The 8 Mode Shapes of a plane finite element

[Trying2Learn]

TL;DR Summary

What are the eight mode shapes

I recall, about 30 years ago, seeing the eight mode shapes (and eigenvalues) of a single plane stress (or strain) finite element.

Also, years ago, I wrote a FORTRAN code to obtain them (using IMSL libraries)

I know there are eight (because the plane quad element had 8 degrees of freedom)

I also saw them in a book somewhere (but I do not remember the book).

There were eight mode shapes: stretch in 1, stretch in 2, a horizontal shear, a vertical shear and one other. THen there were three zero eigenvalue modes (free translation in two directions and a free rotation)

I am trying to write a MATLAB code to produce them, but I get strange results taht make no sense and am confusing myself (I do not know what Matlab is doing -- or maybe I am coding it wrong).

Can anyone point me to a site that has the eight shapes?

I am NOT looking for a eigenvalue analysis on a mesh (all my google searches bring up modal analysis on a mesh--I do not want that). I am looking for the analysis on ONE element

 

[FEAnalyst]

So, you are looking for mode shapes of a first-order quad element with no boundary conditions applied? Here's what I got in Abaqus (outline of the underformed shape is shown for each mode for reference):

 

[Trying2Learn]

EXACTLY! That was what I remembered. I KNEW there is something wrong with my Matlab code. Now I must find the error.

THANK YOU VERY MUCH!