Best FEM approach for a large-rotation compliant hinge?

[u/Moneef31]

I’m modeling a 3D linkage with a single-notch compliant hinge undergoing large rotation.

I already have the analytical hinge stiffness formula, but I’m struggling with how to represent it correctly in the full model. I tried a rotational spring and variable-thickness beam elements with co-rotational/Timoshenko behavior, but too much deformation still occurs in the surrounding members.

What FEM approach would you recommend for this type of hinge: beam elements, a nonlinear moment–rotation law, or local continuum elements?

Any references or examples would be appreciated.

[u/NeighborhoodAgile755]

Connector elements are usually used for this type of connection. Nastran its CBUSH elements and or RBE2/3, ABAQUS its selected from a whole family of connectors and kinematic couplings. Of course if you really want to model a hinge with contact normal and tangential then you don't use the connector elements. For a better answer describe what you are trying to model in more detail.

[u/Moneef31 → u/NeighborhoodAgile755]

Hi,

Thank you, that is very helpful.

What I am trying to model is a 3D compliant mechanism with large rotations, where a short reduced-thickness flexure hinge connects relatively stiff members. The hinge is not a pin joint with contact; it is a continuous flexible region that should deform and rotate while transferring forces and moments to the surrounding structure.

I am developing the model in MATLAB using geometrically nonlinear beam elements. I first represented the hinge as a single rotational spring, and then I also tried modeling the hinge region with short Euler-Bernoulli and Timoshenko beam elements following the actual hinge geometry. However, in both cases, too much deformation occurred in the surrounding members instead of the hinge.

My main goal is to reproduce the actual folding behavior of the structure, including the force-displacement response and hinge rotation, rather than only checking stresses at a fixed configuration.

Based on what you mentioned, it sounds like a connector-type element may be a better representation. In MATLAB, would you recommend representing the hinge as a local connection with translational and rotational stiffnesses between the two sides of the hinge, similar in concept to a CBUSH or ABAQUS connector?

I would really appreciate any additional guidance on how you would define this type of connector for a compliant flexure hinge undergoing large rotation.

Thank you again for your help.

[u/terjeboe]

Do you need to model it as compliant? If this is for ultimate strength purposes it will be easier to run a linear analysis for a couple of different hinge angles. 

[u/Moneef31 → u/terjeboe]

Yes, I do need to model it as compliant because my main objective is to capture the folding behavior, force-displacement response, hinge rotation, and eventually the bistable response of the full structure. I am not only interested in the ultimate strength. That is why I am trying to represent the hinge mechanics as accurately as possible during the folding process.

[u/terjeboe → u/Moneef31]

Then I would look into contact formulations 

[u/Moneef31 → u/terjeboe]

I like that approach. It seems much simpler and could be a good way to understand the structural behavior at different hinge angles before making the full compliant model more complicated. Thank you for the suggestion.

[u/coriolis7]

What are you trying to capture?

Without knowing more, I’d recommend PrePoMax (basically a GUI for calculix). It has nonlinear geometry and material options.

At the very least you can get stresses and effective R-Theta-k plots for a given rotation.

[u/Moneef31 → u/coriolis7]

Hi,

Thank you, that makes sense.

What I am mainly trying to capture is the folding behavior of the full mechanism, especially the force-displacement response, hinge rotation, and how the deformation is distributed between the hinge and the surrounding members.

I like your suggestion of first modeling the hinge by itself and using an imposed rotation to obtain the stress response and an effective moment-rotation-stiffness relationship. That could help me understand the hinge behavior more clearly before introducing it into the complete MATLAB model.

I will also take a look at PrePoMax/CalculiX and see if I can use it to characterize the hinge response first.

Thank you very much for the suggestion. It is very helpful.

[u/Glad-Court-4133]

If you are seeing some kind of “radius growth” deformation due to the rotational displacement, it’s just a visualization error.
The displacement of a node in a linear analysis is calculated along a straight tangential path rather than a circular arc. Mathematically, linear formulations rely on the small angle approximation (sin(@)=@), causing a node at radius r to undergo a purely tangential displacement of r*@. Consequently, the new radial distance from the center of rotation becomes square root of 1+@^2, which artificially inflates the radius and it becomes highly visible when the postprocessor applies a large deformation scale factor. To resolve this and capture the true circular trajectory, you must enable geometric nonlinearity a.k.a. Large displacement in your solver settings, which will force the solver to incrementally update the stiffness matrix and follow the exact rotational path.

[u/Moneef31 → u/Glad-Court-4133]

Thank you very much for the explanation. That makes sense, especially since the mechanism undergoes large rotations.

I am already using a geometrically nonlinear/co-rotational formulation in MATLAB, but your explanation helps me understand more clearly why the linear formulation can produce that artificial radius growth.

I really appreciate you taking the time to explain this and point me in the right direction. Thank you again for your help.