Learning Forum

[Alessandro Agostinelli]

Hi, 

I'm trying to find the compliance factors of a curved beam flexure. The geometry is a simple curved beam (R=30mm, angle=45°) with a rectangular shape section (w=6 mm,t=1.2mm), like that:

I fixed one end and applied the force vector components (one by one) at the other one; then, I measured the displacements/rotations at the free end and divide displacement by force (or rotation by moment) to obtain the compliance factors, but I dind't get the correct results.

The correct compliance factors are analitically calculated (m/N or rad/Nm) compared to coordinate system "g" fixed at free end (like in previous picture, where x_g is red and z_g is green):

How can I do to obtain the same results with a FEA?

 

[peteroznewman]

Can you calculate the correct analytic compliance factors for a straight cantilever beam? If so, please show an example.

[Alessandro Agostinelli]

Hi,

To calculate compliance factors for a straight cantilver beam you have to apply the components of force vector (one by one) at the free end constraining all the others DOFs. For ex., to measure compliance factor Fy - y:

 

The boundaries conditions are: fixed support at one end and sliding climp at other one. Solving the equation of the elastic curve of a beam, you can find the relationship between Fy and y (stiffness Fy/y, compliance y/Fy..)

[peteroznewman]

You are describing what I call a stiffness matrix. The lower left end of the shell mesh is a Fixed Support. I displace the right end with a Remote Displacement, Behavior = Rigid, keeping all other DOF = 0 except for the one unit value.

I will skip the other three load cases. In each case, I Probe the Force and Moment Reactions of the Remote Displacement.

This is a stiffness matrix.  The inverse of this is the compliance matrix. This is for your geometry using Structural Steel.

Note that Finite Element Models are an approximate solution. Better approximations are obtained when the mesh is refined.

This model gives results that are closer to the expected zero values for the moments about X and Y.

[Alessandro Agostinelli]

Thank you for the answer, but unfortunately I still need your help. I tried to calculate and invert the stiffness matrix for my curved beam (volume solid) in the same way you did but I didn't get the correct results. 

1. It's better create a CAD solid, a line body or a surface body for this type of problem? I used a CAD file, but I don't if it's correct?

2. I used shell elements..How can I choose shell mesh? It's only for Surface Bodies, it isn't..? 

3. In the case you used volume solid, could be helpful the option "Beam Flexible" in Definition of the body?

4. I put Large Deflection On (because it's a "compliant part"), is it correct?

[Alessandro Agostinelli]

Sorry..

* 2. You used shell elements..

[peteroznewman]

1. I used SpaceClaim to draw an arc, then extruded that into a sheet body with a width of 6 mm.
2. That sheet body was meshed with shell elements and assigned a thickness of 1.2 mm.
3. If I had used solid elements, a minimum of 4 elements through the thickness is required if using linear elements.
4. Don't use Large Deflection. You want the stiffness/compliance for small displacements/rotations from the undeformed geometry.

[peteroznewman]

The Young's Modulus I used was 2e+11 Pa.  What Young's Modulus was used for the Analytic values you showed?

[Alessandro Agostinelli]

The Young's Modulus is 3 GPa and Poisson's Ratio is 0,33 (is an Acrylic Plastic)

[Alessandro Agostinelli]

I tried any way to obtain the correct results but I get only the compliance factors for y-Fy and thetaX-mX (where y is collinear with beam axis at free end)

I tried to improve mesh, and I used sheet, line or volume bodies but in every case I didn't solve the problem..it seems very easy but I don't get something

[Peter Newmann]

Drag a new Static Structural out of the toolbox and drop it onto the Model cell of your first Static Structural analysis. Repeat this 4 times.

Open Mechanical from the A4 Model cell. Drag and drop the Fixed Support and Remote Displacement on every Static Strucural analysis, and edit each of the five Remote Displacements to move the unit displacement down the list of DOF.

What version of Ansys are you using Year and R#?

[Alessandro Agostinelli]

I'm using Ansys 2023, R1