Do finite elements have to be planar?

Question

Is it possible to define a finite element that isn't planar? For example the shell element shown in the picture below...

Answer 1

Finite elements can have curved edges or faces. See the pictures of the element library for almost any FE program.

It probably doesn't make much sense to try to define a curved shell element with straight edges as in your picture. Curved elements usually have mid-side nodes as well as corner nodes, to give "smooth" curved shapes.

Answer 2

It is possible, however depending on the formulation of the element and the geometry of the nodes, there will be performance issues (i.e. loss of accuracy).

In general, a "concave" shape like the one you included should (generally speaking) be avoided. It would be preferable to split it to two triangular element. The accuracy (in my experience) will be better.

Answer 3

The object being modelled can be non-planar. But for each element in FEA is assumed planar.

You can reason from the stress/strain formula of FEA elements (even in polynomial elements) the force is in-plane.