Analysis on a plate with a hole (Finite Element Analysis using Solidworks)

Abstract:-

To Perform a static analysis on two models of a plate with holes via SolidWorks, one analysis for a plate with one hole and one analysis for a plate with three holes. Finally, compare the obtained results between the two plates.

Introduction:-

When loads are applied to a body, the body deforms and the effect of loads is transmitted throughout the body. The external loads induce internal forces and reactions to render the body into a state of equilibrium. Linear Static analysis calculates displacements, strains, stresses, and reaction forces under the effect of applied loads. The linear static analysis makes the assumptions that all loads are applied slowly and gradually until they reach their full magnitudes. After reaching their full magnitudes, loads remain constant (time-invariant). This assumption allows us to neglect inertial and damping forces due to negligibly small accelerations and velocities.

Modeling:-

Two plates were modeled via Solidworks:

1.  Plate with one hole
2.  Plate with three holes

For the first model, the following dimensions were used: 

Length=300mm
Height=120mm
The diameter of the hole=60mm

Figure 1 shows the sketched model 

Figure 1: 2D model of the first plate

Then the part was extruded to a thickness of 30mm as shown below in figure 2.

Figure 2: Three-dimensional model of the first plate

The second model was sketched and the dimensions below were used. 

Length=300mm
Height=120mm
Thickness=30mm
Center of the Diameter=60mm

Two circles were placed 90mm away from the central hole = 30mm. The two circles were formed using the function "Extruded Cut". Figure 3 shows the new model. 

Figure 3: Three-dimensional model of the second plate

Simulation:-

Before starting the simulation, A material was applied to the plate (Alloy steel was chosen in both cases), Figure 4 shows the properties of alloy steel.

Figure 4: Alloy Steel properties

The next step of the simulation is to apply a fixed relation to one of the short sides of the plate and apply a force of 1000N on the other such that the plate is stretched, Figure 5 and 6 shows the loads and fixtures for both models.

Figure 5: The fixtures and loads applied to the first model                                                                                        Figure 6: The fixtures and loads applied to the second model

After applying the loads and fixtures to the plates, a mesh will be applied.  Figure 7 shows the properties of the mesh used for both plates.

Figure 7: mesh parameters

Figure 8 and 9 shows the two models being meshed.

Figure 8: The meshed model of the first model                                                                                                     Figure 9: The meshed model of the second model

Results:-       

Model 1: Plate with one hole                                  

The results are obtained based on the boundary conditions. Figure 10,11 and 12 shows the Von Mises stress, Displacement, and Strain for the first model.

Figure 10: Von Mises Stresses for the first model

Figure 11: Displacement Plot for the first model

Figure 12: Strain plot for the First model

Model 2: Plate with three holes

Figure 13,14 and 15 shows the Von Mises stress, Displacement, and Strain for the second model.

Figure 13: Von Mises Stresses for the second model

Figure 14: Displacement Plot for the second model

Figure 15: Strain plot for the second model

Conclusion:-

The results show that the second model has a bit less stress than the first model, this means that the increase in the number of holes in a plate decreases the stress on a plate. This is because stress is inversely proportional to the area, so when the area increases the stress decreases and vice versa. In addition, the chances of rupture are increased in the first model too. The second model exhibits a slightly higher displacement value than in model 1. Finally, the strain is also marginally lower in model 1 than model 2. When talking into account the economical and structural point of view, Plate 2 is the more efficient design since it has slightly less stress and strain values, and model 2 has a lower material cost.