Relationships between bending solutions of Reissner and Mindlin plate theories

Of the many shear deformable plate theories proposed over the years, the Mindlin plate theory and Reissner plate theory are fundamentally simpler to adopt for modelling the shear deformation behaviour of thick plates. However, both of these theories have been perceived to be the same, despite their profound differences in assumptions and formulations. This study aims to establish these differences between both theories by deriving bending relationships between Mindlin and Reissner plate quantities for a general plate problem. This general set of novel relationships is then specialized for the cases of rectangular plates with (1) all sides simply supported, (2) two opposite edges simply supported with the other two edges free, and (3) two opposite edges simply supported with the other two edges clamped. The specialized bending relationships clearly show the dissimilarity of the two theories for these plate problems.