Diamond Open Access

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Numerical treatment of frictionless contact optimization problems is presented on the basis of linear elasticity. The minimum of the pressure maximum or other mechanical values (torque, frictional power loss) is sought by controlling the pressure distribution. Smooth contact pressure distribution can be achieved by using an appropriate controlling function on the controlling subdomain. The contact problems are investigated by means of the principle of minimum complementary energy and using the augmented Lagrangian technique. Axially symmetric problems are discretized by p-version finite elements. The optimal shape of a roller bearing is determined by the application of a new controlling function, which takes the rigid body translation and rotation of the roller into consideration. Effectiveness of the proposed algorithms is demonstrated by numerical examples.