement in technology developed a combined structure by joining two or more different materials in macro level to meet the material requirement which is called as composite material. 1.1 Composite materials A composite material is one in which two or more materials are combined to form a single structure with an identifiable interface. Composite materials have many advantages over conventional materials in structural performance with their superior strength to weight ratios as well as stiffness to weight ratios. Laminated composites are widely used in aerospace, automobiles and marine 1|P a g e

IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017 industries. Laminated composite are made up of plies(layers) each ply being composed of straight parallel fibres (e.g. glass, boron, graphite and carbon)embedded in and bonded together by a matrix material(e.g. epoxy resin, Polyether, ketone ,nylon).

1. 2. 3.

Composite Laminates have high stiffness and strength to weight ratios ,superior fatigue response characteristics, facility to vary fibre orientation, material and stacking pattern ,resistance to electro chemical corrosion and other superior material properties of composite. It requires better understanding of the structural behaviour and failure conditions for safe and more economical design .Laminated composite plate mainly fail in buckling due to presence of inplane loadings.

4. 5.

Parallel ply : all plies at the same arbitrary orientation Unsymmetric cross ply: all plies oriented at either 0° and 90°. Symmetric cross ply: all plies orientated at either 0° or 90° and arranged symmetrically about the midplane. Alternating balanced angle ply: Even number of plies oriented alternately at +θ and – θ. Symmetric balanced angle ply: Even number of plies arranged symmetrically about the midplane with an equal number of plies oriented at +θ and at – θ.

1.2: PLATES

The orientation of the fibres and stacking sequence has a large effect on the deformation and stress throughout the laminate

Plates are flat structural elements whose thickness is smaller than other dimensions and they are the most widely used slender structural elements subjected to both inplane and out of plane loadings.

FIG 1:Composite Laminates 1.1.1: Characteristics and Classification of composite plates: 1. Fibrous composite materials: consists of fibres in a matrix. 2. Laminated composite materials : consists of layers of various materials 3. Particulate composite materials : composed of particles in a matrix 4. Combination of some or all of the three.

FIG 2: Dimension, coordinate axes and displacement systems of Rectangular plate Plates may be classified into three types :  Thin plates with small deflection  Thin plates with large deflection  Thick plates Thin plates with small deflection : if the ratio of thickness (h) to the smaller span length (a) shold be less than 0.05 and the deflection (w) in z-direction is less than thickness (t0 then the plates are considered as thin plates with small deflections.

1.1.2: General theory and classification of simple lamination type: The following are the laminate arrangements which are most widely used and simply analyzed IDL - International Digital Library

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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017 Thin plates with large deflections : if the ratio of thikness (h) to smaller span length (a) should be less than 0.05 and the deflection (w) in z-direction is greater than thickness (t) then the plates to be considered as thin plates with large deflection

Buckling strength of simply supported composite laminated plate for graphite epoxy, material with various aspect ratio and number of plies and different fibre orientation subjected to uniaxial and biaxial compression load

Thick plates : if the ratio of thickness 9t) to the smaller span length (a) is greater than 0.05, the plate to be considered as thick plates. 2. Objectives: To determine the 1.

Buckling strength of simply supported isotrophic plate with various aspect ratios when subjected to uniaxial and biaxial loads 3.Geometry,boundary conditions and material properties For complex geometrical and boundary conditions, analytical method are not so easily adaptable, so numerical methods like finite element method have been used. In this work, Eigen buckling analysis is used for predicting the buckling load of a rectangular composite plate through the use of finite element package ANSYS. The SHELL 281(8 noded shell element). The SHELL281 structural element is chosen from ANSYS14.5 element library. SHELL281 has 8 Material constants nodes with Young’s Poisson’s 6 modulus ratio Material 2 degre (µ) (E)in N/mm es of Boundary Position of the edge freed condition 0.3 210924 Steel om at U=w=θx=0 @ V=w= Simply each x=0 θy=0@y=0 supported node, And And w= translati w=θx=0@x=a θy=0@y=-b on along x,y ,z directions and rotations about nodal x,y and zaxes. SHELL281 can be used for layered applications of a structural SHELL model up to 250 different layers are permitted for application.

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Fig 2 : SHELL 281 element (ANSYS element reference)

Table 3.1 :Geometric boundary condition

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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017

Table 3.2: Isotropic material constants 4.RESULTS AND DISCUSSIONS: Case 1: Critical buckling load (Ncr ) for SSSS isotrophic unperforated plate a. Uniaxial compression loading having thickness 8mm.:Table 4.1 gives the value of Critical buckling load for various aspect ratio(β) and fig Critical 4.1 a in b in Aspect Buckling show load (Ncr) mm mm ratio (β) s the variat 2343.3 100 200 0.5 ion of critic 1706.1 200 200 1.0 al 1185.6 300 200 1.5 buckl ing 1202.32 400 200 2.0 load (Ncr), The critical buckling load of a plate having β=0.5 is approximately,2,1.28,1 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively.

