On the classical theory of plates

In the traditional description of the classical theory of plates the shear forces, by definition, are integrals over the plate thickness of the transversal shear stresses. This leads to a breakdown of Hooke's law for these stresses, inconsistency of the equations of equilibrium of the classical theory of plates with the principle of virtual work and the occurrence of contradictions of the type which exist in the problem of a beam bent statically by equivalent loads. These drawbacks of the traditional description can be eliminated if we assume that the shear forces, by definition, are statically equivalent to "rotated" bending and twisting moments (which, in the case of the classical theory of plates, is not related to the St Venant principle). This treatment of the shear forces is the basis of a proposed version of the description of the classical theory of plates. An analysis is also given of publications in which doubts are expressed regarding the correctness of the classical theory of plates. It is shown that the arguments put forward in these publications do not justify dispensing with the classical theory of plates.