Theoretical and Numerical Investigation of Buckling of ... · method using Ansys Package Ver. 14 was employed. The ... deflection of plate due to buckling of the plate may be

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:15 No:04 1

I J E N S IJENS © August 2015 IJENS-IJMME-2929-041515

Theoretical and Numerical Investigation of Buckling

of Orthotropic Hyper Composite Plates

Prof. Dr. Muhsin J. Jweeg, Dr. Muhannad Al-Waily, Alaa Abdulzahra Deli

Abstract— The current work covered the investigation of the

effect of powder reinforcement on the buckling load of

orthotropic hyper composite plate composed from powder and

unidirectional or woven reinforcement and resin materials . An

analytical solution has been suggested to evaluate the buckling

load of orthotropic hyper composite plate. The general equations

of properties of hyper composite plates have been presented

taking into consideration the effect of powder reinforcement and

unidirectional of woven and resin materials. The finite element

method using Ansys Package Ver. 14 was employed. The

comparison has shown a good agreement with a maximum

discrepancy of ( 1.9% ). The results cover the determination of

buckling load of simply supported orthotropic hyper composite

plates manufactured from powder reinforcement and

unidirectional or woven fiber and resin materials with different

volume fractions. Also ,the results showed that the buckling load

of the plate is increasing with the increase the reinforcement

powder and slightly affected by the powder reinforcement types.

Also, it has been shown that the buckling load increases with the

increase the unidirectional or woven reinforcement fiber is more

than the increase in the buckling load of composite with the

increase of powder reinforcement.

Index Term-- Buckling , Hyper Composite Materials, Finite

Element Method.

I. INTRODUCTION

Fiber Reinforced Plastics (FRP) is a general term for

composite materials or parts that consists of a resin matrix that

contains reinforcing fibers such as glass or fiber and have

greater strength or stiffness than the resin. FRP is most often

used to denote glass fiber-reinforced plastics. Fiber hybrids

capitalize on the best properties of various fiber types, while

reducing raw material costs. Hybrid composites combining

carbon/aramid and carbon/glass fibers have been used

successfully in ribbed aircraft engine thrust reversers,

telescope mirrors, drive shafts for ground transportation and

infrastructure column-wrapping systems, [1].

Many studies were performed to examine the buckling study

of different composite plate and reinforcement fiber and

matrix resin types, as

Ozgur Erdal et al, [2], presented a method to find globally

optimum designs for two-dimensional composite structures

Prof. Dr. Muhsin J. Jweeg

Mechanical Engineering Department, College of Engineering, Alnahrain

University, Ministry of Higher Education & Scientific Research, Iraq, [email protected]

Dr. Muhannad Al-Waily Mechanical Engineering Department, Faculty of Engineering, Al-Kufa

University, Ministry of Higher Education & Scientific Research, Iraq,

[email protected] & [email protected] Alaa Abdulzahra Deli

Mechanical Engineering Department, Faculty of Engineering, Al-Kufa

University, Ministry of Higher Education & Scientific Research, Iraq,

[email protected]

subject to a given in-plane static loads for which the critical

failure mode is buckling. The aim was to maximize the

buckling load capacity of laminated composites. For this

purpose an improved version of simulated annealing

algorithm, which is direct simulated annealing (DSA), was

utilized. Fiber orientation in each layer was taken as a design

variable.

Duosheng Xu et al, [3], investigated the buckling behavior of

several simple tri-axial woven composite structures is studied.

These structures include basic tri-axial structure, modified tri-

axial structure and enlarged tri-axial structure. The structure is

subjected to a bi-directional loading. Approximate analytical

method using equivalent anisotropic plate theory is presented .

Shih-Yao Kuo et al, [4], presented the effect of shape

memory alloy (SMA) on the buckling behavior of a

rectangular composite laminate by the finite element method.

The influence of SMA on buckling of composite laminates by

varying the SMA fiber spacing was studied. The formulation

of the location-dependent stiffness matrix due to non-

homogeneous material properties and the temperature-

dependent recovery stress stiffness matrix were derived.

Muhsin J. Jweeg et al, [5], presented ean xperimental and

theoretical study of mechanical properties for composite

materials reinforcement fiber types. The experimental work

and the theoretical investigation covered the study of modulus

of elasticity for long, short, woven, powder, and particle

reinforcement of composite materials types with difference

volume fraction of fiber. The results show that the effect of

fiber and resin types on modulus of elasticity for composite

materials are presented. In addition the effect of volume

fraction of fiber and matrix materials on modulus of elasticity

for composite materials shown a presented.

