Analysis of interfaces of variable stiffness

The e€ects of an interface of variable sti€ness joining two elastic half-planes have been investigated under the hypothesis that the load is constituted by two equals and opposites concentrate forces applied at a certain distance from the interface. The integro-di€erential equation governing the problem has been determined by superposition principle and making use of the classical solution for concentrate force in an elastic plane. By applying the complex variable methods and the results of Muskhelishvili, the problem is reduced to that of two ordinary di€erential equations which have been easily integrated. The closed-form solution has been obtained for an arbitrary distribution of sti€ness and without restrictions on the position of the loads. Successively, the speci®c cases of a constant and parabolic distribution of sti€ness have been discussed in detail, and it has been shown how the general solution can be simpli®ed in these examples. These cases deserve an interest in practical applications, the former because permits to compute the distribution of interface stress, the latter because allows to detect the e€ects of the lost of interface sti€ness due, for example, to a damage or to a defect. The proposed solution can be used as a Green function to solve problems with arbitrary, but symmetric, distributions of loads