# Constraints

In the most general sense constraints are where the user is putting some restriction on the free displacement of the structure. Some constraint is required on all structures to prevent pure rigid body motions. Thus in general the minimum number of constraints on a 3D structure is six, three suppressing the translational rigid body modes and three suppressing the rotational rigid body modes.

In most cases there will be considerably more constraints than the minimum to suppress rigid body motion. The general case of a constraint can be described by a constraint equation of the form

$u_{s,i} = \sum_j \alpha_j u_{p,j} + \beta$

where $u_p$ refers to the primary node, and $u_s$ to the secondary (restrained) node.

The types of constraints consist in GSA are:

These are discussed in more detail below.

It is important to avoid conflicting constraints. This is where there is more than a single constraint on a particular degree of freedom. For example one degree of freedom on a node participating in both a joint and a rigid constraint. Note that the constraints act on degrees of freedom so a node with a joint constraining the z direction and a rigid constraint constraining the x, y and zz degrees of freedom, does not cause any conflict.

There are two situations where GSA temporarily adds constraints to the model during an analysis. With 2D elements automatic constraints can be added to account for the non-stiff degrees of freedom. The other is when the user chooses additional restraint in a modal dynamic analysis.