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

Abstract

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.

On ensuring structural integrity for configurations with stress singularities: a review

“…Often these additional identifications are for more complex local configurations than those in the references in the cited reviews: sometimes they simply fill in a gap in the literature. For classical elasticity with local configurations comprised of isotropic and piecewise homogeneous, linear elastic materials, all the stress singularities asymptotically identified that have been found to date since 2004 are discussed in the studies . Examples of stress singularities identified since 2004 for anisotropic elastic materials are given in the previous studies ; for functionally graded elastic materials; for finite strain in elastic materials; and for varying size scales …”

Plane elasticity problem for a multi-wedge system with a thin wedge

“…The authors reported that in this case (i) there was no complex roots of the characteristic determinant, and (ii) the singularity was not stronger than the inverse root of the distance d to the wedge apex. No complex roots were reported later for the Coulomb law of dry friction by Gdoutos and Theocaris (1975), Comninou (1976) and Churchman et al (2004), and for an arbitrary system with frictionless contacts by Linkov and Rybarska-Rusinek (2010). Meanwhile, the extended studying has shown that in some cases the power of the singularity may be stronger than Oð1= ffiffiffi d p Þ both for dry friction (Churchman et al, 2004) and for smooth contacts (Linkov and Rybarska-Rusinek, 2010).…”

“…No complex roots were reported later for the Coulomb law of dry friction by Gdoutos and Theocaris (1975), Comninou (1976) and Churchman et al (2004), and for an arbitrary system with frictionless contacts by Linkov and Rybarska-Rusinek (2010). Meanwhile, the extended studying has shown that in some cases the power of the singularity may be stronger than Oð1= ffiffiffi d p Þ both for dry friction (Churchman et al, 2004) and for smooth contacts (Linkov and Rybarska-Rusinek, 2010). For the Coulomb friction law, it depends on the slip direction what is of importance for fretting problems (Churchman et al, 2004;Mugadu et al, 2004).…”

“…This approach provides a general model of contact interaction, which includes those of the paper (Mishuris and Kuhn, 2001) as particular cases. A further step in developing a general technique for simulating the influence of a thin wedge consisted in distinguishing those quantities, which do not turn to infinity when the angle H 0 tends to zero, and in solving the equations for embedding wedges with respect to these quantities (Linkov and Rybarska-Rusinek, 2010). The approach proved to provide simple physical models and remarkably accurate numerical results 0020-7683/$ -see front matter Ó 2010 Elsevier Ltd. All rights reserved.…”

“…The approach proved to provide simple physical models and remarkably accurate numerical results 0020-7683/$ -see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijsolstr.2010.08.004 (Linkov and Rybarska-Rusinek, 2010) in the particular case of smooth contacts in the plane-strain or plane-stress problems. In this case, the problem reduces to equations for scalar quantities.…”