Generally, shell elements are used in models, where the thickness is significantly smaller than other dimensions. Shells with a thickness of more than about 1/15 of the span of the shell are considered as thick shells; otherwise as thin shells . In this report, the exact bending solution from the classical plate theory  and the Mindlin plate theories  are used. These theories are applied to calculate the out-of-plane displacement-pressure relationship of thin and thick solid isotropic plates, respectively.
In case of thick plates, where the shear deformation is significant, shear – deformation plate theories can be applied. There are numerous shear – deformation plate theories available, the simplest of which is the first-order shear-deformation plate theory (FSDT) also known as the Mindlin plate theory. The deflection equation of the FSDTcan be expressed in terms of the corresponding quantities of the classical plate theory for axisymmetric bending of isotropic circular plates as shown in Eq 1 . A similar equation was used by Fini et al.  to calculate the out-of-plane displacement for a thick circular plate (see Fig. 2) under axisymmetric uniform pressure with built-in edge constraint
where p0 = pressure, r = distance from the center of the thick circular plate, R = radius of the thick circular plate, h = thickness of the thick circular plate, wo = displacement at a distance r from the center of thick circular plate, S = shear correction factor (5/6 for the thick circular plate), D = flexural rigidity of the plate, D = Eh3/[12(1 — v2)], G = shear modulus of the plate, G = E/[2(1 + v)], E = modulus of elasticity, and v = Poisson’s ratio.