Hi all,
My question is about this transformation matrix T for beam elements using 3 or more nodes (quadratic or higher formulation).
When
programming beam elements in 2D or 3D one usually formulates the shape
functions etc. in ‘local’ beam coordinates (e.g. x’). So the beam stiffness matrix
will be formulated using this local coordinate system. For assembly of the ‘global’
system one transforms this local matrix to global coordinates using a
transformation matrix T.
In general
the transformation matrix for a beam element with N nodes has the form:
{T1, 0, …, 0}
T = {0, T2, …, 0}
…
{0, 0, …, TN}
So the sub-matrix T1, T2, …, TN is created using the slope of the element at the N
points. For a 2-node beam element it is very obvious which slope to use. But
how about beam elements with 3 or more nodes?
-
Does one use the slope between the first and last element node?
- For e.g Node 2: does one use the slope between node 1 and 2? Or 2 and 3? Or do I have to calculate the average slope of 1-2 and 2-3?
Thanks in
advance,
Jörg