Periodic Condition
Use a Periodic Condition to prescribe that the displacements and rotations on two different sets of edges with the same geometrical shape are related, as in a periodic structure. In the Plate interface the connection is between boundaries rather than edges as is the case in the Shell interface.
Several different types of periodicity properties of the solution can be prescribed using this boundary condition.
The Continuity, Antiperiodicity, and User defined periodic conditions directly prescribe relations both between displacements and between rotations. They can be used for any type of study.
The Floquet periodicity can be used for frequency domain problems with a spatial periodicity of the geometry and solution. The modeled structure is typically a unit cell of a repetitive structure.
The Cyclic symmetry is a special case of a Floquet condition, intended for structures which consist of a number of sectors which are identical when rotated around a common axis, like in a fan.
The two sets of edges between which there is a periodicity condition are called the source and destination. It is not required to have the same mesh on the source and destination, but the local accuracy of the solution near the edges will be better if you use the same mesh.
For periodic conditions on shells the periodicity condition acts on edges, as opposed to solids and plates where it acts on boundaries. This means that the orientation cannot be determined automatically. You must provide coordinate systems using the Orientation of Source and Orientation of Destination sections. The default coordinate system is the Global coordinate system, which works well if the edges are parallel. In other cases, you need to add a Destination Selection subnode, in order to supply the coordinate system for the destination.
Edge Selection
Select both the source and destination edges.
The software automatically identifies the edges as either source edges or destination edges. This works fine for cases like opposing parallel edges. In more general cases, use the Destination Selection subnode to specify the edges which constitute the destination. By default this node contains the selection that COMSOL Multiphysics has identified.
In cases where the periodic edge is split into several edges within the geometry, it might be necessary to apply separate periodic conditions to each pair of geometry edges for the matching to work properly.
In the Plate interface, Edge Selection is replaced by Boundary Selection.
Periodicity Settings
With Type of periodicity you select the form of periodicity that your solution should have.
For Continuity the displacements and rotations on the destination are set equal to their counterparts on the source; and . If the source and destination objects are rotated with respect to each other, a transformation is performed using the selected coordinate systems, so that corresponding components of the degrees of freedom are connected.
For Antiperiodicity the displacements and rotations on the destination are set equal to their counterparts on the source but with the sign reversed; and . If the source and destination objects are rotated with respect to each other, a transformation is performed using the selected coordinate systems, so that corresponding components of the degrees of freedom are connected.
For Floquet periodicity enter a k-vector for Floquet periodicity kF. This is the wave number vector for the excitation.
For Cyclic symmetry the settings differ slightly between the Plate and Shell interfaces.
In either case, also enter an Azimuthal mode number for the mode to be studied. It can vary from 0 to N/2, where N is the total number of sectors on a full revolution.
In the Plate interface, choose how to define the sector angle that the geometry represents using the Sector angle list. If Automatic is selected, the program attempts to find out how many full repetitions of the geometry there will be on a full revolution. If User defined is selected, enter a value for the sector angle θS.
If any point on the edges having the periodic condition is located on the axis of cyclic symmetry, enter the Axis direction vector, tc. This orientation of the axis of cyclic symmetry is then needed for eliminating conflicting constraints.
For User defined select the check box for any of the displacement or rotation components as needed. Then for each selection, choose the Type of periodicityContinuity or Antiperiodicity. Each selected displacement component will be connected by or . Each selected rotation component will be connected by or If the source and destination objects are rotated with respect to each other, a transformation is performed using the selected coordinate systems so that corresponding components of the degrees of freedom are connected.
Constraint Settings
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
In the COMSOL Multiphysics Reference Manual:
Orientation of Source
In Transform to intermediate map, select a coordinate system representing the orientation of the degrees of freedom on the source selection. The corresponding setting for the destination is given in the Destination Selection subnode.
Cyclic Symmetry and Floquet Periodic Conditions in the Structural Mechanics Theory chapter.
Orientation of Source and Destination in the COMSOL Multiphysics Reference Manual.
Vibrations of an Impeller: Application Library path Structural_Mechanics_Module/Dynamics_and_Vibration/impeller
Location in User Interface
Context Menus
Ribbon
Physics tab with Shell selected:
Physics tab with Plate selected:
Physics tab with Periodic Condition node selected in the model tree: