Stress Analysis of Plate with Elliptical Hole

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 Department of Mechanical Engineering R.C.E.R.T, Chandrapur, India

Vaishnav Tarone UG Student Department of Mechanical Engineering R.C.E.R.T, Chandrapur, India

Kartik Alyadwar UG Student Department of Mechanical Engineering R.C.E.R.T, Chandrapur, India

S. R Zaveri Associate Professor Department of Mechanical Engineering R.C.E.R.T, Chandrapur, India

S. D Khamankar Associate Professor Department of Mechanical Engineering R.C.E.R.T, Chandrapur, India

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 stress 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: stress analysis, finite element analysis, oblique hole, photo elasticity _______________________________________________________________________________________________________ I.

INTRODUCTION

Localised stress around geometric discontinuity such as hole, shoulders and grooves cannot be predicted using elementary stress formulas. The concentration of stress 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 stress 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 stresses 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 stress 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 Ó¨= 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

Stress Analysis of Plate with Elliptical Hole (IJIRST/ Volume 3 / Issue 01/ 031)

Ө = Angle of obliquity parallel to the plane 0≤Ө≤ 0 III. METHODOLOGY To find out the stresses 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 stress 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 stresses for different angle of obliquity given in Table 1.

Table - 4.1 FE stresses for different angle of obliquity with varying load.

Fig. 4.1: Show the stress distribution around an elliptical hole with angel= 0, and load 548 N

All rights reserved by www.ijirst.org

184

Stress Analysis of Plate with Elliptical Hole (IJIRST/ Volume 3 / Issue 01/ 031)

Fig. 4.2: how the stress distribution around an elliptical hole with angel= 0, and load 935 N

Fig. 4.3: Show the stress distribution around an elliptical hole with angel= 0, and load 1080 N

Fig. 4.4: how the stress distribution around an elliptical hole with angel= 0, and load 323.6 N

All rights reserved by www.ijirst.org

185

Stress Analysis of Plate with Elliptical Hole (IJIRST/ Volume 3 / Issue 01/ 031)

Fig. 4.5: how the stress distribution around an elliptical hole with angel= 0, and load 484 N

Fig. 4.6: how the stress distribution around an elliptical hole with angel= 0, and load 644 N

Fig. 4.7: how the stress distribution around an elliptical hole with angel=, and load 453.22 N

All rights reserved by www.ijirst.org

186

Stress Analysis of Plate with Elliptical Hole (IJIRST/ Volume 3 / Issue 01/ 031)

Fig. 4.8: Show the stress distribution around an elliptical hole with angel= , and load 679.8 N

Fig. 4.9: Show the stress 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 AREAThe comparison is done between FE and experimental (photo elasticity, actual failure test) to check the stress concentration factor is given in table 5.1 Table - 5.1 Comparison between FE and experimental stress concentration factor.

Stress concentration factor Sr Type of FEM Photo Actual No. hole Result elasticity 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

Stress Analysis of Plate with Elliptical Hole (IJIRST/ Volume 3 / Issue 01/ 031)

VI. EVALUATION OF STRESS CONCENTRATION FACTOR FOR PLANE WISE OBLIQUITY OF HOLEThe evaluation of S.C.F. for plane wise obliquity for hole is shown in table 6.1 b/a ratio

0.1

0.3

0.5

0.7

FE stress Mpa TH stress Mpa SCF FE stress Mpa TH stress Mpa SCF FE stress Mpa TH stress Mpa SCF FE stress Mpa TH stress Mpa SCF

0

10

1.636

2.85

20

Angles of obliquity (degrees) 30 40 50 60

70

80

90

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

1.596

2.81

5.85

13.1

16.8

19.95 21.85

21.5

16.7

1.723

2.03

2.886 4.046 5.316

6.55

7.69

8.158 8.515

8.74

1.081

1.07

1.062 1.054 1.057

1.06

1.087 1.141 1.245

1.33

1.59

1.89

2.717 3.838 5.029

6.16

7.07

6.839

6.88

2.292

2.42

2.808

3.38

4.064

4.79

5.484 6.019 6.377

6.50

1.142

1.13

1.133 1.132

1.14

1.15

1.188 1.241

1.3

1.33

2

2.12

2.47

2.98

3.56

4.14

4.616

4.9

4.88

2.968

3.03

3.25

3.517 3.858

4.25

4.595 4.953 5.078

5.22

1.212

1.21

1.211 1.215 1.225

1.24

1.268 1.298 1.322

1.33

2.44

2.5

2.68

3.42

3.62

3.93

9.11

2.89

3.149

7.15

4.85

3.81

3.84

Fig. 6.1: Evaluation of stress concentration factor for plane wise obliquity of hole for b/a=0.1

All rights reserved by www.ijirst.org

188

Stress Analysis of Plate with Elliptical Hole (IJIRST/ Volume 3 / Issue 01/ 031)

Fig. 6.2: Evaluation of stress concentration factor for plane wise obliquity of hole for b/a=0.3

Fig. 6.3: Evaluation of stress concentration factor for plane wise obliquity of hole for b/a=0.5

Fig. 6.4: Evaluation of stress 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 stress 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

Stress Analysis of Plate with Elliptical Hole (IJIRST/ Volume 3 / Issue 01/ 031)

2) 3) 4) 5)

6) 7)

experimental photo elasticity and actual failure test is got to be in the deviation of range 15% - 30% which shows good agreement.

In case of horizontal elliptical hole we can see that the maximum stress is generated at the edges of minor axis. And it gradually decreases to the edges of major axis.

In case of vertical elliptical hole we can see that the maximum stress is generated at the edges of major axis and gradually reduces till the edges of minor axis.

In case of inclined elliptical hole we can see that the maximum stress 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.

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. s we increase the angle e ond 0 we can observe a constant nature of S.C.F with increase in angle of obliquity.

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 stress concentration factor Stress concentration factor Sr Photo Actual Type of hole FEM No. elasticity result Failure test result Result 1 2 3

Horizontal 2.7 Vertical 1.601 Inclined 3.63

2.53 1.256 3.67

3.21 1.74 4.16

8) The stress concentration factor evaluated for oblique holes for various condition of obliquity will be use-full for designer to estimate the maximum stress in a plate with oblique holes.

Fig. 7.1: Evaluation of Stress Concentration Factor for Plane wise Obliquity of Hole

REFERENCES [1] [2] [3] [4] [5]

H.W.McKENZIE and D.J.WHITE "Stress concentration caused by an oblique round hole in a flat plate under uniaxial tension".

Baban C. Patle “tress nal sis of plate with oblique hole".

Khurmi & R.S.Gupta "Machine Design".

D.V.Bhandari "Design of Machine Elements".

B.D.Shiwalkar "Design Data book'.

All rights reserved by www.ijirst.org

190