Fig 4.1 : Variation of critical buckling load Ncr for SSSS isotropic unperforated plate subjected to inplane Uniaxial

Critical a in

b in

Aspect

Buckling

ratio (β)

load (Ncr)

100

200

0.5

3768.3

200

1.0

1934.7

300

200

1.5

1515.7

400

200

2.0

1516.5

load. b. Biaxial compression loading having thickness 8mm.: Table 4.2 gives the value of critical buckling load (Ncr) for various aspect ratio(β) and fig 4.2 shows the variation of critical buckling load, The critical buckling load of a plate having β=0.5 is approximately 1.3,1.5 and 0.9 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively.

Table 4.1:Critical buckling load Ncr for SSSS isotrophic unperforated plate with respect to aspect ratio(β) subjected to inplane uniaxial compression loading having thickness 8mm.

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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

Available at: www.dbpublications.org

International e-Journal For Technology And Research-2017

Table 4.2:Critical buckling load Ncr for SSSS isotrophic unperforated plate with respect to aspect ratio(β) subjected to inplane biaxial compression loading having thickness 8mm.

Aspect ratio (β)

a in mm

b in mm

Critical buckling load (Ncr) 8 plies

16 plies

0.5

100

26.43

203.05

1.0

100

13.37

105.85

1.5

150

100

12.65

93.91

2.0

200

100

14.82

80.63

Table 4.3 : Critical buckling load (Ncr) for SSSS graphite/epoxy composite laminate plate with respect to aspect ratio (β) subjected to inplane uniaxial compression loading with fibre orientation (0°/90°/-90°/0°)

Fig 4.2 :Variation of critical buckling load Ncr for SSSS isotropic unperforated plate subjected to inplane Biaxial load. Case 2: critical buckling load(Ncr) fibre orientation (0°/90°/-90°/0°)s for graphite /epoxy Composite laminated plate a. Uniaxial compression loading for 8 plies and 16 plies: Table 4.3 gives the buckling load (Ncr) for graphite /epoxy Composite laminated plate having various aspect ratio(β), fig 3.3 and fig 3.4 shows the the variation of critical buckling load (Ncr) for 8 plies and 16 plies.The critical buckling load(8 plies)of a plate having β=0.5 is approximately,2, 2.1 and 1.8 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively and for 16 plies,critical buckling load (Ncr) having β=0.5 is approximately, and 13 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively.

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Fig 4.3 :Variation of critical buckling load(Ncr) for 8 plies with fibre orientation (0°/90°/-90°/0°)s subjected to inplane Uniaxial compression loading

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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017 aspect ratio (β) subjected to inplane biaxial compression loading with fibre orientation (0°/90°/-90°/0°)s Fig 4.4 :Variation of critical buckling load (Ncr) for 16 plies with fibre orientation (0°/90°/-90°/0°)s subjected to inplane Uniaxial compression loading b.

biaxial compression loading for 8 plies and 16 plies:Table 4.4 gives critical buckling load (Ncr) for

various aspect ratio(β),fibre orientation(0°/90°/90°/0°)s and fig 4.5 and 4.6 variation of critical buckling load (Ncr).For 8 plies, critical buckling load of a composite laminated plate having β=0.5 is approximately 3.8,9 and 12.5 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively.For 16 plies, The critical buckling load of a composite laminated plate having β=0.5 is approximately 2.9,1.8 and 2.2 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively.

Aspect ratio (β)

a in mm

b in mm

Fig 4.5 :Variation of critical buckling load(Ncr) for 8 plies with fibre orientation (0°/90°/-90°/0°)s subjected to inplane biaxial compression loading

Critical buckling load (Ncr) 8 plies

16 plies

0.5

100

26.83

249.61

1.0

100

14.43

131.77

1.5

150

100

17.42

129.69

2.0

200

100

16.93

146.57

Fig 4.6 :Variation of critical buckling load(Ncr) for 16 plies with fibre orientation (0°/90°/-90°/0°)s subjected to inplane biaxial compression loading Case 3 : : Critical buckling load (Ncr) for SSSS graphite/epoxy composite laminate plate with fibre orientation (0°/30°/-30°/90°)s a.

