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Update rotation matrices based on abaqus rotation nodal values

Update rotation matrices based on abaqus rotation nodal values

Update rotation matrices based on abaqus rotation nodal values

(OP)
Hi All!
Imagine you have a two noded beam in space, defined by extreme nodes 1 and 2, see figure.

To simplify, initially, the longitudinal axis of the beam, defined by the unit vector of the line that connects the nodes 1 and 2, is coincident with the X axis of the global coordinate system. Also the local frame x,y and z axis of each node are coincident with the global frame X, Y and Z axis.

Now assume that the beam rotated, with independent rotations in nodes 1 and 2. I know the rotations along global X, Y and Z axis of nodes 1 and 2.

How can I know the updated rotation matrix that transforms the original local frame at node 1 (or 2) to the rotated (updated) local frame at node 1 (or 2), i.e. matrices R1 and R2 in the figure?
Also, I belive it is not possible to obtain from any of these rotation matrices the updated local frame of the beam (matrix Rr in the figure): i.e. I can know the local x axis (which is defined by the line that connects node 1 and node 2), but T have to arbitrate the local y and z axis of the beam, right?
Thanks!

Andre

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