Inequality constraints with elastic impacts in deformable bodies. The convex case

The aim of the present paper is to present some new results for problems wh en impacts occur. We prove, in the framework of linear elastic body, certai n equivalent form of the d'Alembert's principle, including velocity discont inuity. We show that the theorem of stationary action still holds as an ine quality. The consideration of the variation of the unknown impact time impl ies for the impact problem certain new variational expressions in inequalit y form.