Uniaxial compression loading for 8 plies and16plies:

Table 3.4 : Critical buckling load (Ncr) for SSSS graphite/epoxy composite laminate plate with respect to

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table 4.5 gives the value of Critical buckling load (Ncr) for various aspect ratio(β),fig 4.7 and fig 4.8 shows 6|P a g e

IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017 various aspect ratio(β).for 8 plies and 16 plies, The critical buckling load of a plate having β=0.5 is approximately,1.75,1.5 and 1.5 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively. For 16 plies, . The critical buckling load of a plate having β=0.5 is approximately, 1.85,1.9 and 1.7 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively. Aspect ratio (β)

a in mm

b in mm

Critical buckling load (Ncr) 8 plies 16 plies

0.5

100

18.90

155.53

1.0

100

4.92

52.925

1.5

150

100

2.09

83.02

2.0

200

100

1.49

70.10

Table 4.5: Critical buckling load (Ncr) for SSSS graphite/epoxy composite laminate plate with respect to aspect ratio (β) subjected to inplane uniaxial compression loading with fibre orientation (0°/30°/-30°/90°)s

Fig 4.8: Variation of critical buckling load(Ncr) for 16 plies with fibre orientation (0°/30°/-30°/90°)s subjected to inplane Uniaxial compression loading

Fig4.7: Variation of critical buckling load (Ncr) for 8 plies with fibre orientation (0°/30°/-30°/90°)s subjected to inplane Uniaxial compression loading

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b.Biaxial compression loading for 8plies and 16 plies: table 3.6 gives the value of Critical buckling load (Ncr) for variousaspect ratio(β),fig 3.9 and fig 3.10 shows various aspect ratio(β) for 8 plies and 16 plies. The critical buckling load of a composite laminated plate having β=0.5 is approximately 2.8,2 and 2.1 times higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively for 8 plies. The critical buckling load of a composite laminated plate having β=0.5 is approximately 3.1,1.7 and 1.5 times 7|P a g e

IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017 higher than the buckling load of plate having β equal to 1.0,1.5 and 2 respectively for 16 plies

Table 4.6: Critical buckling load (Ncr) for SSSS graphite/epoxy composite laminate plate with respect to aspect ratio (β) subjected to inplane biaxial compression loading with fibre orientation (0°/30°/-30°/90°)s

Aspect ratio (β)

a in mm

b in mm

Critical buckling load (Ncr) 8 plies 16 plies 19.34 202.09

0.5

100

1.0

100

6.98

65.88

1.5

150

100

9.84

119.32

2.0

200

100

9.45

136.97

Fig 4.9: Variation of critical buckling load(Ncr) for 8 plies with fibre orientation (0°/30°/-30°/90°)s subjected to inplane biaxial compression loading

Fig 4.10: Variation of critical buckling load (Ncr) for 16 plies with fibre orientation (0°/30°/-30°/90°)s subjected to inplane biaxial compression loading

CONCLUSION This study considers the determination of critical buckling load of a composite laminated plate made up of Graphite-Epoxy with all round simply supported plate boundary condition.The considered laminated composite plate has varying aspect ratio(β) 0.5-2.0 and fibre IDL - International Digital Library

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IDL - International Digital Library Of Technology & Research Volume 1, Issue 6, June 2017

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International e-Journal For Technology And Research-2017 orientation(0°/90°/-90°/0°)s ,(0°/30°/-30°/90°)s.From the present work following conclusions are drawn. 1.

For Isotrophic plate the critical buckling load is maximum at the plate aspect ratio β=0.5,and for β=1.0 to 2.0 the critical buckling load decreases about 31.8% under inplane uniaxial compression loading.

For Isotrophic plate the critical buckling load is maximum at the plate aspect ratio β=0.5,and for β=1.0 to 2.0 the critical buckling load decreases about 65-74% under inplane biaxial compression loading.

The buckling load is maximum for the plates having aspect ratio equal to 0.5 for all the fibre orientations.

The Critical buckling load of composite laminated plate for all the three fibre orientation having 8 and 16 plies subjected to inplane uniaxial compression loading is approximately 28% to 23% higher than the plate subjected to inplane biaxial loading for β=0.5-2.0 respectively.

Mechanics research communications, 2009, vol.36, pp933-938. 5.

Priyanka Dhueveyana and Mittal.N.D, “Buckling behaviour of an orthotropic composite laminate using FEA”’ International journal of scientific Engineering and Technology, 2012, vol.1, pp93-95.

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Abdulkareem AI Humdany and Emad Q.Hussein, “Theotical and numerical analysis for buckling of Antisymmetric simply supported laminated plate under Uniaxial loads”, Journal of kerala university,2012,vol.10,pp 149-160.

Eugenio Ruocco and Vincenzo Mallardo,”Buckling analysis of Levy type Orthotropic stiffened plate and shell based on different strain displacement model”, International journal of non-liner mechanics,2013,vol.50,pp 40-47.

Loptain.A.V and Morozov.E.V, “Buckling of SSCF rectangular orthotropic plates subjected to linearly varying in-plane loading”, Composite structures,2011,vol93,pp1900-1909.

Murmu.T and Pradhan.S.C, “Buckling of biaxial compressed orthotropic plates at small scales”, IDL - International Digital Library

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