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 shownthat, when employing the integral formulation to describe contact problemsbetween Kirchhoff plates and irregular linear supports, the equivalent shear force concept maybe incompatible with the integral approach. In such circumstances the equivalent shear forceconcept has to be abandoned in favour of an equivalent twisting moment approach. A classicalexample of an infinite plate resting on a linear central segment is revisited in the light of theequivalent 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 basedupon the equivalent twisting moment concept remains valid even when the equivalent twistingmoment is applied at a plate border along which the twisting moment must be null, as it occursin a partially clamped border. The reaction singularity at the endpoints of a linear support isexamined with theWilliams asymptotic method. Finally, a physical interpretation is proposed forthe adoption of a distributed twisting moment among the contact reactions