Some New Developments in Contact Pressure Optimization

Relatively few works have dealt with the optimization problems of bodies in contact. The present work is intended as a contribution to the determination of contact pressure distribution in the frame of linear elasticity. Solution of frictionless contact problems are investigated not only on the basis of minimum complementary energy principle, but also on the basis of minimum total potentional energy by the use of an augmented Lagrangian technique. The goal is to optimize the pressure distribution along the contact region. The minimum of maximal pressure is looked for by controlling the pressure distribution. The optimization problem can be handled by a so-called restricted linear programming problem. Effectiveness of the augmented Lagrangian technique has been proved by axisymmetric and plane stress type numerical examples, i.e., the pressure can be calculated directly, solution of the contact problem can be obtained by means of a relatively small penalty parameter, solution of the optimization problem can be found in a relatively easy way.