Erik Lund, [6], investigated the design problem of

maximizing the buckling load factor of laminated multi-

material composite shell structures using the so-called

Discrete Material Optimization (DMO) approach. The design

optimization method is based on ideas from multi-phase

topology optimization where the material stiffness is

computed as a weighted sum of candidate materials, thus

making it possible to solve discrete optimization problems

using gradient based techniques and mathematical

programming.

Muhannad Al-Waily, [7], evaluated the critical thermal

effect caused the buckling of unidirectional and woven

composite plate with different aspect ratios of plate combined

from different types of long and woven reinforcement fiber

and different resin material types .The general equation of

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motion of orthotropic composite simply supported plate with

buckling thermal effect has been achieved. The research

covered the evaluation of the effect of reinforcement type and

resin types on the buckling temperature with effect of volume

fraction of reinforcement fiber and resin materials. The results

were the critical thermal buckling temperature of orthotropic

composite plate with effect of different reinforcement fiber as

unidirectional or woven fiber and different resin materials

with various volume fractions of reinforcement fibers.

In this work ,the buckling behavior of orthotropic hyper

composite plate is investigated with different powder and

unidirectional or woven reinforcement fiber and different resin

materials types. The research will be achieved analytically to

derive the general buckling equation and numerically using

the FEM.

II. A SUGGESTED THEORETICAL INVESTIGATION

The theoretical study of buckling of hyper composite plate

included the determination of mechanical properties of hyper

composite materials composed from unidirectional or woven

reinforcement fiber and reinforcement powder used to be

combined with polyester resin materials. Also, the theoretical

analysis of general equation of buckling study for orthotropic

composite plate will be achieved.

II.1. Mechanical Properties of Hyper Composite Plate Structural

The evaluation of the mechanical properties of hyper

composite plate (combined from powder reinforcement and

resin materials) and hyper composite plate as unidirectional

or woven reinforcement fiber and composite matrix (powder

and resin materials) will be determined as follows:

II.1.1. Mechanical Properties of Composite Matrix, (Resin and

Powder Reinforcement)

Spherical fillers are reinforcements associated with polymer

matrices. They are in the form of micro-balls, either solid or

hollow, with diameters between 10 and 150 m. They are

made of glass, carbon, or polystyrene. The composite (matrix

+ filler) is isotropic, with elastic properties E, G, are given

by the following relations, [8],

(

( )[ (

)

]

( ) [

(

)

]*

(

( )[ (

)

]

( ) [

(

)

]*

(

)

[(

( )

[ (

)

]

( ) [

(

)

]*

(

( )[ (

)

]

( ) [

(

)

]*]

( )* (

)

+ ,

( ) *

(

)

+ (1)

Where, are mechanical properties of resin materials

and are volume fractions of reinforcement powder and

resin materials, respectively.

, , (2)

And, the volume fraction of composite matrix,

(3)

Then, by using Eq. 1 the mechanical properties of

orthotropic hyper composite materials can be evaluated. II.1.2. Hyper Composite Materials Plate, (Combined From Resin

Materials, Reinforcement Powder, and Unidirectional or Woven

Fiber)

The mechanical properties of hyper composite plate evaluated

from combined of unidirectional or woven fiber and

composite matrix as,

A. Unidirectional Hyper Composite Plate The mechanical characteristics of the fiber/matrix mixture can

be obtained based on the characteristics of each of the

constituents. With the definitions in the previous paragraph,

one can use the following relations to characterize the

unidirectional ply, [8],

Modulus of elasticity along the direction of the fiber E1 is

given by,

( ) (4)

Modulus of elasticity in the transverse direction to the

fiber axis, E2:

*

( )

+ (5)

Shear modulus G12,

*

( )

+ (6)

Poisson coefficient 12,

(7)

And, density of hyper composite plate is,

(8)

Where, are mechanical properties of unidirectional

fiber, is the volume fraction of unidirectional fiber, and

is density of unidirectional fiber.

Then, by substitution Eq. 2 into Eqs. 4 to 7, the mechanical

properties of unidirectional hyper composite materials

properties are obtained as follows:

( ) ,

*

( )

+

[ (

( ) [

(

)

]*

(

( )

[

( ) *

(

)

+]

,

]

(

) (9)

B. Woven Fabrics Hyper Composite Plate

The fabric layer is replaced by one single anisotropic layer, x

being along the warp direction and y along the fill direction.

