Bending of a cantilever beam

What you’ll learn

• How to create a simple box geometry and define its dimensions in the Allsolve geometry editor.
• How to assign materials, define regions, and apply clamp and load boundary conditions for solid mechanics.
• How to generate a mesh, run a static structural analysis, and visualize deformed results with the Warp filter.

In this tutorial, the bending of a cantilever beam is simulated.

A cantilever is a rigid structure that extends horizontally and is unsupported at one end ¹. It is widely used in construction and serves as a baseline simulation for structural mechanics.

Model definition

The model comprises a small aluminium beam built from a single box element. The beam is clamped from one of its end surfaces, and extends horizontally like a flagpole attached to a wall.

A load is evenly applied to the top surface of the beam, bending it downwards. The maximum Z-displacement is solved during simulation.

Model geometry

Name	Element type	XYZ dimensions [mm]
Cantilever beam	Box	24 x 2 x 3

Material Data

Aluminium

Property	Value
Poisson’s ratio	0.32
Young’s modulus [Pa]	68e9

Boundary conditions

Name	Target	Type	Value [X, Y, Z]
clamp	left X-plane	Clamp	[0, 0, 0]
load	top Z-plane	Load [N]	[0, 0, -1000]

Output Results

Maximum Z-displacement.

Step-by-step guide

Below, you’ll find a detailed step-by-step tutorial on how to set up a cantilever beam simulation in Quanscient Allsolve.

Step 1 - Build the geometry

1. Start with a new project and name it Cantilever beam.

2. Start out with a box element. A 1 x 1 x 1 m box is built by default.

3. Edit the size of the box in settings:

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   box	Box	X: 0	X: 24e-3	X: 0
   		Y: 0	Y: 2e-3	Y: 0
   		Z: 0	Z: 3e-3	Z: 0

4. Rebuild the box with correct dimensions.

5. Confirm model changes before moving on.

Step 2 - Define regions

1. Go to the Common sidebar.

2. Define regions:

   Name	Region type	Target
   clamp	Surface	X direction bottom surface
   top	Surface	Z direction top surface.

Step 3 - Define the material

1. Go to the Physics section.

2. Add the predefined Aluminium material from the library. Assign it to the beam volume.

Step 4 - Define physics & boundary conditions

1. Add the Solid mechanics physics to Physics set 1.

   There is no need to select a target for solid mechanics, as it will default to the whole geometry.

   Physics	Target
   Solid mechanics	Beam volume (default)

2. Add a Clamp interaction to Solid mechanics.

   This boundary condition constrains all components of the displacement vector in the target region to zero displacement: $u_x = 0$, $u_y = 0$, $u_z = 0$.

   Name	Interaction type	Target
   Clamp	Clamp	clamp region

3. Add a Load interaction to Solid mechanics.

   Name	Interaction type	Target	Value [X; Y; Z]
   Load	Load	top region	[0; 0; -1000]

   

Step 5 - Generate the mesh

1. Go to the Simulations section.

2. Generate a new mesh with default settings.

3. Select Default mesh to open a preview of the mesh in the model view.

Step 6 - Apply simulation settings & run

1. Create a new simulation.

2. Set Analysis Type to Static.

3. Select the mesh you generated as the mesh for your simulation.

4. Add the displacement field output u.

5. Run the simulation.

Step 7 - Visualize results

1. Add a visualization for the u field.

2. Add Warp to the visualization and activate it.

3. Click Refresh next to Warp scale factor. Refreshing sets scale factor automatically to a reasonable number, in order to see the warping clearly.

4. Render the deformed geometry scaled up according to scale factor.

   

   Here, the scale factor is set to 10000.

References

Footnotes

1. https://en.wikipedia.org/wiki/Cantilever ↩