Superposition Principle for the Tensionless Contact of a Beam Resting on a Winkler or a Pasternak Foundation

AbstractA Green function–based approach is presented to address the nonlinear tensionless contact problem for beams resting on either a Winkler or a Pasternak two-parameter elastic foundation. Unlike the traditional solution procedure, this approach allows determination of the contact locus position independently from the deflection curves. By doing so, a general nonlinear connection between the loading and the contact locus is found, which enlightens the specific features of the loading that affect the position of the contact locus. It is then possible to build load classes sharing the property that their application leads to the same contact locus. Within such load classes, the problem is linear and a superposition principle holds. Several applications of the method are presented, including symmetric and nonsymmetric contact layouts, which can be hardly tackled within the traditional solution procedure. Whenever possible, results are compared with the existing literature.