# Exercise 1: Model Cantilever Beam Bending

In this exercise, you will model a 1m long cantilever beam with a cross-section dimension of 110mmx14mm to perform a bending test and compare it with an analytical solution.

Before you begin, copy the centerline.csv file, located in the mbd_modeling\nlfe\intro folder, to your <working directory>.

## Model a Beam with Linear Elastic Material

In this step, you will model the cantilever beam with linear elastic material.

1. Start a new MotionView session.
2. On the Reference toolbar, right-click on the (Body) icon.
3. In the Add Body or BodyPair dialog, specify the Label as Cantilever Beam and the variable name as nlfeb_cantilever.
4. In the drop-down menu, click NLFE Body. Then click OK.
This will display the NLFE Body with the Properties tab active.
Note: Table 1 shows the various tabs available in the NLFE Body panel.
Table 1.
Tab name Sets NLFEBody
Properties Type (Beam/Cable), Cross-section, and materialproperties
Connectivity Center line data or body profile
Orientation Start and End orientations
Mass Properties Displayed for information only
Initial Conditions Initial velocities
5. Configure the Properties tab.
1. For Type, choose Beam.
2. For Cross section: choose Bar.
3. For dim1, enter 14.0.
4. For dim2, enter 110.0.
The panel also displays the image of the cross-section indicating what the different dimensions (dim1 and dim2) refer to.
Note: The Properties tab has two sub-tabs called Start and End. These sub-tabs are used to set the dimensions at two different ends of the beam. By default, the End dimensions are parametrically equated to the Start dimensions. If a different set of dimensions are provided at the start and end, the cross section varies linearly along the length of the beam.
6. Click the End sub-tab and review dim1 and dim2.
7. Click the Manage Materials button to display the Material Properties dialog.
Tip: You can also access the Material Properties dialog from the Model menu.

MotionSolve provides a list of commonly used Linear Elastic, as well as Hyper Elastic material by default.

8. On the Materials list, choose Steel.
9. Review the property values and notice that the Elastic line check box for Approach is selected.
10. Then click Close to close the dialog.
The default standard materials provided are defined with the Elastic Line option checked on. Materials without the Elastic Line are solved using the continuous mechanics approach, where in the cross-section deformation is taken into consideration. The Elastic Line approach ignores cross-section deformation effects, which gives results closer to an analytical solution.
11. In the Connectivity tab, define the beam centerline by importing point data from a CSV file. Click the Import Points button.
The Import Points From Coordinates In File dialog appears.
12. Browse to your <working directory> and choose the centerline.csv file. Then click OK to import the points.
The .csv file must be in the following format: the first column must hold the X-coordinates, the second column the Y-coordinates, and the third column the Z-coordinates. There can also be a header row that begins with a # indicating a commented line.
13. Press the 'F' key on your keyboard to fit the newly created NLFE Body model to the modeling window.
14. Click on the Orientation tab and review the Start and End orientations.
Note: You can use the Orientation tab to set the cross section orientation (YZ plane of the beam). Use the XY Plane or XZ Plane option to position the Y or the Z-axis (the remaining axis will be positioned so that it is orthonormal to the remaining two axes).

For this exercise, use the default orientations.

Intermediate Beam elements orientation is linearly varied from Start orientation to End orientation. The Orientation option is useful in defining twist along the beam length.

15. Click the Mass Properties tab to review the calculated values.
16. Click the Initial Conditions tab to review the NLFEBody initial velocities.
Leave initial velocities equal to zero.

## Add a Constraint and Force

In this step, you will add a constraint and a force to the cantilever beam model.

1. Create a fixed joint at the beam origin point (Point_1) using the specifics shows in Table 2:
Table 2.
S. No Label Variable Name Type Body 1 Body 2 Origin(s) Orientation Method Reference 1 Reference 2
1 Fix Joint j_fix Fixed Joint Cantilever Beam Ground Body Point_1
Note:

Each grid on an NLFE body has 12 DOFs: 3 translational, 3 rotational, and 6 related to the length and angle between the gradient vectors. Using a fixed joint constrains the positions of the grid and the rigid body rotations. However, the gradients at the grid are free. This means that the cross-section at the fixed joint can twist about the grid and also deform based on Poisson’s ratio. To arrest these DOFs, an NLFE element called “CONN0” can be used.

There is no graphical user interface support for creating this constraint. By default, MotionView creates a CONN0 element at all of those grids of the NLFE body through which it is attached to a constraint/force entity.

2. Create a load at the cantilever beam end point (Point_11) using the specifics shown in Table 3:
Table 3.
S. No Label Variable Force Properties Action force on Apply force at Ref. Marker
1 Load frc_load Action only Scalar Force along Z axis of Ref Frame Cantilever Beam Point_11 Global Frame
3. From the Trans Properties tab, specify the expression for force as  -1000*time.
Note: Negative value is specified to apply load along negative Z-axis direction.
4. Turn off gravity to eliminate deflection due to beam self-weight.

## Create Outputs

In this step you will create outputs to measure cantilever beam end deflection.

Cantilever beam end deflection from linear-elasticity theory:

Deflection for load applied at end =

Where,

= Beam length = 1000mm

= Youngs Modulus = 2.1e+05 N/mm2

= Second Moment of Area = = 114 * = 25153.33mm4

1. Right-click the (Outputs) button.
2. In the dialog, specify a label of Deflection - Analytical (F2), NLFE(F3). Then click OK.
3. In the panel, specify the Type as Expressions.
4. In F2, enter -1*SFORCE({frc_load.idstring},0,1,0)*1000^3/(3*2.1e5*25153.33333). For F3, enter {frc_load.DZ}.
5. Click the (Check Model) button to check the model for errors.
This will measure the magnitude of the applied load.
7. Click and save the model as nlfe_cantilever.mdl.

## Solve and Post-Process the Model

Now you will solve the model with MotionSolve and view the results.

1. Click the (Run) panel icon.
2. Specify the MotionSolve file name as Cantilever_beam.xml.
3. Specify the Simulation type as Quasi-static, the End time as 1 second, and the Print interval as 0.01.
4. Click the Run button.
5. After the simulation is complete, click the Animate button to view the animation in HyperView.
You can use the (Start/Pause Animation) button to play the animation.
6. In the MotionView Run panel, click Plot to load the .abf file in HyperGraph.
7. Plot Deflection versus Load calculated from linear elasticity theory and NLFE by selecting the data from Table 4 and Table 5 in HyperGraph.
Table 4.
X-axis Data
X Type Marker Force
X Request REQ/70000001 Load - (on Cantilever Beam)
X Component FZ
Table 5.
Y-axis data
Y Type Expression
Y Request REQ/70000000 Deflection - Analytical (F2), NLFE (F3)
Y Component F2 & F3
8. Click the (Define Curves) icon.
9. In the panel, rename the two curves Analytical and NLFE.
From the plot (shown in Figure 21), you can see that the two curves almost overlap.
10. Click inside the HyperView animation window to make it the active window.
11. Click the (Contour) button to activate the Contour panel.
12. Under Result type, select NLFE Stress (t) and XX.
13. Click Apply.
This will show you the bending stress contours plot.
Note: You can also view Displacement, Strain, etc. for an NLFE body in HyperView. All FE contours and types are available in HyperView for an NLFE body.
14. Click and save the session as nlfe_cantilever.mvw.