Boundary Conditions
How constraints work in FEM — fixed supports, symmetry, and degrees of freedom.
Boundary conditions tell the solver where and how the structure is supported. Without them, the structure is free to move as a rigid body — the solver cannot find a unique solution and will fail.
Degrees of freedom
Every node in the FEM mesh has degrees of freedom (DOF): three translations (X, Y, Z) and three rotations. A boundary condition removes one or more of these DOFs at the selected nodes.
| DOF | Description | | --- | --- | | UX, UY, UZ | Displacement in X, Y, Z | | RX, RY, RZ | Rotation about X, Y, Z axes |
Solid elements (Tet, Hex) only have translational DOFs. Shell and beam elements also have rotational DOFs.
Common support types
Fixed support
Locks all translational DOFs at a surface. No displacement in any direction. In Dr.Q this is the standard "fixed" constraint.
Use it to model: bolted flanges, welded connections, rigid clamps.
A fully fixed support is stiffer than reality. If the support deflects even slightly in practice, your model will overestimate stiffness and underestimate stress near the constraint.
Symmetry condition
If the geometry, material, and load are all symmetric about a plane, you only need to model half the structure. Apply a symmetry constraint to the cut plane: displacements normal to the plane are zero.
Benefits: half the elements, shorter solve time, same accuracy.
Symmetry only works when geometry, material, and load are all symmetric. A symmetric geometry with an asymmetric load cannot use symmetry planes.
Roller / pin support
Locks displacement in one direction only, leaving others free. Useful for modelling simple supports (beams resting on bearings) or guided supports (a rail slot).
What happens without boundary conditions
The stiffness matrix is singular — the solver cannot invert it. You will get an error about "rigid body motion" or "singular matrix." The structure has no way to resist the applied load.
Practical guidelines
- Place supports as far from the region of interest as possible. Stresses concentrate near constraints and are less accurate close to them (Saint-Venant's principle).
- When in doubt, use more supports and check that reaction forces match the applied load.
- Avoid over-constraining: locking DOFs that should be free introduces artificial stiffness and distorts results.