Week 1 Stress Concentration on a Plate with hole

OBJECTIVE

To carry out a static structural analysis on two different steel plates using ANSYS Workbench. The plates are to be created using the software and analysis will be carried out on them. Through the analysis, the maximum deformation and stresses formed in the model are to be derived and compared. Through observation, the better design is to be decided from both an analysis and manufacturing standpoint.

DIMENSIONS OF MODELS TO BE CREATED

Case 1

Case 2

Boundary Conditions

1. The plate is to be fixed on the left face.

2. A load of 500N is to be applied on the right face.

PROCEDURE

The procedure for both cases will be the same so the following is a general procedure of this entire project.

CREATING THE MODEL

1. After opening ANSYS Workbench, we are met with the Project Schematic window. Here, we can select the 'System Structural' analysis system on the left. Doing so creates a new project. Here, we can rename the project and also change the material if needed. The material for this project is Structural Steel and the default was the same so it didn't need changing.

We can go ahead and right-click Geometry > New SpaceClaim Geometry. Doing so takes us to the SpaceClaim window, where we can create our geometry.

2. Here, we can make use of the geometry tools in the top toolbar to create our model.

In this project, the rectangle, circle, and reference line tools are especially important. While using these tools, SpaceClaim lets us set dimensions. We can enter the dimensions while the tool is active. After we have created the 2D image of the model, we can delete the area inside the circle (simply by clicking it and pressing the delete button on the keyboard). The construction lines are required to find the center point of the rectangle where the circle needs to be created. They can be deleted afterward.

3. After that, we can use the 'pull' tool from the same toolbar to extrude the model. As in the previous step, we can specify the dimension here as well. After selecting the tool, we simply need to hover over one of the edges and select the right extrusion axis and drag the edge accordingly. This brings up the dimension box where we can specify the thickness.

Once that's done, we simply need to exit SpaceClaim and return to the Project Schematic window. There, we can right-click 'Model' and click 'Update'.

MESHING THE MODEL

1. Next, we can right-click 'Model' again and click 'Edit'. This takes us to the 'Mechanical' interface where we can edit the mesh, set up boundary conditions and run the analysis. As mentioned, we shall take a look at the mesh.

By default, the algorithm would have meshed the model using hexahedrons and the 2D mesh size would not be ideal. To fix this, we simply need to select the mesh and edit the entity in its window on the bottom left. Going to the 'Defaults' section and change the mesh to a preferable size (the finer the mesh, the more accurate the final results - at the cost of time). We can press 'enter' and then right-click 'Mesh' from the outline and click 'generate'.

2. After doing so, we can then right-click mesh and then select insert > Method. This is where we need to change the mesh type to tetrahedrons. We will need to select the geometry and then click 'apply' for the geometry option. For method, we shall pick 'Tetrahedrons'. After that, we simply right-click 'Mesh' from the Outline and click 'Generate'.

Doing so generates a tetra mesh for the whole model:

SETTING UP AND RUNNING THE ANALYSIS

1. After the mesh is created, we can move on to the Static Structural entity in the Outline. Here, the idea is to create the two conditions that are required in this project - the fixed support and the load application.

2. To create either of them, we need to right-click Structural Support and select each of the options shown in the screenshot. For fixed support, in the geometry option, we are to select the face that is to be fixed and click 'apply'.

For load, a similar process is followed. The opposite face is selected for Geometry and we can click 'apply'. Then, based on the global axes, we can enter the value of force exertion. We need to select 'Components' for the 'Define By' option so the entire model is considered when the force is applied.

Then, we can enter the magnitude of force to be applied as per the axes in the project. As we can see here, with the fixed end on the left, the force will be applied from the right, in the direction of the positive X-axis. Therefore, we can enter a positive value for X Component. As per requirement, the value would be 500N.

We can then right-click 'Solution' from the Outline and click 'Solve'.

3. Now we can generate the output. To do this, we can right-click Solution again > Insert > Deformation > Total (for maximum deformation) and again, right-click Solution > Insert > Stress > Equivalent (Von-Mises) (for stress). This creates two new entries in the tree below 'Solution'.

Now, all we need to do is right-click solution again and click 'Evaluate all results'.

4. This runs the analysis as per the required outputs. When it's done, we can view the results by simply clicking each of these solution entities we created, in the Outline menu.

OUTPUTS

In each case, there is a force of 500N on the right face with the left face fixed. Each screenshot also shows the absolute maximum and minimum values generated in each case.

CASE 1

Deformation

Stress

CASE 2

Deformation

Stress

OBSERVATIONS

For the plate with a single hole, the maximum stress generated was 0.24191 MPa and the average stress was 0.0136 MPa. Compared to the plate with 3 holes in case 2 (Max Stress: 0.18481 MPa & Avg. Stress: 0.00948 MPa), the plate in case 1 had higher stress concentration values.

The lower values in case 2 are due to the additional holes helping prevent the accumulation of stress around the center hole. Stress concentrations occur at sections where the cross-sectional area changes abruptly. The more severe the change, the larger the stress concentration.

This is taken care of by the additional holes since one of the smaller holes would be in the path of the load propagation. This reduction in abruptness helps reduce the stress concentration generated in case 2.

RESULT

Structural analysis was carried out on the plates that were created as per required dimensions and features. Each of these plates was analyzed for their stress and deformation values. It was established that the plate with a single hole had higher stress values due to higher stress concentration as a result of its geometry.

From an analysis standpoint, the plate in case 2 would be the preferred choice due to the alleviation of stresses as a result of better stress distribution with the addition of holes in the geometry. As a result, there is lower stress concentration in the model making it a better option.

From a manufacturing standpoint, the plate in case 1 would be preferred due to a couple of major factors in the manufacturing process - time and material wastage. Manufacturing the second plate (with 2 additional holes) will require more time and as a result, it can increase costs. In addition to that, there is additional material being wasted in case 2 (compared to case 1), with the creation of extra holes.