One can therefore obtain, [8],

( ) ,

( ) ,

,



( ( ) ) (10)

where,

, number of warp yarns per meter,

number of fill yarns per meter.

And, , , , and are mechanical properties of

woven fabrics in 1 and 2-directions; and , , , and

are mechanical properties of unidirectional composite

materials as in Eqs. 4 to 7.

Then, by substitution Eqs. 4 to 7 in to Eq. 10, get,

[ (

( )*

( ) (

*

( )

+)]

[ ( ) (

( )*

(

*

( )

+)]

[ (

( ) [

(

)

]*

(

( ) [

( ) *

(

)

+]

,

]

(

(

) )

( ( ) )

(11)

And, the density of woven hyper composite materials can be

evaluated as,

(12)

Where, , , , and are mechanical properties and

density of woven reinforcement fiber, respectively, and is

volume fraction of woven reinforcement fiber.

II.2. Buckling Analysis of Orthotropic Hyper Composite Plate Thin plates of various shapes used in naval and aeronautical

structures are often subjected to normal compressive and

shearing loads acting in the middle plane of the plate (in-plane

loads). Under certain conditions such loads can result in a

plate buckling. Buckling or elastic instability of plates is of

great practical importance. The buckling load depends on the

plate thickness: the thinner the plate, the lower is the buckling

load. In many cases, a failure of thin plate elements may be

attributed to an elastic instability and not to the lack of their

strength. The expressions for the bending and twisting

moments with the displacement and strain field are as follows,

[9]:

,

,

(13)

And, the strain field are,

,

,

(14)

The stresses-strain field can be written as follows,

(15)

By substituting for strain Eq. 14 into Eq. 15 gives

(

*

(

*

(16)

The bending moments (per unit length) , and are

then determined as,

∫ ⁄

⁄

∫ ⁄

⁄(

)

( )

∫ ⁄

⁄

∫ ⁄

⁄(

)

( )

∫ ⁄

⁄

∫

⁄

⁄ (17)

Where,

( ) ,

( ) ,

( ) ,

(18)

Then from the general differential equation for plate

(19)

And with substitution for the bending and twisting moments

from Eq. 17 into Eq. 19. gives:

* ( ) ( )

( ) +

Or,

( ) (20)

The equation of buckling orthotropic plate is, [10],

* ( )

+ (21)

To solve the general equation of buckling plate Eq. 21, the

deflection of plate due to buckling of the plate may be

assumed and using the following boundary conditions of the

simply supported plate, [9],

( ) ,

On the edge And,

( ) ,

On the edge (22)

The solution of Eq. 20 satisfying the boundary conditions Eq.

22 can be written as,

(23)



The deflection surface in the form of Eq. 23 satisfies exactly

the boundary conditions Eq. 22. Substituting Eq. 23. into Eq.

21 and letting , gives the following

expression for the compressive forces ,

√

[√

(

)

( )

√ √

(

)

]

(24)

Where, [11],

– for unidirectional reinforcement fiber, and,

– for woven reinforcement fiber.

– for unidirectional reinforcement fiber, and –

for woven reinforcement fiber.


– for woven reinforcement fiber.


– for woven reinforcement fiber

It is evident that a minimum value of is reached for

.

Then, by substituting Eq. 9 in to Eq. 18, and substituting the

results in to Eq. 24, gives the buckling load of orthotropic

unidirectional hyper composite plate, as,

√(

( )*(

( )*

[ √(

( )*

(

( )*(

)

√(

( )*

(

( )*(

)

((

( )* (

*)

√(

( )*(

( )*

]

(25)

And, by substituting Eq. 11 in to Eq. 18, and substituting the

results in to Eq. 24 the general equation of buckling load of

orthotropic woven hyper composite plate is obtained as

follows:

√(

( )*(

( )*

[

√(

( )*

(

( )*(

)

√(

( )*

(

( )*(

)

((

( )* (

*+

√(

( )*(

( )*

]

(26)

To evaluate the buckling load of simply supported orthotropic

hyper composite plate, Eqs. 25 and 26 with different volume

fractions of reinforcement powder and unidirectional or

woven fiber. A computer program with Fortran Power Station

program Ver. 4. has been built. The theoretical results are

compared with those obtained numerically by using finite

element method with using of Ansys program Ver. 14. Fig. 1

shows the flow chart of the developed computer program.

Fig. 1. Flow Chart Fortran Program to Evaluated the Buckling Load of Plate.

