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

Abstract

International audienceIn 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. (C) 2006 Elsevier Ltd. All rights reserved

Stress analysis of the adhesive resin layer in a reinforced pin-loaded joint used in glass structures

“…In particular, it is shown that the difference between the analytical solution and the finite element one is negligible once the resin is sufficiently soft. The analytical results obtained by the present work can be used to predict the first cracking loading of a reinforced pin-loaded joint [10]. They are also useful for obtaining a closed-form solution for the contact stress on the bolt-ring surface (see [10] for details).…”

“…The softer the resin becomes, the analytical solution fits the better the numerical solution (see Figs. [5][6][7][8][9][10]. This conclusion can be extended to the case where the compliance increase has a geometrical origin, for instance, the resin layer becomes thicker.…”

On the conforming contact problem in a reinforced pin-loaded structure with a non-zero second Dundurs’ constant

“…Under the condition that the shear modulus l 2 of the resin layer is much smaller than the shear moduli l 1 and l 3 of the bolt and glass plate, i.e. l 2 ( minðl 1 ; l 3 Þ, To et al (2007) have shown that the integral equation governing the foregoing frictionless contact problem takes the form…”

“…However, approximate solutions can be obtained by making some physically based simplifications. It is known from To et al (2007) that, if q is sufficiently large, the infinite series P 1 n¼2 b n H n sin nh= sin h can be approximated by a finite one P k n¼2 b n H n sin nh= sin h so as to derive a simple closed-form solution to Eq. (11).…”

Failure analysis of tempered glass structures with pin-loaded joints

“…Third, the residual stresses in the tempered glass plate must be taken into account. In the past, works were carried out on the elastic analysis and failure analysis of pin-loaded joints (see Noble & Hussain (1969), Lin & Lin (1999), Hyer & Klang (1969), To et al (2006), Ramazan et al (2006), Tserpes et al (2002) and the cited references). However, to the best of the authors' knowledge, they did not account for the ring reinforcement and the residual stresses.…”