In this paper, the method of Muskhelishvili’s complex potentials is used to solve the boundary value problem of elasticity theory for a domain in the form of a ring with piecewise constant boundary conditions on the contour. The solution is obtained in an analytical form and it is put to a form suitable for numerical simulation. It is established that in the neighborhood of the contour there is deformation of the region close to the shift (on the sections of the boundary with a nonzero boundary condition) or to radial compression (on the parts of the boundary with the zero boundary condition).
[1] Muskhelishvili, NI (1966). Some basic problems of mathematical theory of elasticity. Moscow: Science.
[2] Anpilohov, D., Snizhko, N. (2017). The angular deformation of the ring with reference to the centrifugal forces. Lobachevskii Journal of Mathematics, 38 (3), 395-399.
[3] Anpilohov, D., Snizhko, N. (2017). Deformation of the ring by an unevenly distributed moment. Modern Problems of Physics and Mathematics: Materials of the III International Scientific and Practical Conference. Orel: OGU, 225-231.
- ACS Style
- Anpilohov, D.I.; Snizhko , N.V. On one border problem of ring domain deformation. Bukovinian Mathematical Journal. 2018, 6 https://doi.org/https://doi.org/10.31861/bmj2018.01.006
- AMA Style
- Anpilohov DI, Snizhko NV. On one border problem of ring domain deformation. Bukovinian Mathematical Journal. 2018; 6(1-2). https://doi.org/https://doi.org/10.31861/bmj2018.01.006
- Chicago/Turabian Style
- Dmytro Igorovich Anpilohov, Natalia Viktorivna Snizhko . 2018. "On one border problem of ring domain deformation". Bukovinian Mathematical Journal. 6 no. 1-2. https://doi.org/https://doi.org/10.31861/bmj2018.01.006