Week 1 Stress Concentration on a Plate with hole

CONCENTRATION ON A HOLE

OBJECTIVE:

The objective of this challenge is to design a plate with single hole and multi
hole, and to Simulate the two cases and compare its deformation and maximum stress
results. As well as to STATE that among the two cases, which case will prefer for Analysis
and which case will prefer the manufacturing process.

SOFTWARE USED:

• ANSYS Workbench and ANSYS Mechanical for Analysis
• Space claim for design
  
  

THEORY:

A thin rectangular plate under a uniaxial tension has a uniform stress
distribution. Introducing a circular hole in the plate disturbs the uniform stress
distribution near the hole, resulting in a significantly higher than average stress. Such a
thin plate, subject to in-plane loading, can be analyzed as a 2-D plane-stress elasticity
problem. In theory, if the plate is infinite, then the stress near the hole is three times
higher than the average stress. For a rectangular plate of finite width, the stress
concentration factor is a function of the ratio of hole diameter to the plate width.

PROCEDURE:

Case :1

Stress Concentration on a Plate with single center hole

1. Open the ANSYS Workbench software. Under the Analysis system select the Static
     structural and wait for few seconds to pop up the window, which contains Engineering
    data, Geometry, Model, setup, Solution and Results.
2. Rename the static structural as Plate with hole.
3. Update the Default material (Structural steel) to the System, under the Engineering
    data.
4. Design a rectangular plate with hole by using space claim and assign the Dimensions
   such as

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

5. Update the model by right click and edit the Model for meshing.
6. Wait for few seconds and ANSYS Mechanical will open as shown below.

7. In ANSYS automatic mesh will be performed with Default mesh size and change the
mesh size as 5mm.

Be aware of ANSYS Student Edition and don't go beyond the size limit.

As it is a solid structure we have to change the 2D Element to 3D Element. So click on
mesh and select the insert option. Under insert option select the method and slect the
gemetry as well as under the method, select the tetrahedrons.

8. In order to get the results we have to fix the left end of the plate by using the fixed
support option and apply the tensile force at right side of the plate.

Fix the left end of the plate by using the fixed support option.

Apply the force at right end of the plate as a load of 500N

9. SOLVE the solution and we can see the simulation run under soluion information.

Result :

deformation

normal stress:

strain:

Case :2

Stress Concentration on a Plate with MULTIPLE holes

1. Open the ANSYS Workbench software. Under the Analysis system select the Static
structural and wait for few seconds to pop up the window, which contains Engineering
data, Geometry, Model, setup, Solution and Results.
2. Rename the static structural as Plate with hole.
3. Update the Default material (Structural steel) to the System, under the Engineering
data.
4. Design a rectangular plate with hole by using space claim and assign the Dimensions
such as

Plate dimensions:
Length=300mm
Height=120mm
Thickness=30mm
Circular Hole at the center:
Diameter=60mm
Smaller holes 90mm away from the center:
Diameter = 30mm

 

By using pull option assign the thickness of the plate as 30mm.

5. Update the model by right click and edit the Model for meshing

Be aware of ANSYS Student Edition and don't go beyond the size limit.

7. In ANSYS automatic mesh will be performed with Default mesh size and change the
mesh size as 5mm.

As it is a solid structure we have to change the 2D Element to 3D Element. So click on
mesh and select the insert option. Under insert option select the method and slect the
gemetry 

8. In order to get the results we have to fix the left end of the plate by using the fixed
support option and apply the tensile force at right side of the plate.

Fix the left end of the plate by using the fixed support option

Apply the force at right end of the plate as a load of 500N

9. SOLVE the solution and we can see the simulation run under soluion information.

10. Then request for the output results such as equivalent (von-mises) stress and total
deformation.Finally evaluate all results.

total deformation:

strain:

stress:

1)RESULTS COMPARISM:

cases	Deformation	stress	strain
CASE_1	2.7543e-004 mm	4.1176e-003 MPa	1.5738e-006 mm/mm
CASE_2	0.0002973	0.16358 MPa	8.199e-007 mm/mm

From the above table the deformation in the second case (Stress Concentration on a
Plate with MULTIPLE holes) is high when compared to first case(Stress Concentration
on a Plate with single center hole). Where as For Maximum stress, it will be high in first
case(Stress Concentration on a Plate with single center hole) when compared with the
second case(Stress Concentration on a Plate with MULTIPLE holes).

2) From an analysis standpoint, which of the design will you select? Explain why?

From the analysis point of view, we can select the case-2 (Stress Concentration on a
Plate with MULTIPLE holes)

EXPLANATION:

The main ajenda of any analysis is to reduce the stress, based on that in our two cases,
case-2 will have less stress when compared with case-1. For that reason we had
selected the case-2 in analysis point of view.

3) Selection of Design from the Manufacturing point of view

From the Manfacturing point of view, we can select the case-1 (Stress Concentration
on a Plate with single center hole)

EXPLANATION:
The main ajenda of any manufacturer is to reduce the wastage of material as well as to
reduce the production time. So the first case is very simple in design and requires less
time for manufacturing as well as wastage of material will be less, where as in case-2 it
requires more time for manufacturing as well as wastage of material will be high For