Identification of contact pressures between deformable bodies by combining finite elements and a novel hybrid minimization strategy

The contact pressure between elastic bodies is of foremost importance in connection with the design and manufacturing of machines. The analysis of contact problems has attracted considerable attention from many industries and researchers. This study presents a novel methodology based on a constrained optimization technique for the inverse problem of determining the contact pressure and the size of the contact region using known displacements on the traction-free boundary. Two examples are utilized to demonstrate the proposed method. The first problem is a rigid block pressing across the edge of an elastic plate while the second problem is the contact between a washer and a base body widely used as a joining method in automotive applications. Various constraint equations on the minimization are presented and their effects on the results are inspected. It is found the calculated results in both contact pressure and size of the contact region are in close agreement with the simulation.