Author: Benjamin Mullen, Cornell University

Problem Specification

1. Pre-Analysis & Start-Up

2. Geometry

3. Mesh

4. Physics Setup

5. Numerical Solution

6. Numerical Results

7. Verification & Validation

Exercises

Comments

# Numerical Solution

Now we are ready to choose what kind of results we would like to see.

### Deformation

To add deformation to the solution, first click ** Solution** to add the solution sub menu to menu bar

Now in the solution sub menu click ** Deformation > Total** to add the total deformation to the solution. It should appear in the outline tree.

### Normal Stresses

#### Sigma_xx

To add the normal stress in the x-direction, in the solution sub menu go to ** Stress > Normal**. In the details view window ensure that the

**is set to**

*Orientation***. Let's rename the stress to**

*X Axis*`Stress_xx`

by right clicking the stress, and going to rename.#### Sigma_r

To add the polar stresses, we need to first define a polar coordinate system. In the outline tree, right click ** Coordinate System > Insert > Coordinate System**.

This will create a new Cartesian Coordinate System. To make the new coordinate system a polar one, look to the details view and change the ** Type** Parameter from Cartesian to Cylindrical. To define the origin, change the

**parameter from Geometry to Global Coordinate System. Put the origin coincident with the global coordinate systems origin (x = 0, y = 0). Now that the polar coordinates have been created, lets rename the coordinate system to make it more distinguishable. Right click on the coordinate system you just created, and go to**

*Define By***. For simplicity sake, let's just name it**

*Rename*`Polar Coordinates`

.Now, we can define the radial stress using the new coordinate system. Click ** Solution > Stress > Normal**. This will create "Normal Stress 2", and list its parameters in the details view. We want to change the coordinate system to the polar one we just created; so in the details view window, change the

**parameter from "Global Coordinate System" to "Polar Coordinates". Ensure that the orientation is set to the x-axis, as defined by our polar coordinate system. Now the stress is ready. Let's rename it to**

*Coordinate System*`Sigma_r`

and keep going.#### Sigma_theta

Now let's add the theta stress. This is too a normal stress, so create a new normal stress as you did for Sigma_xx and Sigma_r. Now, change the coordinate system to Polar Coordinates, as you did for Sigma-r. Next, change the Orientation to the Y axis. The Y axis should be in the theta direction by default. Rename the stress to `Sigma_theta`

.

#### Tau_r-theta

Finally, let's add the shear stress in the r-theta direction. To do this, we go to ** Solution > Stress > Shear**. You'll notice that now, in the details view window, the stress needs two directions to define it. In order to solve for the r-theta shear, we need to change the

**parameter from the Global Coordinate System to Polar Coordinates. Also, ensure that the Orientation is in the XY direction (in polar, this will be r_theta by the coordinate system we created). Rename the stress to**

*Coordinate System*`Tau_r-theta`

.This is what your outline tree should look like at this point:

#### Solve!

To solve for the stresses and deformation, we now hit the solve button.

Keep going! Almost done!