 Open Access
 Total Downloads : 315
 Authors : K. Rajesh, V. Ramakrishna Rao, S. Mahesh Babu
 Paper ID : IJERTV2IS120899
 Volume & Issue : Volume 02, Issue 12 (December 2013)
 Published (First Online): 30122013
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Linear Buckling Analysis on Thin FRP Cross Ply Rectangular Laminates with Square CutOuts of curved corners under Biaxial Compression
K. Rajesp, V. Ramakrishna Rao2 and S. Mahesh Babu3

K. Rajesh, Dept. of Mechanical Engineering, DVR & Dr. HS MIC college of Technology, Kanchikacherla, 521180, Krishna dt, A.P.

V. Rama Krishna rao, Dept. of Mechanical Engineering, DVR & Dr. HS MIC college of Technology, Kanchikacherla, 521180,Krishna dt, A.P.

S. Mahesh Babu, Dept. of Mechanical engineering, AMRITHA SAI Institute of Science & Technology, Paritala, Krishna dt, A.P
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Abstract
The main objective of the present study abstract is to determine the buckling load for cross ply(0Â°/90Â°/90Â°/0)rectangular plate with square cuts having curved corners under biaxial compression using 2D finite element analysis ANSYS is the commercial software, which has been successfully executed and finite model is validated. the present problem is evaluated by changing the position of the square cut with curved corners, aspect ratio(a/b) and thickness ratio(b/t).the results show that the buckling load is more at the bottom positioned square hole, increases with increase in aspect ratio, decreases with increase in thickness ratio and increases with increase in number of layers (N).
Key words: FRP, FEM buckling analysis and biaxial load.

Introduction
A composite material consists of two or more materials and offers a significant weight saving in structures in the view of its high strength to weight ratio and high stiffness to weight ratios. In fiber reinforced composites, the mechanical properties can be varied as required by suitably orienting the fibers. In such materials fibers are main load bearing members and matrix are supporting members to the fibers because of their low elastic modulus and high ductility.

Problem statement
The objective of present research is to find the buckling load of rectangular laminates with square cuts having curved corners subjected to biaxial compression by changing the position of the square holes in the plate, aspect ratio, thickness and number of layers.

Geometric modeling
The width of the rectangular plate is varying from 50mm, 100mm, 150mm, 200mm in Xdirection and span of the rectangular plate (b) is 100mm which is fixed in Y direction. Then corresponding a/b ratios are 0.5, 1, 1.5 and

The thickness of the plate is determined from b/t ratios
i.e. varied from 20 to 100 (20, 40, 60, 80 and 100). The numbers of layers (N) are varied from 4, 8, 12, 16 and 20. The area of the square hole with fillet corners is 79sqmm and the radius of the fillet is 1mm.
Fig.1 shows the geometrical modeling of rectangular plate with square cuts of curved corners of various positions of cuts as shown below.
top
middle
bottom
Fig.1 FE Model (Top, Middle and Bottomsquare hole) (a/b=0.5, b/t=100, ss Boundary and N=4)

Material Properties
The following material properties
are considered for the present analysis Youngs Moduli,
E1=147E3MPa, E2=10.3E3MPa, E3=10.3E3MPa
Poissions ratio v12=0.27,v23=0,54,v31=0.27
Rigidity Moduli,
G12=7E3MPa, G23= 3.7E3MPa, G13=7E3MPa
0.124
buckling load
buckling load
buckling load
buckling load
0.122

Validation of FE Model
The present work is validated from J. Leela Krishna and he has chosen that buckling of thin FRP rectangular plates with rectangular cuts of curved corners under biaxial compression.
0.120
top middle bottom
hole position
Table. 1 Validation of present value with Leela Krishnas value
Hole position
Leela krishna s Buckling load
in KN/mm
Present value for Buckling
load in KN/mm
TOP
0.11684
0.12198
Fig. 2 Effect of Square Hole location at different position
Fig.3 shows that values of various buckling loads of first five modes for a/b ratios. It is observed that the buckling load increases as the mode number increases and also increases for different a/b ratios. The reason is due to the number of cycles increases when the mode number increases, so that the stiffness of the laminates is more.

