Stress Concentration on a Plate with hole

Case 1 :

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

The Dimension of the plate are as follow,

Length=300mm

Height=120mm

Thickness=30mm

Circular Hole at the center:

Diameter=60mm

2.The 2D geomentry is then extruded with spaceclaim to get the model to be improved into ANSYS.The extruded model is as Shown in image below,

The properties of the material used are as stated below,

3.The Model is meshed using ANSYS mesher with an element size of 4mm and patch Conformation method using tetrahedrons was employed,This is done to get the best refinement within the limitation of an ANSYS Academic Licence,

Most of the element have very high quality in the range of 0.5 to 0.9.The meshed model is shown in the figure,

5.Fixed Support is applied on one side and a tensile Load of 500N appplied on the other side,

Case 2:

For case 2 , Static structural Analysis is carried out on a plate with 3 holes.It is a modification of the model case 1 and there are two extra hole with diameter 30mm placed 90mm away from the centre.The dimensions of the plate and the material usedi are same as in case 1.The 3D modelof the palte is as shown in the image below,

The Model is meshed using ANSYS mesher with an element size of 4mm and patch Conformation method using tetrahedron.The number of nodes and elements can be seen below and not to exceed the Acadamic licence limit,

A mesh metric that identifies elements according to their quality was employed.Most of the element have very high quality in the range of 0.5 to 0.9.The meshed model is shown in the figure,

Fixed Support is applied on one side and a tensile Load of 500N appplied on the other side,

Finaly the simulation is run and the result are obtained,

RESULTS:

The Total Deformation for the two cases are compared first,

Case Time(S) Minimum(mm) Maximum(mm) Average(mm)

1 1 0 2.7485e-004 1.3833e-004

2 1 0 2.9718e-004 1.4502e-004

The Total deformation is plotted in model and is as shown below,

CASE 1 CASE 2

The Equivalent stress for the two cases are compared ,

Case Time(S) Minimum(mpa) Maximum(mpa) Average(mpa)

1 1 1.4565e-002 0.6048 0.16944

2 1 1.7522e-003 0.58042 0.16986

The Equivalent stress is plotted in model and is as shown below,

CASE 1 CASE 2

CONCLUSION:

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

On comparision of the total Deformation experienced by the model in the 2 cases,Maximum deformation in the two models have a difference of the order of 0.22mm and slight difference in the average value of the order of 0.06mm with case 2 having higher Value.

On comparision of the Equivalent stress experienced by the model in the 2 cases,the maximum and minimum value of stress experienced in case 1 compared to case 2.

On the basic of these result,from an analysis point of view ,case 2 ca be chosen because the stress undergoes with the same of tensile force is lesser than case 1 and also the difference in defromation values are also very small.

From the 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.