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Fundamental solution of a plane problem of elasticity theory for a composite anisotropic medium

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Abstract

The plane problem on the action of an arbitrarily oriented concentrated force, applied at some point of an elastic plane, composed of two different anisotropic half-planes, is considered. By a special choice of a particular solution the problem reduces to a well-known differential equation of the anisotropic theory of elasticity with discontinuous coefficients. The latter reduces, by the method of the integral Fourier transform, to the Riemann boundary value problem. Expressions for the stresses and displacement derivatives at an arbitrary point of the plane are obtained. The application of the obtained results is illustrated on the example of a problem on an elastic linear inclusion (strap).

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Additional information

Translated from Dinamicheskie Sistemy, No. 4, pp. 40–45, 1985.

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Krivoi, A.F., Radiollo, M.V. Fundamental solution of a plane problem of elasticity theory for a composite anisotropic medium. J Math Sci 60, 1365–1368 (1992). https://doi.org/10.1007/BF01679639

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Keywords

  • Differential Equation
  • Fourier
  • Fourier Transform
  • Fundamental Solution
  • Plane Problem