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Mindlin plate element - stiffness matrix

Mindlin plate element - stiffness matrix

Mindlin plate element - stiffness matrix

(OP)
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.



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