IJIRST International Journal for Innovative Research in Science & Technology Volume 3 Issue 01 June 2016 ISSN (online): 2349-6010 Stress Analysis of Plate with Elliptical Hole Ankit Tiwari UG Student Kartik Alyadwar UG Student Vaishnav Tarone UG Student S. R Zaveri Associate Professor S. D Khamankar Associate Professor Abstract Stress analysis of an infinite length plate employing an elliptical hole subjected to axial tension has been carried out using numerical, analytical and experimental method. Different angles of obliquity have been considered to find concentration factor at such holes. The work covers plate hole obliquity angles 0, 45, 90 degree. The comparison is made between the results obtain from photo elasticity, FEA and actual failure test. Keywords: analysis, finite element analysis, oblique hole, photo elasticity I. INTRODUCTION Localised around geometric discontinuity such as hole, shoulders and grooves cannot be predicted using elementary formulas. The concentration of resulting from these abrupt transitions is frequently too high to be attributed solely to the decrease in net cross sectional area. Stress concentration factors, often determined experimentally and computationally are used to scale the nominal in a continuous structure to account for the effect of discontinuity. Stress analysis of thin flat plate with oblique hole subjected to axial tension has been carried out using the Finite Element Method (FEM). An oblique may be defined as one having its axis at an angle with respect to the surface. In the present work, the finite element method (FEM) has been used to determine es around oblique holes in plate subjected to axial tension and comparisons made with the other approaches. II. TECHNICAL DETAILS The research work by H. W. McKENZIE AND D.J. WHITE, reports the experimental works for determination of concentration in an oblique hole in flat plate with thickness of 5mm, width of 80mm and overall length of 250mm as shown. The hole is having major axis of 40mm and minor axis of 20mm and various angles of obliquity with respect to plane are considered as Ө= 0 to 90 degrees. Tension loading is applied in the direction of the length of the specimen. It is intended to use same geometrical parameters of plate describe earlier for proposed work. The experimental results will be verified using FEM. Where, All rights reserved by www.ijirst.org 183
Ө = Angle of obliquity parallel to the plane 0 Ө 0 III. METHODOLOGY To find out the es in plate, a plate under tensile load will consider Finite Element Method will be used with 2D element.the plate will be assumed with constrained at one end.it is expected that the concentration effect will be vary with respective obliquity of the hole and effort will be made to correlate the experimental existing expected result with FEA result. IV. FEA SOLUTION FOR OBLIQUE HOLE The plate with oblique elliptical hole having thickness t= 5mm, width= 80mm, and overall length l= 254mm, as shown in Fig1. The elliptical hole has major axis 2a=40mm, 2b=20mm, and three angles of obliquity with respect to the plane are used, Ө= 0,, 0 nd with var ing load The value of max, von-misses es for different angle of obliquity given in Table 1. Table - 4.1 FE es for different angle of obliquity with varying load. Fig. 4.1: Show the distribution around an elliptical hole with angel= 0, and load 548 N All rights reserved by www.ijirst.org 184
Fig. 4.2: how the distribution around an elliptical hole with angel= 0, and load 935 N Fig. 4.3: Show the distribution around an elliptical hole with angel= 0, and load 1080 N Fig. 4.4: how the distribution around an elliptical hole with angel= 0, and load 323.6 N All rights reserved by www.ijirst.org 185
Fig. 4.5: how the distribution around an elliptical hole with angel= 0, and load 484 N Fig. 4.6: how the distribution around an elliptical hole with angel= 0, and load 644 N Fig. 4.7: how the distribution around an elliptical hole with angel=, and load 453.22 N All rights reserved by www.ijirst.org 186
