# On Solvability of the BVP Formulated in Terms of Displacement Orientations on the Interface between Dissimilar Elastic Materials

On Solvability of the BVP Formulated in Terms of Displacement Orientations on the Interface between Dissimilar Elastic Materials

Galybin, A.N.

The Schmidt Institute of Physics of the Earth (IPE RAS), Moscow, Russia

Page:
369-376
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DOI:
https://doi.org/10.2495/CMEM-V5-N3-369-376
N/A
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Accepted:
N/A
| | Citation

OPEN ACCESS

Abstract:

This article addresses a specific type of boundary conditions in plane elastic boundary value problems, BVP. An elastic plane composed of two dissimilar isotropic materials is considered. It is assumed that the displacement vector orientations are known on both sides of the contour that separates the entire plane into interior and exterior domains. The stress vector is assumed to be continuous across the contour.

The aim of this study is the investigation of solvability of this BVP and the development of appropriate numerical methods for solving the corresponding singular integral equation. The latter is necessary as the integral equation is homogeneous.

It is shown that depending on the behaviour of the displacement vector orientations the solution of the problem may include a certain number of arbitrary linear parameters. A numerical approach is proposed based on the solution of the homogeneous Riemann BVP to form a non-homogeneous right hand side of the integral equation.

Keywords:

boundary value problems, complex potentials, plane elasticity, singular integral equations

References

[1] Gakhov, F.D., Boundary value problems. Moscow, Nauka, 1977, 3rd Russian edition, see also the translation of the first edition by Pergamon Press, 1966.

[2] Galybin, A.N., Boundary value problems of plane elasticity involving orientations of displacements and tractions. Journal of Elasticity, 102, pp. 15–30, 2011.

http://dx.doi.org/10.1007/s10659-010-9259-4

[3] Muskhelishvili, N.I., Some basic problems of the mathematical theory of elasticity. Springer-Verlag: Netherland, 1963.

[4] Galybin, A.N., Boundary integral equations for plane elastic problems posed in terms of stress orientations. Proceeding of the 8th UK Conference on Boundary Integral Meth-ods, ed. D. Lesnic, University of Leeds, UK, July 2011.