Week 1 Stress Concentration on a Plate with hole

Abstract:

To analyze and compare the deformation and maximum stress developed on two rectangular plate structural steel models namely Case 1 and Case 2.

Introduction:

A body undergoes deformation when a sufficient force is applied which supersedes the internal forces in the body. This analysis can be useful for various applications that involve similar rectangular models in many complex components.

The material of these models is Structural Steel. Its properties are given in Figure 1.

Figure 1. Properties of Structural Steel

Modeling:

Case 1: A rectangular plate with dimensions

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

Figure 2. Case1 CAD Model

Case 2: A rectangular plate with dimensions

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

Figure 3. Case 2 CAD Model

Simulation and Results:

Boundary conditions specified and applied are:

1. Plate fixed on the left face.
2. Load of 500N applied on the right face.

Figure 4. Boundary Conditions for Case 1 model.

Figure 5. Boundary Conditions for Case 2 model.

The following are results obtained by applying the boundary conditions on the above models:

1. Total Deformation
   • Case 1
     • Minimum = 0 mm
     • Maximum = 0.34343 mm
     • Average = 0.1717 mm
   • Case 2
     • Minimum = 0 mm
     • Maximum = 0.29733 mm
     • Average = 0.14536 mm
2. Maximum Stress Developed
   • Case 1
     • Minimum = -0.011 MPa
     • Maximum = 0.77098 Mpa
     • Average = 0.19276 MPa
   • Case 2
     • Minimum = -0.00902 MPa
     • Maximum = 0.59651 MPa
     • Average = 0.16015 Mpa
3. Illustrations of results

Figure 6. Total Deformation for Case 1 Model

Figure 7.Maximum Principal Stress for Case 1 Model

Figure 8. Total Deformation for Case 2 Model

Figure 9. Maximum Principal Stress for Case 2 Model

Conclusion:

As evident from the results, the maximum principal stress and total deformation of the Case 2 model i.e., the rectangular plate with 3 holes is less than that of the Case 1 model i.e., the rectangular model with one hole at the center. Hence, from an analysis standpoint Case 2 model is better as it undergoes less deformation and principal stresses. From the standpoint of manufacturing these models, Case 1 model is better. This is because additional equipment is required to produce a plate with 3 holes of which 2 holes are of different dimensions (Case 2 model).