Standard

Modified Kirsch problem incorporating surface stresses under plane stress. / Vakaeva A.B., ; Grekov M.A.

X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023. Vol. Simulation methods for coupled problems, 42 2023.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Vakaeva A.B., & Grekov M.A. 2023, Modified Kirsch problem incorporating surface stresses under plane stress. in X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023. vol. Simulation methods for coupled problems, 42 , X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023, Chania, Greece, 5/06/23.

APA

Vakaeva A.B., & Grekov M.A. (2023). Modified Kirsch problem incorporating surface stresses under plane stress. In X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023 (Vol. Simulation methods for coupled problems, 42 )

Vancouver

Vakaeva A.B. , Grekov M.A. Modified Kirsch problem incorporating surface stresses under plane stress. In X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023. Vol. Simulation methods for coupled problems, 42 . 2023

Author

Vakaeva A.B., ; Grekov M.A. / Modified Kirsch problem incorporating surface stresses under plane stress. X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023. Vol. Simulation methods for coupled problems, 42 2023.

BibTeX

@inproceedings{a3e2c29e9e4b42f78b55e844736ae6f5,
title = "Modified Kirsch problem incorporating surface stresses under plane stress",
abstract = "We consider the Kirsch problem, taking into account the surface stresses at the boundary of the circular hole and on the front surfaces of the plate, in the framework of the original Gurtin–Murdoch model. The boundary conditions on the cylindrical surface of a circular hole in a nanoplate are derived in terms of a complex variable in the case of the plane stress state. The solution of the two-dimensional problem for an infinite plane with a circular hole under remote loading is explicitly obtained. Based on the analytical solution, we investigated the dependence of the elastic stress field on the nanosised plate thickness and dimension of the hole. Numerical examples are given in the paper to illustrate quantitatively the effect of the plate thickness at the nanoscale on the stress field at and near the cylindrical surface. The results are presented graphically as the dependence of the components of the stress tensor on the polar angle.",
keywords = "Surface Stress, Gurtin{Murdoch Model, 2-D Boundary Conditions, Kirsch Problem, Circular Hole, Plane Stress",
author = "{Vakaeva A.B.} and {Grekov M.A.}",
year = "2023",
month = nov,
day = "2",
language = "English",
volume = "Simulation methods for coupled problems, 42 ",
booktitle = "X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023",
note = "X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023, COUPLED 2023 ; Conference date: 05-06-2023 Through 07-06-2023",
url = "https://coupled2023.cimne.com/",

}

RIS

TY - GEN

T1 - Modified Kirsch problem incorporating surface stresses under plane stress

AU - Vakaeva A.B., null

AU - Grekov M.A., null

N1 - Conference code: 10

PY - 2023/11/2

Y1 - 2023/11/2

N2 - We consider the Kirsch problem, taking into account the surface stresses at the boundary of the circular hole and on the front surfaces of the plate, in the framework of the original Gurtin–Murdoch model. The boundary conditions on the cylindrical surface of a circular hole in a nanoplate are derived in terms of a complex variable in the case of the plane stress state. The solution of the two-dimensional problem for an infinite plane with a circular hole under remote loading is explicitly obtained. Based on the analytical solution, we investigated the dependence of the elastic stress field on the nanosised plate thickness and dimension of the hole. Numerical examples are given in the paper to illustrate quantitatively the effect of the plate thickness at the nanoscale on the stress field at and near the cylindrical surface. The results are presented graphically as the dependence of the components of the stress tensor on the polar angle.

AB - We consider the Kirsch problem, taking into account the surface stresses at the boundary of the circular hole and on the front surfaces of the plate, in the framework of the original Gurtin–Murdoch model. The boundary conditions on the cylindrical surface of a circular hole in a nanoplate are derived in terms of a complex variable in the case of the plane stress state. The solution of the two-dimensional problem for an infinite plane with a circular hole under remote loading is explicitly obtained. Based on the analytical solution, we investigated the dependence of the elastic stress field on the nanosised plate thickness and dimension of the hole. Numerical examples are given in the paper to illustrate quantitatively the effect of the plate thickness at the nanoscale on the stress field at and near the cylindrical surface. The results are presented graphically as the dependence of the components of the stress tensor on the polar angle.

KW - Surface Stress, Gurtin{Murdoch Model, 2-D Boundary Conditions, Kirsch Problem, Circular Hole, Plane Stress

UR - https://www.scipedia.com/public/Vakaeva_Grekov_2023a

M3 - Conference contribution

VL - Simulation methods for coupled problems, 42

BT - X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023

T2 - X International Conference on Computational Methods for Coupled Problems in Science and Engineering COUPLED PROBLEMS 2023

Y2 - 5 June 2023 through 7 June 2023

ER -

ID: 114412020