Questions and discussion for this lecture live here. Fire away by hitting Reply below 
Hi Sean,
I have a question regarding the displacement vector U. We defined it to be (u, v, w), but after that, we’ve stripped out the -z component to get (w, \theta_x, \theta_y). Why did we do so? Do we later go into our main FE system of equations with U defined as (w, \theta_x, \theta_y), or do we substitute z back into (w, \theta_x, \theta_y)? Basically, what I’m asking is, what is our motivation to rewrite (u, v, w) as (w, \theta_x, \theta_y), because obviously (u, v, w) \neq (w, \theta_x, \theta_y)? Also, why change the order of variables in (w, \theta_x, \theta_y), why not (\theta_x, \theta_y, w)?
Since our objective is to develop a model of plate deformation that can capture the specific R-M assumption (normals to the middle plane rotate after deformation), we need to think about these displacements as a function of rotation, and specifically, rotation of a normal to the middle plane. This is why we frame the displacement field in terms of theta_x and theta_y (and w) from the beginning, i.e. the displacement vector is
\bf{u} = [w, \theta_x, \theta_y]^T
Re-framing the displacements u and v in terms of theta_x and theta_y also allows us to recognise their dependence on z, the distance from the middle plane.
In terms of the ordering of the elements of the displacement vector, this is not special - you’re free to order it whatever way you like…you’ll just need to follow through with that ordering throughout the rest of the derivations - the ordering I show in the course is quite typical/conventional.
S