Optimal shape design of contact surfaces

The present study is concerned with the developmentand application of optimization techniques in compatiblewith automated direct method to design optimal shape forcontacting surfaces.The design problem is formulated as a nonlinear math-ematical programming model. The minimization for the peakcontact stress is our objective function. The limitationson surface contours and stresses to keep contacting bodieswithin allowable limit are considered as constraints. Thenonlinear mathematical model has been solved by applyingtwo optimization techniques, Fibonacci search method andpenalty function method.A finite element code appended with the automateddirect method algorithm, and the two optimization techni-ques have been implemented for two dimensional problems.The program was used to solve several applications, speci-fically a truss on misaligned supports, a beam on an ~la-stic foundation, a body of curved surface pressed againsta flat elastic strata and Hertzian problem of two cylin-ders in contact. In each case both of the Fibonacci searchand interior penalty function methods are applied and athorough comparison has been illustrated.