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.
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Acknowledgments
The work is supported by the Polish Ministry of Science and Higher Education as a scientific project for 2010-2012 (N N519 440739). The authors also appreciate the support of the Russian Fund of Fundamental Researches (09-05-00104) at the early stage of the work.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Linkov, A., Rybarska-Rusinek, L. Interface conditions simulating influence of a thin elastic wedge with smooth contacts. Arch Appl Mech 81, 1203–1214 (2011). https://doi.org/10.1007/s00419-010-0479-7
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DOI: https://doi.org/10.1007/s00419-010-0479-7