Hi Enthu,
The problem, as you rightly guessed is because of the difference in the degrees of freedom of the solid and shell elements. This has been a topic of discussion for quite a few years now.
My suggestion would be to overlap the plates (shells) with the solids or create an interface between the two. (The coating mesh concept) This is very similar to what Corus suggested about embedding the shell with the solids.
In real life scenario, these overlaps/angles would signify welded joints.
Cheers.