Effect of surface stress on strength of a plate with elliptical and triangular nanoscale holes.

M. Grekov, N. Morozov, A. Yazovskaya

Research output

Abstract

The 2D problem on an arbitrary nanohole in an infinite elastic body under remote loading is solved. It is assumed that complementary surface stress is acting at the boundary of the hole. Corresponding boundary conditions are formulated according to the generalized Young-Laplace equations. The Gurtin–Murdoch surface elasticity model is applied to take into account the surface stress eﬀect. Based on Goursat–Kolosov complex potentials and Muskhelishvili’s technique and using conformal mapping of the outside of the hole on the outside of the circle, the solution of the problem is reduced to a singular integro-diﬀerential equation in an unknown surface stress. For a nearly circular hole, the boundary perturbation method is used that leads to successive solutions of hypersingular integral equations. In the case of elliptical and triangular holes, these equations are solved for the first-order approximation and corresponding expressions for stresses are derived in an explicit form. The influence of the surface st
Original language English 1669-1674 Procedia Materials Science 3 https://doi.org/10.1016/j.mspro.2014.06.269 Published - 2014

Fingerprint

elastic bodies
Laplace equation
conformal mapping
integral equations
elastic properties
boundary conditions
perturbation
approximation

Cite this

@article{db970a0ec54c443986a593bf48a8d1ea,
title = "Effect of surface stress on strength of a plate with elliptical and triangular nanoscale holes.",
abstract = "The 2D problem on an arbitrary nanohole in an infinite elastic body under remote loading is solved. It is assumed that complementary surface stress is acting at the boundary of the hole. Corresponding boundary conditions are formulated according to the generalized Young-Laplace equations. The Gurtin–Murdoch surface elasticity model is applied to take into account the surface stress eﬀect. Based on Goursat–Kolosov complex potentials and Muskhelishvili’s technique and using conformal mapping of the outside of the hole on the outside of the circle, the solution of the problem is reduced to a singular integro-diﬀerential equation in an unknown surface stress. For a nearly circular hole, the boundary perturbation method is used that leads to successive solutions of hypersingular integral equations. In the case of elliptical and triangular holes, these equations are solved for the first-order approximation and corresponding expressions for stresses are derived in an explicit form. The influence of the surface st",
keywords = "Nanohole, surface stress, hypersingular integral equation, stress concentration",
author = "M. Grekov and N. Morozov and A. Yazovskaya",
year = "2014",
doi = "10.1016/j.mspro.2014.06.269",
language = "English",
volume = "3",
pages = "1669--1674",
journal = "Procedia Materials Science",
issn = "2211-8128",

}

In: Procedia Materials Science, Vol. 3, 2014, p. 1669-1674.

Research output

TY - JOUR

T1 - Effect of surface stress on strength of a plate with elliptical and triangular nanoscale holes.

AU - Grekov, M.

AU - Morozov, N.

AU - Yazovskaya, A.

PY - 2014

Y1 - 2014

N2 - The 2D problem on an arbitrary nanohole in an infinite elastic body under remote loading is solved. It is assumed that complementary surface stress is acting at the boundary of the hole. Corresponding boundary conditions are formulated according to the generalized Young-Laplace equations. The Gurtin–Murdoch surface elasticity model is applied to take into account the surface stress eﬀect. Based on Goursat–Kolosov complex potentials and Muskhelishvili’s technique and using conformal mapping of the outside of the hole on the outside of the circle, the solution of the problem is reduced to a singular integro-diﬀerential equation in an unknown surface stress. For a nearly circular hole, the boundary perturbation method is used that leads to successive solutions of hypersingular integral equations. In the case of elliptical and triangular holes, these equations are solved for the first-order approximation and corresponding expressions for stresses are derived in an explicit form. The influence of the surface st

AB - The 2D problem on an arbitrary nanohole in an infinite elastic body under remote loading is solved. It is assumed that complementary surface stress is acting at the boundary of the hole. Corresponding boundary conditions are formulated according to the generalized Young-Laplace equations. The Gurtin–Murdoch surface elasticity model is applied to take into account the surface stress eﬀect. Based on Goursat–Kolosov complex potentials and Muskhelishvili’s technique and using conformal mapping of the outside of the hole on the outside of the circle, the solution of the problem is reduced to a singular integro-diﬀerential equation in an unknown surface stress. For a nearly circular hole, the boundary perturbation method is used that leads to successive solutions of hypersingular integral equations. In the case of elliptical and triangular holes, these equations are solved for the first-order approximation and corresponding expressions for stresses are derived in an explicit form. The influence of the surface st

KW - Nanohole

KW - surface stress

KW - hypersingular integral equation

KW - stress concentration

U2 - 10.1016/j.mspro.2014.06.269

DO - 10.1016/j.mspro.2014.06.269

M3 - Article

VL - 3

SP - 1669

EP - 1674

JO - Procedia Materials Science

JF - Procedia Materials Science

SN - 2211-8128

ER -