Enforcing a constraint condition is more or less a matter of finding a corresponding flux condition that leads to the desired values of the dependent variables. The hidden flux conditions introduced this way appear as reaction terms in the system of equations modeling the physics. These reaction terms normally have a physical meaning and correspond to a flux condition, for example:
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The reaction term enforcing a Prescribed Displacement on a solid model is a reaction force, similar to a Boundary Load boundary condition.
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Most boundary conditions of constraint type, by default, introduce reaction terms in such a way that an otherwise symmetric system of equations remains symmetric. This makes constraints bidirectional in the sense that all dependent variables that appear in a constraint expression are also affected by the reaction terms.
To illustrate this, suppose a Prescribed Displacement boundary condition is applied on a solid model, specifying that the x-displacement of the boundary, u, is proportional to the y-displacement, v, with a constant of proportionality, k, which is a function of the boundary temperature T:
(3-1)
If fully symmetric reaction terms are used to enforce this constraint, reaction forces are applied on both displacement components u and v, as well as a reaction heat flux in the heat transfer equation. Applying symmetric reaction terms this way, on completely different equations, is usually not meaningful.
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As an alternative to the default (symmetric) application of reaction terms, you can choose to have these affect only the equations and variables in the physics interface where the constraint boundary condition is added. For the example in Equation 3-1, the reaction terms can be restricted to act on the displacement variables and equations in the Solid Mechanics interface, leaving the temperature unaffected. Many different restrictions of this type are possible, in principle, and the COMSOL software generally provides two alternatives:
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The most consistent and general way to avoid spurious reaction terms affecting other physics is to start from the globally symmetric formulation and remove the terms entering equations belonging to other physics interfaces. This limits the reaction terms to affecting the current physics as if there were no other physics in the model, so the reaction terms preserve the symmetry. For Equation 3-1, this means that reaction terms are distributed over both u and v equations, in proportions 1:k(T).
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The other alternative is to apply the reaction terms only on certain individual variables. Another way to look at Equation 3-1 is to read it as prescribing a value for the x-displacement u, rather than prescribing a given relation between u and v. Accepting that view, it is reasonable to insert reaction terms only acting on u. Such reaction terms, in general, do not preserve symmetry even for a single physics interface.
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Most constraint nodes have a Constraint Settings section which is only available when Advanced Physics Options is selected from the Show menu (
). This section provides settings controlling how reaction terms are applied and whether standard or weak constraints are used. Choose to Apply reaction terms on:
). This section provides settings controlling how reaction terms are applied and whether standard or weak constraints are used. Choose to Apply reaction terms on:|
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All physics (symmetric) to apply reaction terms symmetrically on all dependent variables taking part in the constraint.
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Current physics (internally symmetric) to apply reaction terms symmetrically only on the dependent variables in the physics where the constraint is added. This leaves other physics unaffected by the constraint.
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Individual dependent variables to apply reaction terms only on selected variables. For most physics, this makes the constraint unidirectional and often nonsymmetric.
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Select the Use weak constraints check box to replace the pointwise standard constraints with weak constraints. Note that this introduces additional equations and dependent variables. If you use pointwise constraints (the default; the Use weak constraints check box is cleared), then select a Constraint method for the pointwise constraints: Elemental or Nodal:
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Choose Elemental (the default) to make the software assemble the constraint on each node in each element; that is, there are usually several constraints at the same global coordinates because elements in the computational mesh overlap at nodes.
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Choose Nodal to make the software assemble a single constraint for each global node point. The nodal constraint method provides an averaging of the constraints from adjacent elements, which can be beneficial when the constraint has discontinuities between mesh elements (for example, due to discontinuities of the boundary normal). Another case where nodal constraints can be useful is in boundary conditions involving a coupling operator (such as continuity or periodic conditions). With elemental constraints, locking effects can sometimes occur because the coupling operator might map to slightly different points in the source boundary when it is applied to the same node point in different mesh elements.
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