For those who don't seem to be understanding, OP is asking if he can define the four grids of a quadrilateral element in a non-planar way, i.e., the plane formed by three of those grids does not contain the fourth point.
It can, but it is very very very bad practice, probably will create all kind of ill-behavior if you try.
For instance, NASTRAN does a geometry check on the warp factor exactly to list all the elements that are "sticking out" of their respective plane. It will not interrupt the solution, but more extreme examples (like yours) may cause the matrices to behave very badly.
I will provide a perspective on something that the OP (probably) is not even wondering about.
Most commonly used elements in general purpose commercial FEM solid mechanics codes today are linear finite elements which use linear interpolation (shape) functions to interpolate displacement (or other field variables) from nodes to integration points (to compute incremental strains, stresses, etc.) AND represent the geometry at the same time (isoparametric elements). Most such codes also offer elements that have second order shape functions. Only a very limited number of such codes offer elements with other interpolation functions. Isoparametric elements that have nonlinear shape functions can have curved faces/edges to them.
If this is not what the OP was asking, never mind the core dump!
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The proposed element is so badly shaped that being non-planar is probably the least of it's problems.
Generally, you can have non-planar (or warped) elements and the accuracy of the results falls off as the warpage increases. Do a single element test to show this for yourself.
The ideal quad element is a square. Test rectangles to see how the element solution degrades if extreme geometries.
another day in paradise, or is paradise one day closer ?
Small Warping or non-planarity in elements is always present. Question is how much warping is allowed and how much it affects the results. Thats why we have mesh quality checks.
Any kind of distortion(aspect ratio, skewness, jacobian ratio, warping etc) of elements increases the stiffness of the element and affects the analysis results. Especially at the stress concentrations.
I do not know if there is a standard definition for warpage so, if you have a way of computing it, you can write your own little script to compute it. That said, click here for some insight.
I should add that while checking element quality up front is a good practice, I do not think one ought to obsess over it either - unless, of course, the situation demands it. Usually, you run in to too many people who do not pay enough attention to their mesh but, occasionally, you also run in to people who spend a little too much time sweating over a mesh when the uncertainty in the material model or loads/BCs/.. can easily overwhelm the signal.
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