Analysis on a plate with a hole (SOLIDWORKS)

1. OBJECTIVES

Perform a static analysis on two models of plate with holes.

Create the model in Solidworks and perform the analysis.

The dimensions are as follows:

CASE 1 CASE 2

Length=300mm Length=300mm
Height=120mm Height=120mm
Thickness=30mm Thickness=30mm
Circular Hole at the center: Circular Hole at the center:
Diameter=60mm Diameter=60mm

Two holes of 30 mm diameter which are placed 90mm away

from the central hole on both sides.

Apply a fixed relation to one of the short side of the plate and apply a force of 1000N on the other such that the plate is stretched.

Run the analysis and compare the results for stress, strain and displacement

Describe your findings in a detailed report.

Type the report in the space provided below itself. Attach appropriate images and tables to the report.

2. THEORY

Stress concentration

A stress concentration (also called a stress raiser or a stress riser) is a location in an object where the stress is significantly greater than the surrounding region. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress. This arises from such details as holes, grooves, notches and fillets. Stress concentrations may also occur from accidental damage such as nicks and scratches.

The degree of concentration of a discontinuity under typically tensile loads can be expressed as a non-dimensional stress concentration factor , which is the ratio of the highest stress to the nominal far field stress. For a circular hole, the stress concentration factor should not to be confused with the stress intensity factor, which is used to define the effect of a crack on the stresses in the region around a crack tip.

For static loading, yielding will typically occur first at a stress concentration and for ductile materials localized plastic deformation can occur causing a redistribution of stress, enabling the component to continue to carry load. Brittle materials will typically fail at the stress concentration. However, repeated loading may cause a fatigue crack to initiate and slowly grow at a stress concentration leading to the failure of even ductile materials. Fatigue cracks always start at stress raisers, so removing such defects increases the fatigue strength.

Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress.

Stress concentration factor

The stress concentration factor, , is the ratio of the highest stress to a nominal stress of the gross cross-section and defined as

Note that the stress concentration factor is a function of the geometry of a crack or notch, and not of its size.These factors can be found in typical engineering reference materials to predict the stresses that could otherwise not be analyzed using strength of material approaches.

E. kirsch derived the equations for the elastic stress distribution around a hole. The maximum stress felt near a hole or notch occurs in the area of lowest radius of curvature.

In an elliptical hole of length and width , under a nominal or far-field stress , the stress at the ends of the major axes is given by Inglis' equation:

where is the radius of curvature of the elliptical hole. For circular holes where {\displaystyle a=b}, the stress concentration factor is . As the radius of curvature approaches zero, like the tip of a sharp crack, the maximum stress approaches infinity and therefore stress concentration factors cannot be used for a crack.

The stress concentration factor should not to be confused with the stress concentration factor, which can be used to define the effect of a crack on the stresses around a crack tip.

3. ANALYSIS

Case-1 (Rectangular plate with 1 X 60mm hole)

Procedure

1. Create the model from the given data.

• 2D sketch

• 3D model

2. Create a new static simulation.

3. Select Alloy steel as a material.

4. Set the fixture on one of the short face (120mm*30mm).

5. Apply a force of 1000N on the other short face such that part is stretched (Tension force).

6. Create mesh of 3 mm size.

7. Run the simulation.

Results

Case-2 (Rectangular plate with 1 X 60mm & 2 X 30mm hole)

Procedure

1. Create the model from the given data.

• 2D sketch

• 3D model

2. Create a new static simulation.

3. Select Alloy steel as a material.

4. Set the fixture on one of the short face (120mm*30mm).

5. Apply a force of 1000N on the other short face such that part is stretched (Tension force).

6. Create mesh of 3 mm size.

7. Run the simulation.

2) Results

4. CONCLUSION

SL No	Description	Rectangular plate with 1 X 60 mm hole	Rectangular plate with 1 X 60mm and 2 X 30mm hole
1	Yeild strength (N/mm2)	6.204 X 108	6.204 X 108
2	Max Von Mises stress (N/mm2)	1.206	1.159
3	Max strain	4.709 X 10-6	4.456 X 10-6
4	Max displacement (mm)	5.241 X 10-4	5.667 X 10-4
5	Mass (g)	7662.86	7336.29

1. Stress increases when cross sectional area decreases. As we can see at the section of hole.
2. In the second case there is a reduction of stress concentration.
3. In the second case there is a reduction of Max strain.
4. In the second case there is a reduction of Maximum displacement.
5. In the second case there is a reduction of Mass.
6. The above results show that the increase in the number of hole reduces stress. The stress concentration can also be reduced by avoiding the sharp edges and filleting the edges.
7. In the first case the stress concentration across the section of hole is more and hence the maximum stress is induced on that section. Also the chances of rupture is increases when continuous loading is applied.
8. By considering manufacturing ease, first case is good.

So, the stress and mass are less in Case-1 but the manufacturing ease is less compare to Case-2.

Thus I will choose Case-1 (because it gives higher advantages).

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