1 PROBLEM STATEMENT

Consider two plates of same dimension 300 x 120 x 30 mm. Plate-1 consists of a single central hole of diameter 60 mm. Plate-2 will be having two additional holes at a distance of 90mm from central hole along length (one at left side & other hole at right side). The diaa of smaller hole is 30 mm.

Tensile load of 500 N is acting along the length on face having dimension of 120 x 30 mm. Face opposite to the application of load will be fixed.

2 INTRODUCTION & THEORY

This problem of plate with a hole is a very standard problem & is having a huge scope in industry. These types of plates have been used in riveted joint application in order to fix some components with the help of two plates. There are many other applications of this model.

The main focus of studying this model is to know stress distribution around hole and variation of stress intensity factor due to presence of hole. SIF plays very important role while designing any component. SIF effects the life of component. We should study stress variation and nature of SIF &try to reduce SIF.

3 AIM

The focus of project is to observe the stress variation in both plates. We will be comparing the total deformation & extreme values of stresses in both cases. We will also be discussing which plate is better for analysis purpose in conclusion section.

4 GEOMETRY & MESHING

4.1 GEOMETRY

Detailed dimension of geometry has been discussed in problem statement in section 1. Reference sketch has been also added there.

Here we will observe 3-D model of the both plate which has been created in space claim.

Figure below shows plate-1 details geometry with dimension.

Figure below shows plate-2 details geometry with dimension.

4.2 MESHING

4.2.1 Plate-1

Hexahedral method of meshing has been chosen for plate 1. Meshing was done uniformly throughout the body. The element size was kept as 3 mm. Above figure shows that how meshing looks like.

4.2.1 Plate-2

Tetrahedral method of meshing has been chosen for plate 2. Meshing was done uniformly throughout the body. The element size was kept as 4 mm. Above figure shows that how meshing looks like.

4.2.3 Hexahedral v/s Tetrahedral

Hexahedral method is chosen when the geometry is very simple. It will give best results under those situations but if complexity in geometry increases then tetrahedral meshing is chosen over hexahedral method of meshing.

In our case both the geometry is simple but if we compare plate-2 with plate-1, we found that plate-2 is more complex. This is the reason behind doing different type of meshing in above two cases.

Table below shows the comparison of statics of meshing in both plates.

Plate	ELEMENT TYPE	ELEMENT SIZE (mm)	NUMBER OF NODES	NUMBER OF ELEMENTS
Plate-1	Hexahedral	3	444885	315376
Plate-2	Tetrahedral	4	185196	128209

Above table shows the meshing comparison of two plates. The element size of plate-2 is smaller than plate-1 by 1mm. Also due to 2 extra hole total number of element & nodes are lesser in plate-2.

3-D ELEMENT IN PLATE-1

3-D ELEMENT IN PLATE-2

5 BOUNDARY CONDITIONS

One face at A has been fixed whose dimension was 120 x 30 mm & face opposite to this has been applied with load along length.

The load is acting normal to the face with a magnitude of 500N.This is shown in below figure.

Same boundary condition was given for plate-2.

6 RESULT & DISSCUSION

6.1 PLATE-1

6.1.1 TOTAL DEFORMATION

From above figure we can see 2 probe one of red colour & other of blue colour. They represent maximum & minimum values of measured parameter. The maximum deformation occurs at the face where load is applied as shown by red colour tag & minimum deformation occurs at the face which has been fixed & blue colour tag shows the point of minimum deformation which is equal to zero.

6.1.2 VON MISES STRESS

Similarly, two probes showing maximum & minimum stress are shown above. The maximum & minimum stresses occur at the circular face as shown red & blue colour tag.

The following tables gives the data regarding maximum, minimum & average value of stresses & deformation.

PARAMETERS	TOTAL DEFORMATION in mm	VON MISES STRESS in MPa
MAXIMUM	2.7495e-004	0.60292
AVERAGE	1.3744e-004	0.15601
MINIMUM	0	1.0949e-002

6.2 PLATE-2

6.2.1 TOTAL DEFORMATION

From figure below we can see 2 probe one of red colour & other of blue colour. They represent maximum & minimum values of measured parameter. The maximum deformation occurs at the face where load is applied as shown by red colour tag & minimum deformation occurs at the face which has been fixed & blue colour tag shows the point of minimum deformation which is equal to zero.

6.2.2 VON MISES STRESS

Similarly, two probes showing maximum & minimum stress are shown above. The maximum stress occurs at the bigger circular face as shown by red & blue colour tag at smaller circle (near to fixed support) shows minimum value of stress.

The following tables gives the data regarding maximum, minimum & average value of stresses & deformation.

PARAMETERS	TOTAL DEFORMATION in mm	VON MISES STRESS in MPa
MAXIMUM	2.9731e-004	0.58111
AVERAGE	1.4533e-004	0.16306
MINIMUM	0	5.2743e-004

7 CONCLUSION

7.1 STRESS COMPARISON IN PLATE-1 & PLATE-2

If we compare location of maximum stress it is same in both plates. The maximum stress occurs at the periphery of larger circle along positive z axis in both plates. If we consider magnitude of stresses then the stress in plate-1 is having larger value. Plate-1 has 3.61% more maximum value of stress than plate-2.

PARAMETERS	PLATE-1	PLATE-2
MAXIMUM STRESS in MPa	0.60292	0.58111
AVERAGE STRESS in MPa	0.15601	0.16306
MINIMUM STRESS in MPa	1.0949e-002	5.2743e-004

The minimum value of stress occurs at different location in both plates. Minimum value of stress lies on periphery of larger circle in plate-1 & in plate-2 its location is at periphery of smaller circle which is near the fixed face of plate. The magnitude of minimum value of stress is more in plate-1 when compared with respect to plate-2.

7.2 DEFORMATION COMPARISON IN PLATE-1 & PLATE-2

If we compare location of maximum & minimum deformation it is same in both plates. The maximum deformation occurs at the face at which load is applied along positive X axis in both plates.

The minimum deformation is 0 and occur at the fixed face shown by blue tag in both plates. If we consider magnitude of deformation then the deformation in plate-2 is having larger value. Plate-2 has 8.13% more maximum value of deformation than plate-1.

PARAMETERS	PLATE-1	PLATE-2
MAXIMUM	2.7495e-004 mm	2.9731e-004 mm
AVERAGE	1.3744e-004 mm	1.4533e-004 mm
MINIMUM	0 mm	0 mm

Above table shows the comparison of deformation.

7.3 OPTIMUM DESIGN OF PLATE

If we consider geometry of plate-1, it is simple when compared with respect to plate-2. Also, plate-1 is a standard geometry which is easy to analyse.

Calculation in plate-2 will be little bit more complex. Stress intensity factor in plate-2 is more as compared with plate-1.

Also FRACTURE MECHANICS suggests that we can impart the analogy from plate-1 to other plate with any number of holes by using principle of superposition.

WE CAN CONCLUDE THAT PLATE-1 WITH SINGLE CENTRAL HOLE IS MORE PREFERRABLE IN ANY CASE.