On the incompatibility between the equivalent shear force concept and the integral formulation of contact problems between Kirchhoff plates and irregular linear supports

It is shown that, when employing the integral formulation to describe contact problems between Kirchhoff plates and irregular linear supports, the equivalent shear force concept may be incompatible with the integral approach. In such circumstances the equivalent shear force concept has to be abandoned in favour of an equivalent twisting moment approach. A classical example of an infinite plate resting on a linear central segment is revisited in the light of the equivalent twisting moment concept, where all the computations are carried out in exact form. An additional example is developed to show that the usefulness of an integral approach based upon the equivalent twisting moment concept remains valid even when the equivalent twisting moment is applied at a plate border along which the twisting moment must be null, as it occurs in a partially clamped border. The reaction singularity at the endpoints of a linear support is examined with the Williams asymptotic method. Finally, a physical interpretation is proposed for the adoption of a distributed twisting moment among the contact reactions.