Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
Stresses analysis of a plane with elliptical inclusion for the model of the semi-linear material. / Малькова, Юлия Вениаминовна; Мальков, Вениамин Михайлович.
8th Polyakhov's Reading: Proceedings of the International Scientific Conference on Mechanics. ред. / Elena V. Kustova; Gennady A. Leonov; Mikhail P. Yushkov; Nikita F. Morosov; Mariia A. Mekhonoshina. Том 1959 American Institute of Physics, 2018. 070022 (AIP Conference Proceedings; Том 1959).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
}
TY - GEN
T1 - Stresses analysis of a plane with elliptical inclusion for the model of the semi-linear material
AU - Малькова, Юлия Вениаминовна
AU - Мальков, Вениамин Михайлович
N1 - Conference code: 8
PY - 2018/5/2
Y1 - 2018/5/2
N2 - The exact analytical solution of nonlinear problem of elasticity (plane stress and plane strain) for a plane with elastic elliptic inclusion is obtained. The external constant nominal (Piola) stresses are given at infinity of a plane. The continuity conditions for the stress and displacement are satisfied on the boundary of the inclusion. The mechanical properties of the plane and inclusion are described by a model of semi-linear material. For this material methods of the theory of functions of a complex variable are using for solving nonlinear plane problems. The stresses and displacements are expressed through two analytic functions of a complex variable, which are defined from the nonlinear boundary conditions on a boundary of inclusion. The assumption is made that the stress state of the inclusion is homogeneous (the tensor of nominal stresses is constant). The hypothesis has allowed to reduce a difficult nonlinear problem of elliptic inclusion to the solution of two simpler problems (first and second) for a plane with an elliptic hole. The validity of this hypothesis has proven to that obtained solution precisely satisfies to all equations and boundary conditions of a problem. The similar hypothesis was used earlier for solving linear and nonlinear problems of elliptic inclusion. Using general solution, the solutions of some particular nonlinear problems are obtained: a plane with a free elliptic hole and a plane with a rigid inclusion. The stresses are calculated on the contour of inclusion for different material parameters.
AB - The exact analytical solution of nonlinear problem of elasticity (plane stress and plane strain) for a plane with elastic elliptic inclusion is obtained. The external constant nominal (Piola) stresses are given at infinity of a plane. The continuity conditions for the stress and displacement are satisfied on the boundary of the inclusion. The mechanical properties of the plane and inclusion are described by a model of semi-linear material. For this material methods of the theory of functions of a complex variable are using for solving nonlinear plane problems. The stresses and displacements are expressed through two analytic functions of a complex variable, which are defined from the nonlinear boundary conditions on a boundary of inclusion. The assumption is made that the stress state of the inclusion is homogeneous (the tensor of nominal stresses is constant). The hypothesis has allowed to reduce a difficult nonlinear problem of elliptic inclusion to the solution of two simpler problems (first and second) for a plane with an elliptic hole. The validity of this hypothesis has proven to that obtained solution precisely satisfies to all equations and boundary conditions of a problem. The similar hypothesis was used earlier for solving linear and nonlinear problems of elliptic inclusion. Using general solution, the solutions of some particular nonlinear problems are obtained: a plane with a free elliptic hole and a plane with a rigid inclusion. The stresses are calculated on the contour of inclusion for different material parameters.
UR - http://www.scopus.com/inward/record.url?scp=85047188760&partnerID=8YFLogxK
U2 - 10.1063/1.5034697
DO - 10.1063/1.5034697
M3 - Conference contribution
VL - 1959
T3 - AIP Conference Proceedings
BT - 8th Polyakhov's Reading
A2 - Kustova, Elena V.
A2 - Leonov, Gennady A.
A2 - Yushkov, Mikhail P.
A2 - Morosov, Nikita F.
A2 - Mekhonoshina, Mariia A.
PB - American Institute of Physics
T2 - International Scientific Conference on Mechanics - Eighth Polyakhov's Reading
Y2 - 29 January 2018 through 2 February 2018
ER -
ID: 36152191