Roller Boundary Condition
The Roller boundary condition is similar to a Symmetry boundary condition, since it constrains the displacement in a direction normal to the boundary. A Roller is however intended to be used also on curved boundaries. The constraint can be formulated as
where the normal nr is computed using different methods depending on the selection in the Roller Constraint section.
When Normal orientation is set to Automatic, the normal orientation is computed from the mesh, or its underlying geometry. Consider for example a roller condition on a planar surface. Theoretically, the normal at all mesh nodes should be parallel. But if there are inaccuracies in the node locations, the computed normals may not be exactly the same everywhere. They can differ not only between nodes, but also between neighboring elements connected to the same node. Thus, there may be constraints acting in somewhat different directions. Such constraints can make the boundary appear as fixed, rather than sliding. This potential problem can be reduced if you select Nodal as Constraint method in the Constraint Setting section.
In the COMSOL Multiphysics Reference Manual:
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Constraint Settings
In the modeling section of the Structural Mechanics User’s Guide:
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Elemental and Nodal Constraints
If you select one of the explicit shapes (Plane, Cylinder, or Sphere) as Normal orientation, then the orientation of he normal nr is instead a user input, so there will be no problem with numerical inaccuracies.
If you select Plane, the you give the direction explicitly as a constant vector.
If you select Cylinder, the normal is computed as being perpendicular to the cylinder axis at each mesh node. The input defining the cylinder is a Point on axis, Xc, and the vector along the cylinder axis, es. For a node located at a an original coordinate X, the normal orientation is computed as
Here it is not necessary to normalize nr. It is actually the radial vector from the cylinder axis to the location X.
In the case of geometric nonlinearity, the orientation of the normal would change. This is implemented as a nonlinear constraint, where the node is forced to maintain its distance from the cylinder axis, while allowed to move freely in the axial and circumferential directions. Thus, the normal orientation is not explicitly computed.
The constraint expression is
where
The radius of the cylinder is not given explicitly, so each node will maintain its own original distance from the cylinder axis.
If you select Sphere, the normal is computed as the direction from the center of the sphere to each mesh node. The only input is a Center of sphere, Xc. For a node located at a an original coordinate X, the normal (actually, the radial vector) is computed as
In the case of geometric nonlinearity, the orientation of the normal would change. This is implemented as a nonlinear constraint, where the node is forced to maintain its distance from the center of the sphere, while allowed to move freely in the two directions on the sphere surface. Thus, the normal orientation is not explicitly computed. The constraint is written as
The radius of the sphere is not given explicitly, so each node will maintain its own original distance from the center.