you can try Incompatible mode brick elements.
here is a good resources of examples:
with these example:
I thought we had the same issue before, but i don’t find any the topic.
I had the same problem, and the solution was to change to these kind of elements!?
Please let me know, if you find a solution according to you hand calc…
Can you post your analytical solution? These would be very helpful for me.
(tip: I would always use a displacement for these king of calc. first and
check the force with the boundary reaction)