Stress Concentration on a Plate with hole

1. Rectangular plate with one 60 mm hole

Static structural analysis is carried out for the rectangular model with a hole diameter of 60mm. Material used in this analysis structural steel from the engineering data at ansys workbench. The plate is initially 2D sketched in Ansys SpaceClaim and the Figure 1. Shows the software  2D plot on the model   

Figure 1. Ansys SpaceClaim  2D plot on the model   

The 2D sketch is extruded to a thickness of 30mm to obtain the 3D model as shown in Figure 2. This model is imported to Ansys

Figure 2. Ansys SpaceClaim  3D model

Structural Steel properties as in Ansys Workbench

Density	7850 kg/m³
Isotropic Elasticity
Young's Modulus Poisson's Ratio Bulk Modulus             Shear Modulus	2e+11 Pa 0.3 1.6667e+11 Pa 7.6923e+10 Pa
Isotropic Secant Coefficient of Thermal Expansion                Compressive Ultimate Strength                                                  Compressive Yield Strength                                                       Tensile Ultimate Strength                                                     Tensile Yield Strength	1.2e-05           1/°C 0             Pa 2.5e+08 Pa 4.6e+08             Pa 2.5e+08 Pa
Thermal
Isotropic Thermal Conductivity                                                          Specific Heat Constant Pressure	60.5 W/m·°C 434 J/kg·°C
Electric
Isotropic Resistivity	1.7e-07 ohm·m
Magnetic
Isotropic Relative Permeability	10000

Tetrahedron mesh using a patch conforming method was used to mesh the model, which has elements with a size of 6.5mm. In accordance with the restrictions of Ansys Academic Licence, this is done to obtain the best refinement. Meshed 3D model is shown in Figure 3.

Figure 3. Meshed 3D model

The elements of the lowest quality are minimum because of the use of a mesh metric that identifies the elements according to their quality. The element quality of the analysis is shown in Figure 4.

Figure 4. Element quality

Load value of 500N is applied in one short face with a fixed support on other short face.

Total deformation of this model shown in Figure 5. 

Figure 5. Total deformation

Time[s]	Minimum[mm]	Maximum[mm]	Average[mm]
1	0	2.7466e-004	1.3594e-004

Equivalent stress of this model shown in Figure 6. 

Figure 6. Equivalent stress

Time[s]	Minimum[MPa]	Maximum[MPa]	Average[MPa]
1	1.849e-002	0.60686	0.16611

2. Rectangular plate with one 60 mm hole and two 30 mm holes

Static structural analysis is carried out for the rectangular model with a hole diameter of 60mm and two hopeless of diameter 30mm at a distance of 90mm from the centre for each holes. 3D model on Ansys SpaceClaim is shown in Figure 7.

Figure 7. 3D model on Ansys SpaceClaim

Tetrahedron mesh using a patch conforming method was used to mesh the model, which has elements with a size of 6.5mm. In accordance with the restrictions of Ansys Academic Licence, this is done to obtain the best refinement. Meshed three holed 3D model is shown in Figure 8.

Figure 8.Meshed three holed 3D model

The element quality of the three holed model of the analysis is shown in Figure 9.

Figure 9. Element quality of the three holed model

Load value of 500N is applied in one short face with a fixed support on other short face.

Total deformation of the three holed model shown in Figure 10. 

Figure 10. Total deformation of the three holed model

Time[s]	Minimum[mm]	Maximum[mm]	Average[mm]
1	0	2.9673e-004	1.439e-004

Equivalent stress of the three holed model shown in Figure 11. 

Figure 11.  Equivalent stress of the three holed model

Time[s]	Minimum[MPa]	Maximum[MPa]	Average[MPa]
1	5.0469e-003	0.57335	0.16759

Results:

• The following table compares the results between the 2 models.

Sl. No	Description	Rectangular Plate with 1X hole	Rectangular Plate with 3X hole
1	Max. Von Mises Stresses (MPa)	0.60686	0.57335
2	Max. Displacement (mm)	2.7466e-004	2.9673e-004

• Due to its greater stress value and simplicity of analysis, the plate with a single hole should be chosen from an analytical perspective. To comprehend the impact of tensile stresses on a plate having a relief feature, such as a hole, we will do a straightforward analytical experiment. The overall difference in deformation between the plates is 20 nm, indicating that the plate with one hole deforms 20 nm less than the plate with three holes. This value is so insignificant that it shouldn't be taken into account while selecting this choice. We don't consider the design's weight, price, or manufacturing processes when doing our research.
• Because it is under less stress, the plate with three holes should be selected from a production perspective. The decision-making process for a manufacturing choice must take into account the material's cost, weight, and machinability. When compared to the plate with one hole, this plate is more cost-effective and has superior stress characteristics since it utilises less material, is lighter, and can be manufactured just as easily.