Thank you for your valueable question. I'm really interested in this topic but i don't have such information to answer your question. I just want add another question on yours. Is there any deffrence in deriving shear correction factor in thick and thin plates? does anybody know what the diffrences are?
You can calculate shear correction factor from stiffness matrix and mass matrix.
Refer following paper of me.
Sayyad A. S., “Comparison of Various Beam Theories for the Bending and Free Vibration Analysis of Thick Beams” Applied and Computational Mechanics, 2011, 5, pp. 217-230.
The shear correction factors could be obtained by some iterative technique as indicated by Vairo by keeping in mind the boundary conditions, plate geometry and loading conditions. please refer to the following paper. I hope it will help.
Stefanos Vlachoutsis, Shear correction factors for plates and shells, International Journal for Numerical Methods in Engineering, Volume 33, Issue 7, pages 1537–1552, 30 May 1992