Week 1 Stress Concentration on a Plate with hole

Stress concentration on different plates

Aim : To perform static structural analysis to determine the stress concentration on a plate with holes.

Objectives :

1) Design a plate with a hole model. (Case 1)

2) Design a plate with three holes of different diameter. (Case 2)

3) Determining the maximum deformation and stress developed in both models.

4) Comparing the result of two cases and deciding which cases to select on analysis and manufacturing point of view.

Software used : Ansys Workbench 2021 R1

Given :

For Case 1 :

Plate dimensions: Length=300mm

Height=120mm

Thickness=30mm

Circular Hole at the center:

Diameter=60mm

Mesh :

There are total 43439 tetrahedral elements and 76366 nodes are generated.
one side of the plate is fixed and other side is given load of 500N.

Total Deformation:

Max. Deformation = 0.000274 mm

Min. Deformation = 0 mm

Equivalent Stress:

Max. stress = 0.60724 MPa

Min. equivalent stress = 0.0077434 MPa

Equivalent Strain:

Max. Strain = 3.0362e-06

Min. Strain = 3.9723e-08

For Case 2 :

Plate dimensions:

Smaller holes 90mm away from the centre:

Diameter=30mm

Circular Hole at the centre Diameter=60mm

Length=300mm

Height=120mm

Thickness=30mm

Boundary Conditions for both the Cases: Plate fixed at left face. Load of 500N on the right face

Mesh

There are total 44544 tetrahedral elements and 68178 nodes are generated.

Total Deformation

one side of the plate is fixed and other side is given load of 500N.

Max. Deformation = 0.00029724 mm

Min. Deformation = 0 mm

Equivelent Stress

Max. equivalent stress = 0.57655 MPa

Min. equivalent stress = 0.0029405 MPa

Equivalent strain

Max. Equivalent Strain = 2.8831e-06

Min. Equivalent Strain = 2.9978e-08

Results:

Solution	Case 1. Plate with hole	Case 2. Plate with three holes
Max. Deformation	0.000274 mm	0.00029724 mm
Min. Deformation	0	0
Max. equivalent stress	0.60724 MPa	0.57655 MPa
Min. equivalent stress	0.0077434 MPa	0.0029405 MPa
Max. Equivalent Strain	3.0362e-06	2.8831e-06
Min. Equivalent Strain	3.9723e-08	2.9978e-08

Conclusion:

1) From the results above, we can conlcude that the plate with a hole has less deformation than the plate with three hole.

2) Stress level in plate with a hole has is higher than the plate with three holes.

3) From analysis point of view, case 2 (plate with three holes) model is better because it reduces the stress concentration near hole which results in longer operational life and case 1 design may fail early due to stress concentration as compared to case 2.

4) From manufacturing point of view, case 1 ( plate with single hole) model is better because it has less manufacturing operations which results in less manufacturing cost as compared to case 2 also case 1 has less material wastage.