Update shell example

[termi-official]

The shell example is a bit "naked" at the moment. I think we should try to integrate the new CellValues #764 into it for a proper abstraction layer and better code reuse for downstream users.

Further, it might be nice to see how implementing some actual shell element works out. Maybe MITC4?

[lijas]

I looked in to the mitc4 paper (and also this blog about mitc4), and it seems like the shell is mostly formulated with coverient coordinates, so one does not really need e.g. cv.dNdx to compute e.g the strain, right? Would it be worth creating a costum ShellValues in the example, perhaps?

[termi-official]

I looked in to the mitc4 paper (and also this blog about mitc4), and it seems like the shell is mostly formulated with coverient coordinates, so one does not really need e.g. cv.dNdx to compute e.g the strain, right?

I am not following here. Don't we need dNdx to compute the covariant strains?

Would it be worth creating a costum ShellValues in the example, perhaps?

I am still trying to figure out what is the best angle here. I was alto thinking that ShellValues = FunctionValues + custom GeometryValues + directors, maybe?

[termi-official]

Do you by any chance have recent literature which presents some general theory/framework for larger classes of shell formulations? I think we need such work to guide the design properly.

[lijas]

This one perhaps: https://onlinelibrary.wiley.com/doi/10.1002/9781119176817.ecm2026, but it is not an short read :P

think most shells theories require that \sigma_33 and/or \epsilon_33 to be zero out-of-plane, so at some point you have to rotate to a local coordinate system oriented with the shell. That is why people formulate them with the curvelinear coordinates directcly.