Constraint Conditions (Constraint) — CAE Glossary

Roughly speaking, yes. In FEM, each node has a maximum of 6 degrees of freedom (DOF: 3 translational + 3 rotational), and the most basic constraint is fixing unwanted directions to zero. For example, if a steel plate is bolted to a wall at one end, all DOFs at that end are constrained — this is called complete fixation (Encastre).

Yes, broadly there are three categories. (1) SPC (Single Point Constraint): Fix a specific DOF at a specific node to a fixed value (usually zero). Simplest type. (2) MPC (Multi-Point Constraint): Relate displacements of multiple nodes through equations. RBE2 and RBE3 belong here. (3) Symmetry and Anti-Symmetry Constraints: Use model symmetry to reduce computational load. They all work as different ways to impose constraints on the global stiffness equation $[K]\{u\} = \{F\}$.

It's essentially removing rows and columns from the global stiffness equation corresponding to constrained DOFs. For example, if you specify node $i$'s X-direction displacement $u_i = 0$, you zero out the corresponding row and column in $[K]$, put a large value on the diagonal, or delete those rows and columns entirely. In Nastran this is the SPC card; in Abaqus it's Boundary Conditions like "ENCASTRE" or "PINNED".

ENCASTRE constrains all 6 DOFs — complete fixation. PINNED constrains only the 3 translational DOFs and allows rotation — it's a pin support. In beam analysis, comparing a cantilever (ENCASTRE at one end) to a simply supported beam (PINNED at one end) is a common practical pattern.

Rigid body motion (RBM) is when the entire structure translates or rotates without deformation. In 3D space there are 6 rigid body modes: 3 translational directions (X, Y, Z) and 3 rotational directions (Rx, Ry, Rz). If these are not constrained, $[K]$ becomes singular, the inverse cannot be computed, and the solver throws an error.

In principle, yes. But how you choose those 6 matters. Constraining all 6 DOFs at a single point concentrates reaction forces and creates unrealistic local stresses. In practice, we often use the "1-2-3 method": Point 1 fixes all 3 translational directions, Point 2 fixes 2 rotational directions, Point 3 fixes the remaining rotational direction. This distributes reaction forces and mitigates local stress problems.

Typical Nastran errors: "FATAL: MATRIX IS SINGULAR" or "MECHANISM DETECTED". Abaqus: "NUMERICAL SINGULARITY" or "ZERO PIVOT". When you see these, the first priority is checking constraints. Also, in Nastran you can use PARAM,BAILOUT,-1 to output results despite errors, and viewing the displacement animation will immediately show which directions have rigid body motion.

Suppose the YZ plane is your symmetry plane. You constrain the nodes on that plane with zero displacement perpendicular to it ($u_x = 0$) and zero rotation within the plane ($\theta_y = 0, \theta_z = 0$). This is mathematically equivalent to having the mirror image model on the other side. If your model size is halved, computation time drops to roughly 1/4 to 1/8 (memory also halves).

Yes. For anti-symmetry, you constrain displacements parallel to the symmetry plane while leaving perpendicular displacement free — the opposite of symmetry. Used for cases like torsion on a symmetric beam. But anti-symmetry only works if both geometry and loading are anti-symmetric. If geometry is symmetric but loading isn't, you can't use it — that's a common mistake.

MPC defines an equation relating displacements across multiple nodes. General form:

The most common mistake is "over-constraint" — same DOF constrained by both SPC and MPC creates a contradiction and causes solver errors or silently wrong results. Also critical is choosing dependent vs. independent nodes correctly. If you make a loaded node dependent, the force may not transfer correctly. Pay attention to this.

This is where nearly all FEM beginners get confused, so let me clarify carefully.

Consider a hole surrounded by nodes. Connecting them to the center with RBE2 makes the hole completely rigid — far stiffer than a real bolted joint. With RBE3, you just distribute loads without adding artificial stiffness; the hole can still deform freely.

Three things stand out.