# Implementation of the roller constraint

What could be the best way to implement the roller constraint in finite element code, i.e. constraint of the type

$$\mathbf{u} \cdot \mathbf{n} = 0$$

I plan to enforce it in the weak sense by incorporating

$$\int_\Gamma \lambda \mathbf{u} \cdot \mathbf{n} \, dA$$

into the weak form. However, it needs to define the Lagrange multiplier at the node, which will increase the system size.

• For what problem? The answer might be very different for, say, the Euler equations vs the Stokes equations. Commented Aug 10, 2023 at 0:09
• This type of constraint is usually implemented by performing a coordinate transformation at the roller node so that the direction n is along one of the coordinate axes. Then a zero constraint is applied in the usual way to that DOF. Commented Aug 10, 2023 at 10:44
• You might find scicomp.stackexchange.com/questions/36432/… useful
– NNN
Commented Aug 10, 2023 at 11:17
• @BillGreene I'm looking for the roller constraint on a cylinder surface. I think nodal constraint does not work for that case.
– kstn
Commented Aug 10, 2023 at 20:54
• Are you doing a linear or nonlinear analysis? If linear, just create a coordinate system with an axis normal to the surface and constrain that dof. Commented Aug 10, 2023 at 22:08