Riemann–Hilbert problem on a hyperelliptic surface and uniformly stressed inclusions embedded into a half-plane subjected to antiplane strain

@article{Antipov2021RiemannHilbertPO,
  title={Riemann–Hilbert problem on a hyperelliptic surface and uniformly stressed inclusions embedded into a half-plane subjected to antiplane strain},
  author={Yuri A. Antipov},
  journal={Proceedings of the Royal Society A},
  year={2021},
  volume={477}
}
  • Y. Antipov
  • Published 28 April 2021
  • Mathematics
  • Proceedings of the Royal Society A
An inverse problem of the elasticity of n elastic inclusions embedded into an elastic half-plane is analysed. The boundary of the half-plane is free of traction. The half-plane and the inclusions are subjected to antiplane shear, and the conditions of ideal contact hold in the interfaces between the inclusions and the half-plane. The shapes of the inclusions are not prescribed and have to be determined by enforcing uniform stresses inside the inclusions. The method of conformal mappings from a… 

Figures from this paper

References

SHOWING 1-10 OF 29 REFERENCES
Method of Riemann surfaces for an inverse antiplane problem in an n-connected domain
  • Y. Antipov
  • Mathematics
    Complex Variables and Elliptic Equations
  • 2019
ABSTRACT An inverse problem of the theory of harmonic functions for an n-connected domain is analyzed. The problem is equivalent to a problem of antiplane elasticity on determination of the profiles
Uniform fields inside two non-elliptical inclusions
The problem of two non-elliptical inclusions with internal uniform fields embedded in an infinite matrix, subjected at infinity to a uniform stress field, is discussed in detail by means of the
Uniform strain fields inside multiple inclusions in an elastic infinite plane under anti-plane shear
This paper constructs multiple elastic inclusions with prescribed uniform internal strain fields embedded in an infinite matrix under given uniform remote anti-plane shear. The method used is based
Slit Maps in the Study of Equal-Strength Cavities in n-Connected Elastic Planar Domains
TLDR
A family of conformal mappings from a parametric slit domain onto the $n-connected elastic domain is constructed and it is shown that for any $n\ge 1$ there always exists a set of the loading parameters for which these zeros generate inadmissible poles of the solution.
Inverse problems of the plane theory of elasticity: PMM vol. 38, n≗ 6, 1974, pp. 963–979
Method of automorphic functions for an inverse problem of antiplane elasticity
  • Y. Antipov
  • Mathematics
    The Quarterly Journal of Mechanics and Applied Mathematics
  • 2019
A nonlinear inverse problem of antiplane elasticity for a multiply connected domain is examined. It is required to determine the profile of $n$ uniformly stressed inclusions when the surrounding
Boundary value problems in the theory of analytic functions in Hölder classes on Riemann surfaces
This paper is based on the papers, written mainly during the last decade, on the investigation and solution of boundary value problems in the theory of analytic functions on finite oriented Riemann
Motion of a Yawed Supercavitating Wedge Beneath a Free Surface
TLDR
A closed-form solution to the governing nonlinear boundary-value problem is found by the method of conformal mappings and the doubly connected flow domain is treated as the image by this map of the exterior of two slits in a parametric plane.
Uniform stresses inside a non-elliptical inhomogeneity and a nearby half-plane with locally wavy interface
We develop a two-parameter conformal mapping function for a doubly connected domain to solve the inverse problem in anti-plane and plane elasticity associated with a non-elliptical inhomogeneity with
...
...