Fundamental Solution for the Generalized Plane Stress of a Nanoplate

Research output

Abstract

The fundamental solution for the generalized plane-stress problem of an infinite, isotropic elastic plate subjected to a point force is presented taking into account surface stresses in the plate faces. Constitutive equations is derived using the stress-strain relations for the bulk material and Gurtin–Murdoch’s linearized surface elasticity equations for the surfaces of the plate supposing that the residual surface stress is negligibly small compared with the surface elasticity parameters. The complex relations (Green functions) for the stresses and displacements in the explicit form are evaluated using Goursat–Kolosov complex potentials and Muskhelishvili representations. It is shown that in the case of the generalized plane stress, the fundamental solution depends on the thickness of the plate that is the size effect intrinsic to the nanoobjects
Original languageEnglish
Pages (from-to)157-164
Number of pages8
JournalAdvanced Structured Materials
DOIs
Publication statusPublished - 14 Mar 2019

Fingerprint

Elasticity
Constitutive equations
Green's function

Cite this

@article{2e76d4f52f0d45b6b98119fcbd8ee4ba,
title = "Fundamental Solution for the Generalized Plane Stress of a Nanoplate",
abstract = "The fundamental solution for the generalized plane-stress problem of an infinite, isotropic elastic plate subjected to a point force is presented taking into account surface stresses in the plate faces. Constitutive equations is derived using the stress-strain relations for the bulk material and Gurtin–Murdoch’s linearized surface elasticity equations for the surfaces of the plate supposing that the residual surface stress is negligibly small compared with the surface elasticity parameters. The complex relations (Green functions) for the stresses and displacements in the explicit form are evaluated using Goursat–Kolosov complex potentials and Muskhelishvili representations. It is shown that in the case of the generalized plane stress, the fundamental solution depends on the thickness of the plate that is the size effect intrinsic to the nanoobjects",
keywords = "Generalized plane stress Surface stress Green functions",
author = "{Grekov M.A.}",
year = "2019",
month = "3",
day = "14",
doi = "10.1007/978-3-030-13307-8_12",
language = "English",
pages = "157--164",
journal = "Advanced Structured Materials",
issn = "1869-8433",
publisher = "Springer",

}

TY - JOUR

T1 - Fundamental Solution for the Generalized Plane Stress of a Nanoplate

AU - Grekov M.A., null

PY - 2019/3/14

Y1 - 2019/3/14

N2 - The fundamental solution for the generalized plane-stress problem of an infinite, isotropic elastic plate subjected to a point force is presented taking into account surface stresses in the plate faces. Constitutive equations is derived using the stress-strain relations for the bulk material and Gurtin–Murdoch’s linearized surface elasticity equations for the surfaces of the plate supposing that the residual surface stress is negligibly small compared with the surface elasticity parameters. The complex relations (Green functions) for the stresses and displacements in the explicit form are evaluated using Goursat–Kolosov complex potentials and Muskhelishvili representations. It is shown that in the case of the generalized plane stress, the fundamental solution depends on the thickness of the plate that is the size effect intrinsic to the nanoobjects

AB - The fundamental solution for the generalized plane-stress problem of an infinite, isotropic elastic plate subjected to a point force is presented taking into account surface stresses in the plate faces. Constitutive equations is derived using the stress-strain relations for the bulk material and Gurtin–Murdoch’s linearized surface elasticity equations for the surfaces of the plate supposing that the residual surface stress is negligibly small compared with the surface elasticity parameters. The complex relations (Green functions) for the stresses and displacements in the explicit form are evaluated using Goursat–Kolosov complex potentials and Muskhelishvili representations. It is shown that in the case of the generalized plane stress, the fundamental solution depends on the thickness of the plate that is the size effect intrinsic to the nanoobjects

KW - Generalized plane stress Surface stress Green functions

U2 - 10.1007/978-3-030-13307-8_12

DO - 10.1007/978-3-030-13307-8_12

M3 - Article

SP - 157

EP - 164

JO - Advanced Structured Materials

JF - Advanced Structured Materials

SN - 1869-8433

ER -