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

Summary The aim of the present paper is to present some new results for problems when impacts occur. We prove, in the framework of linear elastic body, certain equivalent form of the d'Alembert's principle, including velocity discontinuity. We show that the theorem of stationary action still holds as an inequality. The consideration of the variation of the unknown impact time implies for the impact problem certain new variational expressions in inequality form. Received 13 August 1998; accepted for publication 6 May 1999