An elementary derivation of basic equations of the Reissner and Mindlin plate theories

The basic equations of the Reissner and Mindlin plate theories are derived in an elementary way from the underlying assumptions of the theories about the distribution of in-plane stresses in the Reissner case and the distribution of displacement components in the Mindlin case. The derived equations include a parameter which allows the interpretation of the theories as an approximation of isotropic plates or transversally inextensible plates. Qualitative comportment between the theories is also given.