Component Mode Synthesis (CMS) is used to reduce a finite element model of an elastic body to the interface degrees of freedom and a set of normal modes for inclusion as a flexible body in a multi-body dynamics analysis.
The displacement vector may be partitioned into displacements of inner (OSET) and outer (ASET, interface) degrees of freedom
Here, the subscript ‘o’ denotes the inner degrees of freedom, and ‘a’ the interface degrees of freedom.
The interface nodes that are used in the component mode synthesis process for the construction of mode shapes should be coincidental to the set of force-bearing nodes in the subsequent multi-body dynamics analysis. In a multi-body dynamics model, the flexible body interacts with other components of the model through joints, constraints, or force elements, which are connected or applied on the nodes of the flexible body. Except for body forces due to gravity or acceleration of the flexible body, all nodes that are subject to constraint or applied forces in the multi-body dynamics analysis are denoted as force-bearing nodes.
The purpose of specifying the interface nodes for CMS is mainly to account for the static deformation due to constraint or applied forces acting on the interface nodes. A huge number of eigenmodes is required if these static modes are omitted. The flexible deformations due to constraint forces, compared to the deformation due to the body inertia forces, are often dominant in most constrained models, therefore the inclusion of all force-bearing nodes as interface nodes is an essential step to get accurate results from subsequent flexible multi-body dynamics analysis.
The static equilibrium is given as
.
The eigenvalue problem for a normal modes analysis of the body using a diagonal mass matrix represents itself as
.
The task of the component mode synthesis is to find a set of orthogonal modes 
that represent the displacements u of the flexible body such that
where q is the matrix of modal participation factors or modal coordinates which are to be determined by the multi-body dynamics analysis.
The Craig-Bampton and Craig-Chang methods of component mode synthesis are implemented.
This method uses a system constrained in the interface degrees of freedom. Normal modes analysis of the system yields the diagonal matrix of eigenvalue 
and the matrix of eigenmodes 
. In this normal analysis, you can select the cut-off frequency or the number of modes to be solved. This determines the column dimension of .
In addition, a static analysis is performed with a unit displacement in each interface degree of freedom while all other interface degrees of freedom are fixed. The number of subcases in this static analysis is six times the number of interface nodes. Note that it is important to constrain each interface node with its neighboring nodes, if necessary, to ensure that it has non-zero stiffness along the direction of all six DOF. This yields the displacement matrix 
and the interface forces 
.
Reduced modal stiffness 
and mass matrices 
are now generated using
which yields
.
It follows an othogonalization step that transforms the original shapes X a set of orthogonal modes .
The method uses a system that is unconstrained (free-free) and therefore has six rigid body modes. Normal modes analysis of the system yields the diagonal matrix of eigenvalue and the matrix of eigenmodes . In this normal analysis, you can select the cut-off frequency or the number of modes to be solved. This determines the column dimension of . The eigenmodes 
associated with the rigid body modes will be normalized with respect to the mass matrix such that
.
In addition, a static analysis is performed using an equilibrated load matrix 
.
The equilibrated load matrix is applied in an inertia relief static analysis without any SPC constraints, but with proper support to remove the six rigid modes. The vector 
is a collection of the attachment force vectors which otherwise have all zero entries except a unit force along each degree of freedom of the interface nodes. The resulting modes 
are called the inertia relieve attachment modes.
Reduced modal stiffness and mass matrices are now generated using
yielding
.
It follows an othogonalization step that transforms the original shapes X a set of orthogonal modes .
First, a new eigenvalue problem using the reduced matrices above is solved.
The resulting diagonal matrix of eigenvalues D and the normal modes N are used to transform the set of original shapes into the set of orthogonal modes .
It can be shown that the resulting modes are orthogonal with respect to the system stiffness matrix K and mass matrix M.
If the orthogonal modes are normalized with respect to the mass matrix M, the reduced matrices for the multi-body analysis appear as
.
A component mode synthesis subcase is defined using a CMSMETH subcase command that references a CMSMETH bulk data entry which defines the method, Craig-Bampton or Craig-Chang. Only one subcase is allowed per model. The interface degrees of freedom are being defined using ASET, ASET1 bulk data statements. An MPC reference is allowed. All other subcase entities are ignored.
The orthogonal modes and the corresponding eigenvalues D are exported to a flexh3d file by default. The modal stresses and strains can be output optionally using the STRESS and STRAIN output statements. Sets can be applied to reduce the amount of data.
For the Craig-Bampton method using PARAM, EXTOUT, the reduced stiffness and mass matrices can be exported in DMIG format. All necessary SPOINT entries are generated automatically. Currently, no SPC boundary conditions or offset can be applied to the portion of the structure that is being reduced out.