End

Input Dimensions of Plate, a, b and h

Input Mechanical Properties of Reinforcements

Powder and Fiber and Resin Materials, E, G, and

Start

Evaluated Mechanical Properties of

Unidirectional Hyper Composite Plate, Eq. 9.

Evaluated Buckling Load of Unidirectional Hyper Composite Plate, Eq. 25.

Evaluated Mechanical Properties of

Woven Hyper Composite Plate, Eq. 11.

Evaluated Buckling Load of Woven

Hyper Composite Plate, Eq. 26.



III. NUMERICAL STUDY

The numerical study of buckling analysis for orthotropic hyper

composite plate with different reinforcement powder and fiber

volume fraction and types effect evaluated by using the finite

elements emplying the ANSYS program (ver.14). The three

dimensional model were built and the element (Solid Tet 10

node 187) were used. Solid 187 elements is a higher order 3-

D, 10-node element. Solid 187 has a quadratic displacement

behavior and is well suited to modelling irregular meshes. The

element is defined by 10 nodes having three degrees of

freedom at each node: translations in the nodal x, y, and z

directions Fig. 2.

Fig. 2. geometry of Solid 187 Element.

The results evaluated numerically by using Ansys program are

the buckling load of different aspect ratio of orthotropic hyper

composite plate with different volume fraction and types of

reinforcement powder and unidirectional and woven fiber and

different resin materials types.

IV. RESULTS AND DISCUSSION

The results of buckling hyper composite plate included the

buckling load of composite plate combined from powder

reinforcement, unidirectional or woven reinforcement fiber

and resin materials matrix, with mechanical properties as

shown in Table I, [8], with different volume fractions of

reinforcement and polyester resin materials effect and

different aspect ratio of plate. The buckling load of orthotropic

simply supported hyper composite plate is compared with the

results to be obtained by using Ansys program.

The mechanical properties of orthotropic unidirectional and

woven hyper composite plates are shown in Tables II and III.

, with different plate length,

Table I

Mechanical Properties of Different Reinforcement Powder, Reinforcement Fiber and Polyester Resin Materials.

Materials ( kg/m3 ) E (Gpa) G (Gpa)

Glass Fibers 2066 74 30 0.25

Boron Fiber 2600 400 / /

Polyester 1200 4 1.4 0.4

Table II

Hyper Composite Combined of Glass Long Fiber, Glass or Boron Powder and Polyester Resin Material.

m f lf pf

Mechanical Properties

(kg/m3) E1

(Gpa)

E2

(Gpa)

G12

(Gpa) 12

70 30

15 15 16.09 6.81 2.46 0.36 1620

20 10 19.00 6.44 2.32 0.36 1620

25 5 21.97 6.04 2.17 0.36 1620

30 0 25.00 5.58 2.00 0.36 1620

65 35

15 20 16.77 7.73 2.80 0.36 1690

20 15 19.61 7.36 2.66 0.36 1690

25 10 22.51 6.95 2.51 0.35 1690

30 5 25.47 6.50 2.34 0.35 1690

60 40

15 25 17.57 8.80 3.20 0.36 1760

20 20 20.32 8.42 3.06 0.35 1760

25 15 23.13 8.01 2.90 0.35 1760

30 10 26.02 7.55 2.73 0.35 1760

55 45

15 30 18.52 10.06 3.67 0.35 1830

20 25 21.16 9.67 3.53 0.35 1830

25 20 23.87 9.25 3.37 0.35 1830

30 15 26.66 8.78 3.19 0.34 1830

50 50

15 35 19.65 11.56 4.24 0.35 1900

20 30 22.16 11.15 4.08 0.35 1900

25 25 24.75 10.71 3.92 0.34 1900

30 20 27.43 10.23 3.73 0.34 1900

Table III Hyper Composite Combined of Glass Woven Fiber, Glass or Boron Powder

and Polyester Resin MAterioal.

m f lf pf

Mechanical Properties

(kg/m3) E1

(Gpa)

E2

(Gpa)

