Effect of Axes ratio of an Elliptical Hole on the Buckling Load in a Symmetric Angle Laminated Composite Plate

Transcription

1 Effect of Axes ratio of an Elliptical Hole on the Buckling Load in a Symmetric Angle Laminated Composite Plate Saood Ali 1, Farooq Ahmed 2 1,2 Assistant Professor, FoE, Teerthanker Mahaveer University Moradabad Abstract:- Fiber reinforced composite materials are widely used in variety of engineering applications due to its superior properties than the conventional materials. In the present investigation the effect of semi-major to semi-minor axis of an elliptical hole on buckling behaviour in a rectangular composite laminate with central elliptical hole under uniform in-plane loading has been presented. The composite plate were made of E- glass/epoxy material, consist of eight layers and it was angle-ply symmetric (0/30/60/90) s laminated composite plate. Sometimes the composite structures are provided with the holes for the purpose of passing the cables, for inspection etc. The ANSYS13.0 software was used for modelling and analysis of the laminated plates under simply-supported boundary conditions. The eight noded shell99 element was used throughout the analysis. The deformation behaviour of the plate is shown for modes i=1,2,3 and the studies are carried for different semi-major to semi-minor axis ratio (0.25,0.5,0.75 &1) of an elliptical hole. L/h ratio considered is 40 and 200 while the ratio of hole area to the plate area is maintained constant throughout the analysis as From the analysis it has been observed that the fundamental frequency of laminated composite plates increases with increase in semi-major to semi-minor axis ratio for an elliptical hole while the fundamental frequency of laminated composite plates decreases with increase in L/h ratio. Keywords - Fiber reinforced composite,buckling,glass/epoxy, shell element Introduction Composite material is formed by combining materials which are differing in composition & form by mixing on a macro scale for the purpose of obtaining specific characteristics and properties. Many engineering structures as beams, columns or plates fails not only due to large stresses but also due to buckling. The behaviour of the laminated composite plate, subjected to compression load, is known as buckling, till the load on the plate remains relatively small and after that the axial shortening of the plate occurs. The load at which the plate bows out sideways, suddenly, is known as critical load. At critical load, large deformations occurs in the plate which makes the plate to collapse and hence the load at which the buckling occurs would be the design criteria for the compression loaded compressive plates. Buckling behaviour depend not only on the compressive load but also on the aspect ratio, d/d ratio, d/b ratio of the laminated plate. A.K. Sreevastava [1] determine the effect of different aspect ratio on the buckling effect on a laminated composite plate. Ghannadpour et al[2] find out that the plates with holes buckle at higher load as compare to plates with no holes. Kremer et al[3] & Tercan et al[4] determine the effect of different shapes on the buckling behaviour of a composite plate. Eryigit et al[5] determine the effect of different sizes of holes and their locations on the buckling behaviour of a woven fabric laminated composite plate. Komur et al[6] determine the effect of circular/elliptical hole on the buckling behaviour of laminated composite plate made up of woven glass polyester. Kumar et al[7] study the effects of cutout shapes of large size cutouts on the buckling and post buckling behaviour on a quasi-isotropic composite laminate. Ameen et al[8] experimentally determine the critical buckling load for E-glass reinforced polyester plastic material. 136 Saood Ali, Farooq Ahmed

2 The main purpose of the present study is to determine the effect of different semi-major to semi-minor axis ratio of an elliptical hole and the L/h ratio on the buckling frequency of the laminated composite plate. Figure 1 Basic model of the problem DESCRIPTION OF PROBLEM A composite plate of dimension 2mx1m with a central hole of area.05 times the plate area, subjected to uniform in-plane loading, have been used for finite element analysis. The analysis has been carried out for constant thickness (8 layers) for L/h ratio of 40 and 100. The basic model of the problem has been shown in the figure 1. The composite plate is made of E-Glass/Epoxy & its properties are given in Table 1. Material Ex Ey Gxy E-Glass /Epoxy 39GPa 8.6GPa 3.8GPa Νxy 0.28 Table 1 Material Properties Finite Element Analysis In the present study the buckling load for the composite plate with elliptical cut out has been analysed using ANSYS software. The element used to model the plate for numerical analysis is Shell181. SHELL181 is suitable for analyzing thin to moderately-thick shell structures. It is a four-node element with six degrees of freedom at each node: translations in the x, y, and z directions, and rotations about the x, y, and z-axes. (If the membrane option is used, the element has translational degrees of freedom only). The degenerate triangular option should only be used as filler elements in mesh generation. Figure 2 shows the type of element. Figure 3 shows the typical mesh of problem along with the boundary conditions. 137 Saood Ali, Farooq Ahmed

