Flexcom > Theory > Applied Loading > Boundary Conditions > Application of Rotational Constraints

This section discusses the significance of rotational degrees of freedom in terms of boundary conditions.

When defining boundary conditions, a non-zero displacement term may be optionally associated with a constraint. This allows an offset to be modelled in conjunction with a restraint. Such displacements terms have a straightforward definition in a translational sense, but if specifying displacements in degrees of freedom (DOFs) 4-6, is important if specifying displacements in DOFs 4-6 to understand the significance of these DOFs.

You will no doubt be aware that finite (non-infinitesimal) 3D rotations cannot be represented as vectors, since the addition of such vectors is non-commutative, that is, the order in which the rotations are taken affects the result. In Flexcom this problem is handled by means of a consistent 3D kinematics formulation based on the correspondence between a specially defined rotation vector and a transformation matrix. The full details are omitted here but, in summary, a rotation is represented by a vector such that i) the magnitude of the vector represents the magnitude of the rotation, and ii) the direction of the vector represents the axis of rotation. Therefore the inputs in the Displacement column for DOFs 4-6 are the components of this rotation vector. It is particularly important to realise that in general they do not represent individual rotations about the global coordinate X, Y and Z axes. Refer to Global Degrees of Freedom for further information.

Specification of appropriate boundary conditions in DOFs 4, 5 & 6 requires a knowledge of the local undeformed and desired convected axis systems for the constrained element. Armed with this knowledge, it should be possible to compute relevant boundary conditions given a desired hangoff angle. However, in order to expedite this process and to minimise effort on the part of the user, a standalone program has been created to perform the required computations. Refer to our Downloads page if you require access to this program.