Closed-form solution for the contact problem of reinforced pin-loaded joints used in glass structures

In a typical pin-loaded joint used to assemble glass plates, the hole in a glass plate is reinforced by a steel ring glued to the glass plate via a soft resin layer. Thus, the ring is in direct contact with the steel bolt and prevents the glass plate from high stress concentration. This paper proposes an analytical approach to solving the resulting conforming contact problem. The strain and stress fields inside the resin layer are first determined by exploiting the fact that the stiffness of the material constituting it is much smaller than the stiffness of steel and glass. After finding the relevant Green functions for the ring and pin, the frictionless contact between them is then formulated in terms of an integral equation with a Fourier series as the kernel. This integral equation is solved by neglecting the terms of high orders and transforming it into the Cauchy singular integral equation. The derived analytical results for the contact pressure and angle are finally compared to and validated by those obtained by the finite element method.