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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

• DOFs 01 to 06 are, in the following order u, v, w (displacements along the global coordinate axes) and θ_u, θ_v, θ_w (rotations along the same directions)
• DOFs 07 to 12 are, in the following order −u, −v, −w (displacements along the reversed global coordinate axes) and −θ_u, −θ_v, −θ_w (rotations along the same directions). This convention is used in test applications where measurements are often made in those directions and not corrected for the sign change. It should not be used for finite element related functions which may not all support this convention.

While these are the only mandatory conventions, other typical DOFs are used to easily identify data types

• DOFs 13 to 18 are, in the following order F_u, F_v, F_w (force along the global coordinate axes) and M_u, M_v, M_w (torque along the same directions)
• DOFs 19 : pressure
• DOFs 20 : temperature
• DOFs 21 : voltage
• DOFs 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

(7.1)

Typical vectors and matrices associated to a DOF definition vector are

• modes resulting from the use of fe_eig or read from FE code results (see nasread, ufread).
• input and output shape matrices which describe how forces are applied and sensors are placed (see fe_c, fe_load, bc ).
• system matrices : mass, stiffness, etc. assembled by fe_mk.
• FRF test data. If the position of sensors is known, it can be used to animate experimental deformations (see feplot , xfopt, and fe_sens ).

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.