3 u x =u y =u z =0 θ y = θ z =0 u y =u z =0 θ y = θ z =0 Figure 2 Details of element type Figure 3 Mesh model with boundary conditions Results & Discussion Numerical results have been presented for E-glass/epoxy laminated composite plate with central elliptical hole. Table 2 and Table 3 represents the critical buckling load for mode 1,2 &3, different axes ratio for elliptical hole and for L/h ratio of 40 & 200 respectively. Figure 4 & Figure 5 compares the critical buckling loads for different axes for L/h ratio of 40 & 200 respectively.from Figure 4 & Figure5, it has been observed that critical buckling load increases as the axes ratio increases and have maximum value for axes ratio of 1, i.e. for circular hole. The effect of L/h ratio is same as that have been observed in case of circular hole[8]. Critical Buckling Load (N) Mode Elliptical hole axes ratio E E E E E E E E E E E E+06 Table 2 Critical Buckling load for L/h ratio of 40 Critical Buckling Load (N) Mode Elliptical hole axes ratio E E E E E E E E E E E E+04 Table 3 Critical Buckling load for L/h ratio of Saood Ali, Farooq Ahmed

4 Conclusion On the basis of the present study which deal with the effect of axis ratio of an elliptical hole on the buckling behaviour of a eight ply quasi- isotropic glass/epoxy symmetrically laminated rectangular plate [0 /30 /60 /90 ],the following observations have been observed:- (1) for a rectangular composite plate with elliptical central hole, the critical buckling load increases as the ratio of axes of an elliptical hole increases. (2) buckling load is minimum for an axes ratio of 0.25 and stress intensity distribution is also uniform around the hole. (3) buckling load is maximum for the axes ratio of 1.0 i.e for circular hole and stress intensity distribution is not uniform around the hole. (4) buckling load decreases as the L/h ratio increases means the ply becomes progressively thinner. From the above discussion it was clear that elliptical hole with axes ratio of 0.25 was most suitable for buckling applications instead of circular hole but the only problem with the elliptical hole was the manufacturing of it. Figure 4 Figure 5 Figure6 Stress intensity distribution for axis ratio 0.25 Figure7 Stress intensity distribution for axis ratio 0.50 Figure8 Stress intensity distribution for axis ratio 0.75 Figure9 Stress intensity distribution for axis ratio Saood Ali, Farooq Ahmed

5 References [1]A K Sreevastva, R.K Singh, "Effect of aspect ratio on buckling of composite plates", Journal of Composites Science and Technology 59 (1999) [2] Ghannadpour, Najafid, Moammadi, On the buckling behaviour of cross-ply laminated composite plates due to circular/elliptical cutouts, Jr Composite Structures, Vol.75, [3] Kremer, Schurmann, Buckling of tension loaded thin walled composite plates with cutouts, Jr composite Science and Technology, Vol. 68,2008. [4] Tercan,Aktas, Buckling behaviour of 1_1 rib kitting laminated plate with cutouts, Jr Composite Structures, Vol.89, [5] Eryigit, Zor, Arman, Hole effect on lateral buckling of laminated cantilever beams, Jr Composite: Part B, Vol.40, [6] Komor, Sonmez, Elastic buckling of rectangular plateunder linear varying in-plane normal load with circularcutouts, Jr. Mechanics Research Communications,Vol.35, [7] Kumar, Singh, Effect on boundary conditions on buckling and post buckling responses of composite laminates with various shaped cutouts, Jr Composite Structures, Vol.92, [8] Ameen, Buckling Analysis of composite Laminated plate with cutouts, Engg. And Tech. Jr., Vol.27, No.8, [9] Priyanka Dhurvey and N D Mittal," Buckling Behavior of an Orthotropic Composite Laminate using Finite Element Analysis", International Journal of Scientific Engineering and Technology, Vol.1, Issue 4, Saood Ali, Farooq Ahmed