New types of variational principles based on the notion of quasidifferentiability

Abstract

In this paper several new types of variational principles are derived by using the new mathematical notion of quasidifferentiability. As a model problem we consider the static analysis problem of deformable bodies subjected to nonmonotone boundary and interface conditions. The nonmonotone laws are produced from appropriately defined nonsmooth and, nonconvex, quasidifferentiable superpotentials by means of the quasidifferential operator in the sense of V. F. Dem'yanov. The static analysis problem is formulated as a system of variational inequalities which is equivalent, minmax formulation, or equivalently as a multivalued quasidifferential inclusion problem which describes the positions(s) of static equilibrium of the body. The theory is illustrated by numerical examples concerning the calculation of adhesive joints.