Results and Discussion
Fig 2 shows buckling load per unit length for different hole positions. buckling load is maximum for bottom hole position due to the fact that it gets more support compared to other hole positions. and subject to more constraints at this position
2.0
0.4
buckling load per unit length
buckling load per unit length
buckling load per unit length
buckling load per unit length
1.5
0.3
1.0
0.2
0.5
0.0
a/b=0.5 a/b=1 a/b=1.5 a/b=2
0 2 4 6
MODE NUMBER
buckling load for 1st mode
0.01.0 0.5 1.0 1.5 2.0 2.5
a/b ratio
Fig.3 Effect of Aspect ratio on buckling load per unit length
Fig.4 shows the buckling load with respect to a/b ratio for first mode. It is found that the buckling load increases with increase in aspect ratio. It could be attributed to the fact that the width of the plate increases in Xdirection, so it offers more resistance.
Fig. 4 Effect of Aspect ratio on 1st mode buckling load per unit length
Fig.5 shows that the buckling load varies with respect to thickness ratio. It is observed that the buckling load decreases from b/t=20 to b/t=100. It could be attributed to the fact that the resistance of the plate decreases as the thickness of the plate decreases with increase in thickness ratio.
buckling load for 1st mode)
buckling load for 1st mode)
160 20 40 60 80 100 12106
Buckling Load per unit length
Buckling Load per unit length
2.4
buckling load per unit length
buckling load per unit length
12 12
8 8
1.6
layers4 layers8 layers12 layers16 layers20
4 4
00 20 40 60 80 100 1200
b/t ratio
0.8
Fi g. 5 Effect of thickness ratio on 1st mode of buckling load per unit length
Fig.6 shows that the buckling load varies with respect to number of layers. It is observed that the buckling load increases with increase in number of layers for 1st five modes of different layers. It could be attributed to the fact that the plate offers more resistance with increase in number of layers.
0.0
0 2 4 6
Number Of Layers
Fig. 6 Effect of Number of layers(N) on first five modes of buckling load per unit length
Fig.7shows 1st five modes of mode shapes
1. 2.
3. 4.
5.
Fig.7 Buckling mode shapes 1, 2, 3, 4 & 5 (a/b=0.5, b/t=100, number of layers=4 and ss Boundary)
Conclusion
This study considers the buckling response of cross ply rectangular laminates with simply supportedsimply supported boundary conditions along the top and bottom edges. The laminated composite plates rectangular in shape with square cutouts with curved corners at different locations, varying aspect ratio, thickness ratio and number of layers are discussed.

Buckling load is maximum when the location of hole is at bottom.

As a/b ratio increases, the buckling load inreases.

As b/t ratio increases, the buckling load decreases.

As the number of layers increases, the buckling load increases.


References

Timoshenko, J. Gere, Theory of Elastic Stability, McGrawHill, International Book Company, 1961.

R. D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates, Journal of Apllied Mechanics Vol. 18 (Transaction ASME 73), 1951 , Pages 3138.

A.V. Ravi Prakash, A. Adhitya Plato Sidharth, B. Prabu, and N. Alagumurthi, Structural reliability of thin plates with rndom imperfections subjected to uniform axial compression, Jordan Journal ofMechanical and Industrial engineering Vol.4, 2010, Pages 270279.

Khaled M. EISawy and aly S. Nazmy, Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes, ThinWall Structures(39), 2001, pages 983998.

V.Piscopo, Refined Buckling Analysis of Rectangular Plates under Uniaxial and Biaxial Compression , World Academy of Science, Engineering and technology. Vol. 70, 2010, pages 555562.

S. Mahesh Babu, S. Srilakshmi, V,Bala Krishna Murthy and A.Sri Hari Prasad, Buckling Of Thin FRP Composites, International Journal of Systems and Technologies Vol. 4, No. 2, 2011, pages 157166.

J. Leela Krishna, M. sreenivas Raos and S. Mahesh Babu linear buckling analysis if thin FRPrectangular laminates with circular cutouts under biaxial compression

ANSYS reference manuals, 2010.