Analysis on a plate with a hole using solidworks

STATIC ANALYSIS ON PLATE WITH A HOLE

INTRODUCTION

Engineering analysis deals with finding various engineering parameters like displacement,stress and strain. Static analysis is done when the force does not change with respect to time. The displacements are computed from the stiffness matrix and followed by the derived qualtities like stress,strain etc.

General Steps in CAE:

1.Creating a 3d model

2.Material definition: Alloy steel material is selected with following properties

Elastic Modulus 2.1e+11 N/m^2
Poisson's Ratio 0.28
Shear Modulus 7.9e+10 N/m^2
Mass Density 7700 kg/m^3
Tensile Strength 723825600 N/m^2
Yield Strength 620422000 N/m^2
Thermal Expansion Coefficient 1.3e-05 /K
Thermal Conductivity 50 W/(m·K)
Specific Heat 460 J/(kg·K)

3.Meshing the model using appropriate elements.

Baiscally the CAE softwares divide the solid model into small elements whose size can be specified by the user but for this analysis it was automatically set by the software itself. Solid elements were used for meshing.

4.Applying fixed constraint on one of the shorter side.

The structure must be constrained inorder for the force acting on it to make deformation in the structure otherwise there won't be any effect such as compressive stress or tensile stress. Fixed constraint was applied to the left shorter side.

5.Forces are applied on the other side of magnitude 1000N so that stretching happens.

In this case as it is mentioned that stretching is happened so the 1000N force is given in the right direction.

CASE 1 PLATE WITH SINGLE HOLE

Step 1: Creating a 3 D Model

The model was created using solidworks considersing the given dimensions

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

The sketch is shown in fig 1.1 .The sketch was extruded 30mm to obtain the 3d model as shown in the figure 1.2

Figure 1.1 Sketch

Figure 1.2 Model

Step 2: Material Definition

Alloy steel was chosen as the material

Step 3: Meshing

Then meshed model is shown in fig 1.3 and mesh details in fig 1.4. The element size was 9.9862mm and total number of nodes were 11496. Optimum mesh size is chosen by finding at what size the result converges.

Figure 1.3 Meshed Model and Boundary conditions

Figure 1.4 Meshed Model

Step 4: Boundary conditions

The shorter left side of the model was given fixed constraint and a 1000N force is applied on the other side in shuch a way that the plate stretches as shown in fig 1.3

Step 5: Post Processing

The stress plot is shown in fig 1.5 and the maximum stress is 1.178x10^6 Pa which is well below the yield stress.

Figure 1.5 Stress Plot

The displacement plot is shown in fig 1.6 and the maximum displacement is 5.237x10^-4mm

Figure 1.6 Displacement Plot

The strain plot is shown in fig 1.7

Figure 1.7 Strain Plot

CASE 2 PLATE WITH MULTIPLE HOLES

Step 1: Creating a 3 D Model

The sketch was created using the folowing dimensions

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

Two holes of 30 mm diameter which are placed 90mm away from the central hole on both sides.

The sketch is shown in fig 1.8 and the sketch is extruded 30mm to get the 3D model as shown in Fig 1.9

Figure 1.8 Sketch

Figure 1.9 3 D Model

Step 2: Material Definition

Alloy steel was chosen as the material

Step 3: Meshing

The meshed model is shown in fig 1.10.Element size was 9.84mm and total nodes=11306 as shown in fig 1.11.

Figure 1.10 Meshed Model and Boundary conditions

Figure 1.11 Mesh Details

Step 4: Boundary conditions

The shorter left side of the model was given fixed constraint and a 1000N force is applied on the other side in shuch a way that the plate stretches as shown in fig 1.10

Step 5: Post Processing

The stress plot is shown in fig 1.12 and the maximum stress is 1.136178x10^6 Pa which is well below the yield stress.

Figure 1.12 Stress Plot

The displacement plot is shown in fig 1.13 and the maximum displacement is 5.658x10^-4mm

Figure 1.13 Displacement Plot

The strain plot is shown in fig 1.14

Figure 1.14 Strain Plot

COMPARISIONBETWEEN CASE 1 AND CASE 2

Table 1.1

	CASE 1	CASE 2
Stress (Pa)	1.178x106	1.136178x106
Displacement (mm)	5.237x10-4	5.658x10-4
Strain	4.279 x 10-6	4.057x 10-6

Figure 1.15 Stress comparison

Figure 1.16 Displacement comparison

Figure 1.17 Strain comparison

CONCLUSION

From the comparision in fig 1.15,1.16,1.17 it is found out that the maximum stress occurs near the hole and the case 2 has lower von Mises stress value of 1.136178x10^6 Pa. Hence plate with multiple hole is selected considering analysis standpoint.It is found that higher displacement for case 2 and strain is higher for case 1.