G12

(Gpa) 12

70 30

15 15 11.45 11.45 2.46 0.22 1620

20 10 12.72 12.72 2.32 0.18 1620

25 5 14.00 14.00 2.17 0.15 1620

30 0 15.29 15.29 2.00 0.13 1620

65 35

15 20 12.25 12.25 2.80 0.23 1690

20 15 13.48 13.48 2.66 0.20 1690

25 10 14.73 14.73 2.51 0.17 1690

30 5 15.98 15.98 2.34 0.14 1690

60 40

15 25 13.19 13.19 3.20 0.24 1760

20 20 14.37 14.37 3.06 0.21 1760

25 15 15.57 15.57 2.90 0.18 1760

30 10 16.78 16.78 2.73 0.16 1760

55 45

15 30 14.29 14.29 3.67 0.25 1830

20 25 15.41 15.41 3.53 0.22 1830

25 20 16.56 16.56 3.37 0.19 1830

30 15 17.72 17.72 3.19 0.17 1830

50 50

15 35 15.61 15.61 4.24 0.26 1900

20 30 16.66 16.66 4.08 0.23 1900

25 25 17.73 17.73 3.92 0.21 1900

30 20 18.83 18.83 3.73 0.18 1900

The comparison of the results, for simply supported

orthotropic hyper composite plate, are shown in Figs. 3 and 4.

The results show the buckling load of unidirectional and

woven hyper composite simply supported plate, with different

aspect ratio of plate, with various volume fractions of powder

reinforcement, volume fractions of unidirectional or woven

reinforcement fiber and volume fractions of resin materials,

with different reinforcement types. Figures show that the

../AppData/Local/Temp/Temp2_attachments_2015_04_28.zip/Hlp_E_SOLID187.html#ELEM187SOLIDfdb527991030



results of the suggested analytical solution are in good

agreement compared with the results of numerical solution,

with maximum error about (1.9%).

The effect of the reinforcement and resin volume fractions

effect and types materials effect for different aspect ratios of

orthotropic unidirectional and woven hyper simply supported

plate are shown in Figs. 5 to 13.

Figs. 5 to 7, show the buckling load of unidirectional hyper

composite plate reinforcement with powder and unidirectional

fiber and polyester resin materials, with different aspect ratios

of plate as ( ). From figures it is seen that

the buckling load of unidirectional hyper composite plate

increases with increasing of the powder reinforcement and

unidirectional fiber for aspect ratios of plate ( ), but, the buckling load of plate decreases with

increase the volume fraction of the unidirectional

reinforcement fiber. Also, the buckling load increases with

increasing the volume fraction of reinforcement powder for

aspect ratio of plate ( ).

Figs. 8 to 10, show the buckling load of woven hyper

composite plate reinforcement with powder and woven fiber

and polyester resin materials, with different aspect ratios of

plate as ( ). It is noticed that the buckling

load of woven hyper composite plate increase with increasing

of the powder reinforcement and woven fiber for aspect ratio

of plate ( ).

Fig. 11, show the effect of aspect ratio of plate on the buckling

load of hyper composite plate combined from powder

reinforcement, unidirectional or woven fiber and polyester

resin materials, respectively, with different volume fraction of

unidirectional or woven fiber, for volume fraction of

reinforcement (unidirectional or woven fiber and

powder reinforcement).The buckling load of plate with aspect

ratio ( ) is less than the buckling load with aspect ratio

of plate ( ).. Also, the buckling load of woven

composite plate with aspect ratio ( ) is equal to the

buckling load of plate with aspect ratio ( ), and the

buckling load of unidirectional composite plate with aspect

ratio ( ) is more than the buckling load of plate with

aspect ratio ( ). This is because of the reinforcement

with woven fiber gives the same the strength effect in the

direction of plate, and therefore , the buckling load of

rectangular plate is same for that of a plate with aspect ratio

( ).

Fig. 12, show the effect of powder reinforcement materials

types effect, as glass and boron powder reinforcement, on the

buckling load of unidirectional and woven hyper composite

plate with polyester resin materials, with various powder

volume fractions effect (for reinforcement volume fraction

and aspect ratio of plate ). It is seen that

the buckling load has not been affected by using the materials

types of reinforcement powder, since the reinforcement

powder materials types non effect on the materials properties

of hyper composite plate.

