# Thick-Plate Theory

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.