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# What would be the right way to model rigid body motion in FEM?

## What would be the right way to model rigid body motion in FEM?

(OP)
Dear all,

I'm just starting off in the field of FEM. Please bear with me if this is a bad question. I'm curious how do we model rigid body motion in FEM.

The first way I can think of is to discard the stiffness term totally (set stiffness matrix to 0). That way, the equation of motion becomes F = Ma.

Another way is to set young's modulus to an infinite value, although that is not realistic.

However, setting the stiffness matrix to 0 and letting young's modulus increase to infinite seems to be controversial to each other. Increasing stiffness would increase the oscillating frequency. But dropping the stiffness term would not increase the oscillation of the structure. I'm not sure if I've missed something on that problem.

Thanks!

### RE: What would be the right way to model rigid body motion in FEM?

Setting stiffness to 0 would prevent forces being transmitted between any nodes. So only the nodes that you apply a load to would move.

You could use a high stiffness so that vibration frequencies are too high to appear with whatever solution method you're using.

A more elegant way would be using constraint equations to connect the DOFs without using stiffness. That'll allow you to eliminate redundant DOFs the system of equations to leave only the rigid body DOFs. I think this is what RBE2 in Nastran does.

### RE: What would be the right way to model rigid body motion in FEM?

(OP)
Thank you very much whitwas! Your explanation is very clear and helpful.

### RE: What would be the right way to model rigid body motion in FEM?

I think you need to use a mechanism simulation software, like Adams. I think the problem will be in writing equations that correctly describe the motion of the different parts.

### RE: What would be the right way to model rigid body motion in FEM?

Rigid bodies have infinite stiffness terms for the degrees of freedom which are attached to the rigid body and move with it and zero stiffness terms between the degrees of freedom moving with the body and the stationary degrees of freedom (fixed to the ground).

Best regards,

George Papazafeiropoulos

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