Fig. 13, shows the compare between the buckling load of

hyper composite plate reinforcement with unidirectional fiber

and hyper composite plate reinforcement with woven fiber

with different volume fractions of unidirectional or woven

fiber effect and different aspect ratio of plate (AR=0.5, 1 and

2) with polyester resin materials. It is noticed that the

buckling load of composite plate reinforcement with

unidirectional fiber is more than the buckling load of

composite plate reinforcement with woven fiber, for aspect

ratio of plate (AR=0.5 and 1),The effect on the strength of

composite materials of unidirectional reinforcement fiber is

more than the effect of woven reinforcement fiber. The

buckling load of composite plate reinforcement with woven

fiber more than the buckling load of composite plate

reinforcement wit unidirectional fiber, for aspect ratio of plate

( ).

a. f=30%

b. f=35%

c. f=40%



d. f=45%

e. f=50%

Fig. 3.I. Aspect Ratio, AR=0.5

a. f=30%

b. f=35%

c. f=40%

d. f=45%

e. f=50%

Fig. 3.II. Aspect Ratio, AR=1

a. f=30%



b. f=35%

c. f=40%

d. f=45%

e. f=50%

Fig. 3.III. Aspect Ratio, AR=2 Fig. 3. Comparison Between Theoretical and Numerical Results of Buckling

Load (KN/m) for Unidirectional Fiber, Polyester Resin, Different Aspect

Ratio and Reinforcement Volume Fraction.

a. f=30%

b. f=35%

c. f=40%

d. f=45%



e. f=50%

Fig. 4.I. Aspect Ratio, AR=0.5

a. f=30%

b. f=35%

c. f=40%

d. f=45%

e. f=50%

Fig. 4.II. Aspect Ratio, AR=1

a. f=30%

b. f=35%



c. f=40%

d. f=45%

e. f=50%

Fig. 4.III. Aspect Ratio, AR=2

Fig. 4. Comparison Between Theoretical and Numerical Study of Buckling

Load (KN/m) for Woven Fiber, with Polyester Resin, Different Aspect Ratio and Reinforcement Volume Fraction.

Fig. 5. Buckling Load of Composite Plate with Different Volume Fraction of

Unidirectional Fiber and Powder, with Polyester Resin and AR=0.5.


Unidirectional Fiber and Powder, with Polyester Resin and AR=1.


Unidirectional Fiber and Powder, with Polyester Resin and AR=2.

Fig. 8. Buckling Load of Composite Plate with Different Volume Fraction of Woven Fiber and Powder Reinforcement, for Polyester Resin and AR=0.5.




Woven Fiber and Powder Reinforcement, for Polyester Resin and AR=1.


Woven Fiber and Powder Reinforcement, for Polyester Resin and AR=2.

a. Unidirectional Reinforcement

b. Woven Reinforcement

Fig. 11. Buckling Load of Plate with Different Aspect Ratio and Volume

Fraction of Unidirectional and Woven Fiber, Polyester Resin and f=50%

a. Unidirectional Reinforcement

b. Woven Reinforcement

Fig. 12. Buckling Load of Plate with Different Powder and Various Volume

Fraction of Reinforcements Fiber, with Polyester Resin, f=50%, AR=0.5.

a. AR=0.5



b. AR=1

c. AR=2

Fig. 13. Buckling Load with Different Reinforcement (Unidirectional and

Woven Fiber) and Various Reinforcement Volume Fraction, with Polyester

Resin and f=50%, and Different Aspect Ratio.

V. CONCLUSION

The conclusions of the buckling load of hyper orthotropic

composite plate with different parameters of reinforcement are

as follows:

1. The suggested analytical solution is a powerful tool for

buckling load analysis study of unidirectional and woven

hyper composite simply supported plate composed from

three materials as powder reinforcement, unidirectional or

woven reinforcement and rein materials.

2. The comparison between the suggested analytical

solutions results of general equation of buckling

orthotropic hyper composite plate with numerical results

FEM by using Ansys program Ver. 14, showed a good

approximation with a maximum discrepancy of (1.9%).

3. The increasing of the powder reinforcement volume

fraction increases the strength of hyper composite plate,

and the buckling load of hyper composite plate is

increasing with increasing the volume fraction of

reinforcement powder.

4. The effect of unidirectional or woven reinforcement fiber

is more than the effect of powder reinforcement.

Therefore, the buckling load increase by using the

unidirectional or woven fiber is more than the increasing

of buckling load with increasing reinforcement powder.

5. The effect of unidirectional reinforcement fiber on the

buckling load of composite plate is more than the effect

of woven reinforcement fiber on buckling load of

composite plate for aspect ratio of plate less than 1. Also,

the effect of woven reinforcement fiber on buckling load

of composite plate is more than the effect of

unidirectional reinforcement fiber on buckling load of

composite plate for aspect ratio of plate more than 1.

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Documents

Theoretical and Numerical Investigation of Buckling of ... · method using Ansys Package Ver. 14 was employed. The ... deflection of plate due to buckling of the plate may be