DOF definition vector

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7.5 DOF definition vector

OpenFEM keeps track of the meaning of each Degree of Freedom (DOF) trough DOF definition vectors (see details below). As mdof keeps track of the meaning of different DOFs, fe_c can be used manipulate incomplete and unordered DOF sequences. This is used for boundary condition manipulations, renumbering, ...

OpenFEM distinguishes nodal and element DOFs.

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 _u, _v, _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 -_u, -_v, -_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 .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 = [

u₁	u₂
v₁	v₂
w₁	w₂
_u1	_u2	...
_v1	_v2
_w1	_w2
· · ·		· · ·

] and F = [

F_u1	F_u2
F_v1	F_v2
F_w1	F_w2
M_u1	M_u2	...
M_v1	M_v2
M_w1	M_w2
· · ·		· · ·

]

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 Matab 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 6.2). 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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