How to use reactive stresses to improve plate-theory approximations of the stress field in a linearly elastic plate-like body

All plate theories allow for an approximate evaluation of the stress field in the associated three-dimensional plate-like bodies. We here show how such an approximation can be bettered by an appropriate use of the reactive stress fields that maintain in the three-dimensional body the kinematical constraints implicit in the formulation of a given plate theory. In particular, we discuss transversely extensible, linearly elastic plates and Reissner–Mindlin plates, two theories where the built-in second-order internal constraints turn out to be of importance to improve the evaluation of the stress fields in the corresponding three-dimensional bodies. In addition to arguing our point of view in general, we work out a few explicit examples, both analytically and numerically.