Stress Concentration on a plate with a hole

STRESS CONCENTRATION ON A PLATE WITH A HOLE

Case 1:

For Case 1, Static Structural Analysis is carried out on a plate with a single hole of diameter 60mm. The material used is Structural Steel and the analysis is carried out in ANSYS Workbench. The plate is first modelled in ANSYS SpaceClaim software and is as shown in the figure below.

The dimensions of the plate are as follows:

Length	300mm
Breadth	120mm
Thickness	30mm

The 2d geometry is then extruded within SpaceClaim to get the model to be imported into ANSYS. The extruded model is as shown in image below.

The properties of the material used are as stated below:

Density	7.85e-006 kg mm^-3
Isotropic Secant Coefficient of Thermal Expansion	1.2e-005 C^-1
Specific Heat Constant Pressure	4.34e+005 mJ kg^-1 C^-1
Isotropic Thermal Conductivity	6.05e-002 W mm^-1 C^-1
Isotropic Resistivity	1.7e-004 ohm mm

The model is meshed using ANSYS mesher with an element size of 6.8mm and a Patch Conforming method using tetrahedrons was employed. This is done to get the best refinement within the limitations of an ANSYS Academic License.

A mesh metric that identifies elements according to their quality was employed and it can be seen that the elements of lowest quality are minimal. Most of the elements have very high quality in the range of 0.7 – 1. Hence, the mesh is of acceptable quality. The meshed model is as shown in image below.

After the model is meshed, the loads are applied on the model. A fixed support is given on one side while a tensile load of 500 N is given on the other. The loads are as shown in the image below

The Simulation is then run with the settings applied and the results are obtained.

Case 2:

For Case 2, Static Structural Analysis is carried out on a plate with 3 holes. It is a modification of the model used in Case 1 such that there are 2 extra holes of 30mm diameter placed 90mm away from the centre. The dimensions of the plate and the material used are the same as in Case 1. The 3D model of the plate is as shown in the image below.

The model is meshed using ANSYS mesher. An element size of 3.31 mm and a Patch conforming method using tetrahedrons was implemented. The number of nodes and elements can be seen to not breach the license limits.

A mesh metric that identifies elements according to their quality was employed and it can be seen that the elements of lowest quality are minimal. Most of the elements have very high quality in the range of 0.5 – 0.9. Hence, the mesh is of acceptable quality. The meshed model is as shown in image below.

After meshing of the model, the loads are applied.

”Fixed Support” is applied on one side of the model and a tensile load of 500 N is applied on the other side. The Simulation is then run and the results are obtained.

RESULTS:

The Total Deformation for the two cases are compared first.

Time [s]	Minimum [mm]	Maximum [mm]	Average [mm]
1.	0.	2.7489e-004	1.3726e-004
2.	0.	2.9721e-004	1.4589e-004

The Equivalent stress for the two cases are compared.

Time [s]	Minimum [MPa]	Maximum [MPa]	Average [MPa]
1.	1.7299e-002	0.59312	0.15875
2.	1.103e-003	0.57732	0.16697

The Total Deformation is plotted on the model and is as shown below.

The Equivalent stress is plotted on the model and is as shown below.

CONCLUSION:

The analysis was run successfully. Within the limits of the academic license, the simulations for the 2 cases were examined. The mesh size that could be used in both the cases differed significantly as a result of the appearance of the two holes which resulted in lesser material and hence smaller size mesh elements could be used within the confines of the academic license.

On comparison of the Total Deformation experienced by the model in the 2 cases, only a slight difference in the average value is evident of the order of 0.07mm with Case 2 having a higher value. Maximum deformation in the two models have a difference of the order of 0.25mm.

On comparison of the Equivalent stress experienced by the model in the 2 cases, a difference of 0.08 MPa is evident in the average value of equivalent stress. But the maximum and minimum value of stress experienced in case 2 is lesser than that in case 1.

On the basis of these results, from an analysis point of view, Case 2 can be chosen because the stress undergone by it on application of the same amount of tensile force is lesser than it’s counterpart and also because the difference in deformation values are also very small.

From a manufacturing point of view, Case 1 can be chosen because the work that has to be done on the model is lesser when compared to Case 1 and there is not much improvement in performance when you consider the work that has to be done to make the model.