Interface conditions simulating influence of a thin elastic wedge with smooth contacts

The paper presents a method for deriving interface conditions simulating the influence of a thin wedge in a multi-wedge system with smooth contacts. It consists in successive (i) employing the Mellin’s transform, (ii) separation of the symmetric and anti-symmetric parts of a solution, (iii) distinguishing terms tending to infinity, when the wedge angle tends to zero, (iv) appropriate re-arrangement of the terms to avoid degeneration, (v) using truncated power series in equations for the thin wedge and (vi) inspection of the characteristic determinant and finding models simulating the influence of the thin wedge for various combinations of parameters. The paper extends and improves the results previously obtained by the authors for a harmonic problem. The analysis leads to three physical models of contact interaction, which cover all the ratios of shear modules of a thin wedge and neighbour wedges. Numerical examples illustrate the accuracy provided by the method employed and the models derived.