The clamped plate with nonlinear elastic obstable (Q1195010)

Summary: We model the problem of a linear elastic plate resting on elastic subgrade in the case of a nonlinear response of this obstacle. In particular, we assume a unilateral nature of the contact and a cubic force-displacement relationship to describe the constitutive law of the subgrade. This model is a generalization of Winkler's one and is very useful to describe in some approximate way many technical cases. We prove existence and uniqueness results for this problem in the appropriate analytical framework, by using the functional analysis methods and the variational inequalities theory results.