Pre-Analysis & Start-Up — Lesson 2

Ansys Student software can be downloaded for free here.

Pre-Analysis

There are three different theories for finding the solution for the bending of a curved beam. There is elasticity theory, where

$\sigma_r = (\frac{4M}{tb^2N})[(1 - \frac{a^2}{b^2}\ln(\frac{r}{a}) - (1 - \frac{a^2}{b^2})\ln(\frac{b}{a})]$

and

$\sigma_\theta = (\frac{4M}{tb^2N})[(1 - \frac{a^2}{b^2})(1 + \ln(\frac{r}{a})) - (1 + \frac{a^2}{r^2})\ln(\frac{b}{a})]$

where

$N = (1 - \frac{a^2}{b^2})^2 - 4(\frac{a^2}{b^2})\ln^2(\frac{b}{a})$

There is Winkler-Bach Theory, where

$\sigma_x = \frac{M}{AR}[1 + \frac{y}{Z(R + y)}]$

where

$Z = -1 + \frac{R}{h}\ln[(R + \frac{h}{2}) / (R - \frac{h}{2})]$

And there is the straight beam theory, where

$\sigma_x = \frac{My}{I}$

Start-up

1. Now, let's load the problem into Ansys Mechanical and see how a computer simulation will compare. First, start by downloading the files here
The zip file should have the following contents:

• Curved Beam Solution_files folder
• Curved Beam Solution.wbpj

Please make sure to extract both of these files from the zip folder; the program will not work otherwise.

2. Double click "Curved Beam Solution.wbpj," which should automatically open Ansys Workbench (you have to twiddle your thumbs a bit before it opens up). You will be presented with the Ansys solution.

A tick mark against each step indicates that that step has been completed.

3. To look at the results, double click on "Results." This should bring up a new window (again you have to twiddle your thumbs a bit before it opens up).

4. On the left-hand side there should be an "Outline" toolbar. Look for "Solution (A6)."

We'll investigate the items listed under Solution in the next step in this tutorial.