Optimal shape design for contact problems

A new optimization problem of controlling the contact pressurep is presented. We seek the minimum of the maximum contact pressurep _max under the following conditions: (a) the contact pressure should satisfy the inequalityp 0 as well as the controlling condition = v(x) p _max –p(x) 0, wherev(x) is the controller function; (b) the gapd between two bodies should be positive or zerod 0 after deformation; (c) at any possible contact point the conditionpd = 0 should be satisfied and the body that is capable of rigid body motion should be in equilibrium.If the gapd = d(p, h) is a linear function of both the pressurep and the contour changeh, then the optimization problem is a linear programming problem of restricted basis exchange. Three algorithms are presented for the solution of this problem. Finally, numerical examples will demonstrate the controlling technique for the shape optimization problem of a roller bearing.