On almost constant contact stress distributions by shape optimization

Abstract

This paper addresses the problem of finding shapes of contacting bodies avoiding undesirable stress concentrations. It has previously been shown that designing the shape of a rigid body in contact with a fixed linear elastic body by minimizing the equilibrium potential energy under an isoparametric constraint results in a uniform contact pressure distribution. As an extension of this result, it is shown here that when the shape of an elastic body in contact with a flat rigid foundation is chosen on the same premises, the uniform pressure distribution is found only if displacement gradients can be considered small. From the point of view of applications, an important conclusion is that this smallness holds in a case when linear elasticity is physically valid.