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7.5  DOF definition vector

The meaning of each Degree of Freedom (DOF) is handled through DOF definition vectors typically stored in .DOF fields (and columns of .dof in test cases where a DOF specifies an input/output location). All informations defined at DOFs (deformations, matrices, ...) should always be stored with the corresponding DOF definition vector. The fe_c function supports all standard DOF manipulations (extraction, conversion to label, ...)


Nodal DOFs are described as a single number of the form NodeId.DofId where DofId is an integer between 01 and 99. For example DOF 1 of node 23 is described by 23.01. By convention

While these are the only mandatory conventions, other typical DOFs are .19 pressure, .20 temperature, .21 voltage, .22 magnetic field.

In a small shell model, all six DOFs (translations and rotations) of each node would be retained and could be stacked sequentially node by node. The DOF definition vector mdof and corresponding displacement or load vectors would thus take the form

mdof = [
1.01 
1.02 
1.03 
1.04 
1.05 
1.06 
  ⋮ 
] ,  q = [
u1u2 
v1  v2 
w1w2 
θu1θu2… 
θv1  θv2 
θw1θw2 
 ⋱ 
]   and   F = [
Fu1Fu2 
Fv1Fv2 
  Fw1Fw2 
  Mu1Mu2
Mv1Mv2 
Mw1Mw2 
 ⋱ 
]

Typical vectors and matrices associated to a DOF definition vector are

Note that, in Matlab version, the functions fe_eig and fe_mk, for models with more than 1000 DOFs, renumber DOF internally so that you may not need to optimize DOF numbering yourself. In such cases though, mdof will not be ordered sequentially as shown above.

Element DOFs are described as a single number of the form -EltId.DofId where DofId is an integer between 001 and 999. For example DOF 1 of the element with ID 23001 is described by -23001.001. Element DOFs are typically only used by superelements (see section 6.3). Due to the use of integer routines for indexing operations, you cannot define element DOFs for elements with and EltId larger than 2 147 484.


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