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2014 | Vol. 66, nr 2 | 113--125
Tytuł artykułu

Solvability of a theory of anti-plane shear with partially coated boundaries

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the anti-plane shear of an elastic solid whose boundary is partially reinforced by a thin solid film represented by the union of a finite number of open curves. The solvability of the resulting boundary value problems is complicated by the presence of end-point conditions which must be satisfied at the ends of each section of the reinforcing film. In order to avoid complicated solvability conditions which carry no clear physical meaning, we modify the boundary integral equation method using an equivalent (lower-order) reinforcement condition which leads to the desired solvability results for the corresponding boundary value problems.
Wydawca

Rocznik
Strony
113--125
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
  • Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada, sigaeva@ualberta.ca
  • Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada, p.schiavone@ualberta.ca
Bibliografia
  • 1. D.J. Steigmann, R.W. Ogden, Plane deformations of elastic solids with intrinsic boundary elasticity, Proc. R. Soc. Lond. A., 453, 853–877, 1997.
  • 2. P. Chhapadia, P. Mohammadia P. Sharma, Curvature-dependent surface energy and implications for nanostructures, J. Mech. Phys. Solids, 59, 2103–2115, 2011.
  • 3. J. Wang, Z. Huang, H. Duan, S. Yu, X. Feng, G. Wang, W. Zhang, T. Wang, Surface stress effect in mechanics of nanostructured materials, Acta Mechanica Solida Sinica, 24, 1, 52–82, 2011.
  • 4. T. Sigaeva, P. Schiavone, Solvability of the Laplace equation in a solid with boundary reinforcement, Z. Angew. Math. Phys. (ZAMP), accepted.
  • 5. J.R.M. Radok, Problems of plane elasticity for reinforced boundaries, J. Appl. Mech., 77, 246–254, 1955.
  • 6. C. Constanda, Direct and Indirect Boundary Integral Equation Methods, Chapman & Hall/CRC, Boca Raton-London-New York-Washington, DC, 1999.
  • 7. P.A. Martin, End-point behaviour of solutions to hypersingular integral equations, Proc. R. Soc. London A, 432, 301–320, 1991.
  • 8. V.D. Kupradze, Potential methods in the theory of elasticity, [translated from Russian by H. Gutfreund], edited by I. Meroz, Israel Program for Scientific Translations, Jerusalem, 1965.
  • 9. T. Sigaeva, P. Schiavone, The effect of surface stress on an interface crack in linearny elastic materials, to appear.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-b44e3764-fec9-422b-aa0d-91f07ca5dc5e
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