I am trying to take into account the "hourglass" effect in the shear part when composing the finite element stiffness matrix using selective reduced integration.
I am relying on this article from the theoretical manual of ABAQUS: https://classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/stm/default.htm?startat=ch03s02ath63.html#stm-elm-incompatible
Go to item 3.6.5 in the menu when clicking on the link and scroll down to the chapter: One-point integration plus stabilization
The matrices Bd and Br are responsible for this. enter image description here
But my stiffness matrix is the same as the matrix from the ABAQUS only for a square element of size 2x2. For a square element of a different size, the matrix also coincides with the ABAQUS, if I multiply the entire matrix Bd by 2/a, where a is the side of the element.
But I can't get the matrices to match for a rectangular element with different side lengths. And it also doesn't work for a rhomb.
Can the coefficients of Г change in this case? enter image description here
Thanks for any help.