Fig. 4.8: Show the distribution around an elliptical hole with angel=, and load 679.8 N Fig. 4.9: Show the distribution around an elliptical hole with angel=, and load 809.3 N V. COMPARISON BETWEEN S.C.F. FEM PHOTO ELASTICITY AND ACTUAL FAILURE TEST BASED ON GROSS AREA- The comparison is done between FE and experimental (photo elasticity, actual failure test) to check the concentration factor is given in table 5.1 Table - 5.1 Comparison between FE and experimental concentration factor. Stress concentration factor Sr Type of FEM Photo Actual No. hole Resultelasticity result Failure test result 1 Vertical 2.7 2.53 3.21 2 Horizontal 1.601 1.256 1.74 3 Inclined 3.63 3.67 4.16 All rights reserved by www.ijirst.org 187
VI. EVALUATION OF STRESS CONCENTRATION FACTOR FOR PLANE WISE OBLIQUITY OF HOLE- The evaluation of S.C.F. for plane wise obliquity for hole is shown in table 6.1 0.1 0.3 0.5 0.7 b/a ratio FE TH Angles of obliquity (degrees) 0 10 20 30 40 50 60 70 80 90 1.636 2.85 5.898 9.174 13.2 16.9 20.17 22.29 22.83 22.2 1.025 1.012 1.008 1.007 1.00 1.07 1.011 1.02 1.062 1.33 SCF 1.596 2.81 5.85 9.11 13.1 16.8 19.95 21.85 21.5 16.7 FE 1.723 2.03 2.886 4.046 5.316 6.55 7.69 8.158 8.515 8.74 TH 1.081 1.07 1.062 1.054 1.057 1.06 1.087 1.141 1.245 1.33 SCF 1.59 1.89 2.717 3.838 5.029 6.16 7.07 7.15 6.839 6.88 FE 2.292 2.42 2.808 3.38 4.064 4.79 5.484 6.019 6.377 6.50 TH 1.142 1.13 1.133 1.132 1.14 1.15 1.188 1.241 1.3 1.33 SCF 2 2.12 2.47 2.98 3.56 4.14 4.616 4.85 4.9 4.88 FE 2.968 3.03 3.25 3.517 3.858 4.25 4.595 4.953 5.078 5.22 TH 1.212 1.21 1.211 1.215 1.225 1.24 1.268 1.298 1.322 1.33 SCF 2.44 2.5 2.68 2.89 3.149 3.42 3.62 3.81 3.84 3.93 Fig. 6.1: Evaluation of concentration factor for plane wise obliquity of hole for b/a=0.1 All rights reserved by www.ijirst.org 188
Fig. 6.2: Evaluation of concentration factor for plane wise obliquity of hole for b/a=0.3 Fig. 6.3: Evaluation of concentration factor for plane wise obliquity of hole for b/a=0.5 Fig. 6.4: Evaluation of concentration factor for plane wise obliquity of hole for b/a=0.7 VII. RESULTS AND CONCLUSION 1) A series of thick plates with oblique holes under axial tension is analysed using the Finite Element Analysis. For the axial loading case, the concentration factor are compared with the results obtained by the experimental photo elasticity and actual failure test as shown in TABLE 7.2.For the S.C.F values the difference between the FE results and by the All rights reserved by www.ijirst.org 189
experimental photo elasticity and actual failure test is got to be in the deviation of range 15% - 30% which shows good agreement. 2) In case of horizontal elliptical hole we can see that the maximum is generated at the edges of minor axis. And it gradually decreases to the edges of major axis. 3) In case of vertical elliptical hole we can see that the maximum is generated at the edges of major axis and gradually reduces till the edges of minor axis. 4) In case of inclined elliptical hole we can see that the maximum is generated near the edges of major axis but are not exactly on them. This clearly shows that the results of inclined hole lie between the results of horizontal and vertical hole. 5) From the figure 7.1. We can conclude that the variation between S.C.F and angle of obliquity is gradual up to 0. That means S.C.F increases gradually with increase in angle of obliquity in all the three cases of horizontal, vertical and inclined hole. 6) s we increase the angle e ond 0 we can observe a constant nature of S.C.F with increase in angle of obliquity. 7) We can compare the data obtained in different position through different analysis method which can be broadly stated as Table 7.1 comparison between FE and experimental concentration factor Sr No. Stress concentration factor Type of hole FEM Photo Actual Result elasticity result Failure test result 1 Horizontal 2.7 2.53 3.21 2 Vertical 1.601 1.256 1.74 3 Inclined 3.63 3.67 4.16 8) The concentration factor evaluated for oblique holes for various condition of obliquity will be use-full for designer to estimate the maximum in a plate with oblique holes. Fig. 7.1: Evaluation of Stress Concentration Factor for Plane wise Obliquity of Hole REFERENCES [1] H.W.McKENZIE and D.J.WHITE "Stress concentration caused by an oblique round hole in a flat plate under uniaxial tension". [2] Baban C. Patle tress nal sis of plate with oblique hole". [3] Khurmi & R.S.Gupta "Machine Design". [4] D.V.Bhandari "Design of Machine Elements". [5] B.D.Shiwalkar "Design Data book'. All rights reserved by www.ijirst.org 190