Mindlin plate element - stiffness matrix

[futer8]

Hello, I have been trying to program a basic bending element - 4 node quadrilateral, pure displacement formulation. I am stuck - I'm doing something wrong, but I can't find the mistake, therefore I would like to ask you for your help. I can't look for advice from anyone from educational institutions simply because I'm not attending any, I'm doing it for self education - it's not a university project.

I've been formulating the element according to Bathe, K.-J. - Finite Element Procedures.

Here's the displacement vector:

Here are the displacement interpolations matrices:

Strain-sress matrices:

Stiffness matrix integration:

The stifness matrix itself (rectangular element 3x2 mm):

Exemplary response of 1 element (1 edge clamped)

And something that shows that something is obviously wrong, response of 10-element beam clamped on 1 end and loaded with force on the opposite end - I'm getting an unstable oscillator:

Thanks.