In a substructuring analysis, the substructure’s nodal displacement vector,
{u}, is represented in terms of reduced coordinates, 
, by the coordinate transformation:
 | (1–1) |
where [T] is the transformation matrix.
The meaning of the degrees of freedom (DOFs) of {u} depends on the element types of the finite elements of the model. Among all the analysis types available in the program, structural analysis is the most common type to which substructuring analysis is applied. The following equations deal exclusively with structural analysis.
In structural analysis, the general form for equations of motion is:
 | (1–2) |
where:
| [K] = structural stiffness matrix |
| [M] = structural mass matrix |
| [C] = structural damping matrix |
| {F} = load vector |
Introducing Equation 1–1 into Equation 1–2 and left multiplying by [T]T, the reduced equation is obtained:
 | (1–3) |
where:
 = reduced stiffness matrix |
 = reduced mass matrix |
 = reduced damping matrix |
 = reduced load vector |
Two condensation methods are available:
Substructuring analysis: Static reduction which reduces the system matrices to a smaller set of nodal DOFs. Substructuring analysis applies to structural and non-structural analysis types. For structural analysis, this condensation method is also called Guyan reduction (see 14 in the Mechanical APDL Theory Reference).
Component mode synthesis (CMS): reduces the system matrices to a smaller set of nodal DOFs complemented by a set of generalized coordinates. CMS applies to structural analysis only.
For non-structural analysis types, matrices [K], [M], and [C] may no longer correspond to stiffness, mass, and damping quantities, but matrices associated with zero order terms ([K]), first order terms ([C]), and second order terms ([M]) are reduced with the same logic presented above. For coupled-field analyses, only the reduction of [K] is possible.
For more information about specific equations, see Substructuring Analysis in the Theory Reference.