Remove rigid body motions from FEM simulations

[Eric Yao]

Dear all,

I have a question about ways to remove rigid body motions from FEM simulations without fixing nodes in Chrono FEA.

I am interested in simulating the bending behaviors of a flat sheet of material (acrylic, etc). In the real world, I can bend the sheet with my hands on both of its side, like in this illustration. I would like to replicate this with FEM (using tetrahedrons). Since no parts of the sheet is fixed physically, I would like to avoid fixing the nodes in FEM as well.

Without any fixed nodes in FEM, the sheet being bent will move freely in space. To remove rigid motion from the simulated deformation, one method is to project the deformation vector onto the column space of the system-wide stiffness matrix. This works because rigid motions lie in the null space of the stiffness matrix. I have tried this method in my own simple co-rotational FEM code and I have successfully removed rigid motions.

Before trying to code up this method in the Chrono source code, I was wondering if you guys have any tips or pointers on how to remove rigid motions. Perhaps there is a built-in method that I missed. I'd really appriciate any help and feedback!

Thanks so much,

Eric