On a variational formula and its application to contact problems of elasticity theory (Q756515)

A variational formula is obtained for the spatial contact problem (CP) of the theory of elasticity. This formula determines the variation of the normal stress on the contact area caused by a variation in the contact area outline. The efficiency of the variational formula is shown for constructing an asymptotic expansion for the spatial CP with a continuous line of separation of the boundary conditions. The solution of the CP is considered in detail for an elastic half-space when the contact area differs slightly from a circle.