Some optimization problems foe bodies in quasi-steadi state wear

The problem of optimization of contact interaction of a moving rigid punch and an elastic half-space is investigated taking into account friction and wear. The punch shape is accepted as a desirable design variable and the volumetric wear rate under constraints on the friction dissipation power and the total load, applied to the punch, is taken as an optimized quality criterion. The ratio of the volumetric wear rate and the friction dissipation power under constraint on the total load is also considered as a suitable objective functional. A necessary condition for the optimality in quasi-steady state wear process is derived and discussed. The optimization problem is investigated analytically and exact solutions are obtained for the axysimmetric (stamp) punch which has a circular contact region and moves translationally with a constant velocity or rotates with constant angular velocity