# Parametric Structural Mechanics Study with Imported CAD Geometry

This tutorial builds on and continues the previous CAD and Gmsh file import and mesh generation tutorial. A parametric deformation and stress analysis of the imported fixed wrench and spanner CAD model will be performed with a number of different load configuration cases. The following five steps are all that is required to set up and solve this structural mechanics deformation example in FEATool using both the Octave and Matlab GUI as well as the command line interface (CLI).

## 1. New Model and Grid Import from External File

Having the previously generated Gmsh grid, the first step is to start
a new 3D model with the **Linear Elasticity** physics mode
selected. As an external grid will be imported it is not necessary to
create a geometry (FEATool geometries are only used by the built-in
*gridgen* function for meshing and grid generation).

Switch to **Grid** mode and import the spanner.msh Gmsh grid file (*click on the link to
download*) into the FEATool GUI by selecting the ```
Import Grid >
Gmsh Format
```

option found in the `Grid`

menu.

## 2. Equation Settings

Switching to **Equation** mode automatically opens the **Equation
Settings** dialog box. There the material parameters can be
prescribed, in this case a Poisson ratio of *0.29*, and modulus of
elasticity of *190e3 N/mm* is used, which corresponds to tool
chromium-vanadium grade steel alloy (scaled to *mm* units since the
geometry is given in *millimeters*, to convert to *meter* units one can
scale the grid vertex coordinates as ```
fea.grid.p =
fea.grid.p*1e-3;
```

).

## 3. Boundary Conditions

Switch to **Boundary** mode to prescribe loads and
displacements. First, select all boundaries in the **Boundary
Settings** dialog box, prescribe zero *Edge loads* in all directions,
and press **Apply**. This will set all boundaries free by default (the
*Ctrl+a* key combination can be used to select all items in list
selection boxes such as for geometry objects, boundaries, and
subdomains).

For this model the flat surfaces at the front fork are assumed to be
fixed (by wrapping around an fixed and immobile bolt). To do this
select boundaries *11* and *14*, and choose fixed displacement
conditions in all directions.

Lastly, select boundary *1* and enter the force expression
**-1000/(6*80)*(y>140)** for the *Edge load, x-dir.* to
apply a pulling force of *1000 N* over an area of *6*80 mm* at the top
half of the handle (*y > 140 mm*). Here the switch expression *y>140*
will evaluate to *1* if true and *0* if false, and in this way it is
possible to localize and activate equation and boundary coefficients
without having separate discrete boundaries or subdomains.

## 4. Solution and Postprocessing

To solve the model change to **Solve** mode and press the
`=`

button. After the solution has been computed FEATool
switches to **Postprocessing** mode and displays the default solution
plot. Open the **Postprocessing Settings** dialog box and choose
**Surface Plot** with the **Total Displacement** as surface
expression. As can be seen below the maximum displacement in this case
is about *2.5 mm* towards the ring end of the wrench.

## 5. Parametric Study

In order to perform a parametric study, the model can be saved as a
Matlab m-file script using the `Save As M-Script Model…`

option found in the `File`

menu. The script can be opened
and edited in a text editor.

In the following the model has been set up and changed to shift the
load from the strong in-plane x-direction to the weaker lateral
z-direction by introducing the parameter *frac*. For postprocessing a
deformed grid will be computed and displayed.

```
% Fraction of lateral to inline force distribution 0..1
frac = linspace(0,1,200);
% Import Gmsh CAD grid.
fea.sdim = {'x','y','z'};
fea.grid = impexp_gmsh( 'spanner.msh', 'import' );
% Add 3D solid linear elasticity physics mode
% and define material parameters.
fea = addphys( fea, @linearelasticity );
fea.phys.el.eqn.coef{1,end} = { 0.29 };
fea.phys.el.eqn.coef{2,end} = { 190e3 };
% Set all boundaries to no load per default.
n_bdr = max(fea.grid.b(3,:));
bc_sel = cell(3,n_bdr);
[bc_sel{:}] = deal(0);
% Fix all displacements on boundaries 11 and 14.
[bc_sel{:,[11 14]}] = deal(1);
fea.phys.el.bdr.coef{5} = bc_sel;
% Main loop.
fea = parsephys(fea);
fea = parseprob(fea);
for i=1:length(frac)
% Split forces in x/z-directions according to frac.
fea.bdr.n{1}{1} = ['-',num2str((1-frac(i))*1000/(6*80)),'*(y>140)'];
fea.bdr.n{3}{4} = [ num2str( frac(i) *1000/(6*80)),'*(y>140)'];
% Solve problem.
fea.sol.u = solvestat( fea );
% Create fea struct with displaced grid.
dp = zeros(size(fea.grid.p));
for j=1:3
dp(j,:) = 2*evalexpr( fea.dvar{j}, fea.grid.p, fea );
end
fea_disp = fea;
fea_disp.grid.p = fea_disp.grid.p + dp;
% Plot deformed object colored by the total displacement.
clf
postplot( fea_disp, 'surfexpr', 'sqrt(u^2+v^2+w^2)', ...
'colorbar', false, 'linewidth', 0.1 )
view( [-60 20] ), axis off
pause
end
```

After running the parametric script and looking at the results one can
see that the maximum deformation has increased from *2.5 mm* with
in-plane loading to almost *4 cm* with lateral plane
loading. Although, this large deformation most certainly violates the
linear elastic deformation assumption, it is still a useful example
showing how easy and fast it is to define and set up automated
parametric studies with FEATool and Matlab m-file scripts.

The complete parametric structural mechanics study of a fixed spanner, including advanced postprocessing, can be downloaded from the following link (while the actual wrench Gmsh grid file can be downloaded from the link above).