Page History

{include: ANSYS 12 - Tensile Bar - Panel}

h4. Pre-analysis and start-up


h6. Analytical Approach:

Assuming plane stresses:

The two dimensional equilibrium equations are:
\\
{latex}
\begin{eqnarray}
{\partial \sigma_x \over \partial x} + {\partial \tau_{yx} \over \partial y} + F_x = 0 \nonumber\\
{\partial \tau_{xy} \over \partial x} + {\partial \sigma_y \over \partial y} + F_y = 0 \nonumber
\end{eqnarray}
{latex}

\\
Since we are ignoring the effects of gravity; there are no body forces per unit volume.

{latex}
\begin{eqnarray}
F_x = F_y =0\nonumber
\end{eqnarray}
{latex}

Assuming no normal stress in the y direction://
{latex}
\begin{eqnarray}
\sigma_y = 0\nonumber
\end{eqnarray} 
{latex}

The two dimensional equilibrium equations are:
\\
{latex}
\begin{eqnarray}
{\partial \sigma_x \over \partial x} + {\partial \tau_{yx} \over \partial y} + F_x = 0 \nonumber\\
{\partial \tau_{xy} \over \partial x} + {\partial \sigma_y \over \partial y} + F_y = 0 \nonumber
\end{eqnarray}
{latex}

\\
Since we are ignoring the effects of gravity; there are no body forces per unit volume.

{latex}
\begin{eqnarray}
F_x = F_y =0\nonumber
\end{eqnarray}
{latex}

Assuming no normal stress in the y direction://
{latex}
\begin{eqnarray}
\sigma_y = 0\nonumber
\end{eqnarray} 
{latex}

 The equilibrium equation in the y direction becomes:

{latex}
\begin{eqnarray}
{\partial \tau_{xy} \over \partial x} = 0\nonumber
\end{eqnarray}
{latex}

τ_yx must also be a constant, therefore the equilibrium equation in the x-direction becomes:

{latex}
\begin{eqnarray}
{\partial \sigma_x \over \partial x} = 0\nonumber
\end{eqnarray} 
{latex}

Therefore;
\\  {latex}
\begin{eqnarray}
\sigma_x = constant\nonumber
\end{eqnarray} 
{latex}

Apply Boundary Conditions:

If we make a cut at "A", as indicated in the problem specification, then the stress in A must be P/A.

Therefore, !tut1 eqn4.jpg!\\

h6.  ANSYS simulation:

 Open and start the simulation:

The idea of this exercise is to allows you to gain understanding into the difference between analytical solution and numerical solution (ANSYS simulation). Therefore, in this case we have bypassed creation of geometry, mesh and solution and skipped ahead to the results. 

1. Download "Class demo1.rar"

2. Unrar the file

3. Open the folderzip" by [clicking here|^Class demo1.zip]
   The zip should contain:
         class demo1 folder
               class demo 1_files folder
               class demo 1.wbpj
   Please make sure both the files and wbpj are in the folder, the program would not work otherwise.   (Note: The solution was created using ANSYS workbench 12.0 release, there may be compatibility issues when opened with other versions)

4. Double click "Class Demo1.wbpj"

5. Follow further instructions from lab supervisor. 


\\

[*Go to Results*|ANSYS 12 - Tensile Bar - Results]

[See and rate the complete Learning Module|ANSYS 12 - Tensile Bar - Problem Specification]

[Go to all ANSYS Learning Modules|ANSYS Learning Modules]