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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.

nicoguaro
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kstn
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    For what problem? The answer might be very different for, say, the Euler equations vs the Stokes equations. – Daniel Shapero Aug 10 '23 at 00:09
  • 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. – Bill Greene Aug 10 '23 at 10:44
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    You might find https://scicomp.stackexchange.com/questions/36432/inclined-general-dirichlet-boundary-conditions useful – NNN Aug 10 '23 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 Aug 10 '23 at 20:54
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    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. – Bill Greene Aug 10 '23 at 22:08
  • @BillGreene nonlinear dynamics analysis eventually – kstn Aug 11 '23 at 13:07

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