Influence of Surface Stresses on the Nanoplate Stiffness and Stability in the Kirsch Problem

Research output

Abstract

A system of von Karman equations for a nanoplate has been generalized by introducing effective tangential and flexural stiffnesses and elastic moduli, with regard to surface elasticity and residual surface stresses on the outer surfaces. A modified Kirsch problem was solved for the case of an infinite nanoplate with a circular hole under plane stress in terms of effective elastic moduli. Two forms of local stability loss in this problem and the corresponding critical load for two different elastic characteristics of all plate surfaces were determined numerically and analytically. The dependence of the effective stiffnesses and elastic moduli on the plate thickness, and of the critical load on the hole radius (size effect) was discussed.

Original languageEnglish
Pages (from-to)209-223
Number of pages15
JournalPhysical Mesomechanics
Volume22
Issue number3
DOIs
Publication statusPublished - 1 May 2019

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stiffness
Stiffness
modulus of elasticity
Elastic moduli
Von Karman equation
plane stress
Elasticity
elastic properties
radii

Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Surfaces and Interfaces

Cite this

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title = "Influence of Surface Stresses on the Nanoplate Stiffness and Stability in the Kirsch Problem",
abstract = "A system of von Karman equations for a nanoplate has been generalized by introducing effective tangential and flexural stiffnesses and elastic moduli, with regard to surface elasticity and residual surface stresses on the outer surfaces. A modified Kirsch problem was solved for the case of an infinite nanoplate with a circular hole under plane stress in terms of effective elastic moduli. Two forms of local stability loss in this problem and the corresponding critical load for two different elastic characteristics of all plate surfaces were determined numerically and analytically. The dependence of the effective stiffnesses and elastic moduli on the plate thickness, and of the critical load on the hole radius (size effect) was discussed.",
keywords = "effective stiffnesses and elastic moduli, Kirsch problem, nanoplate, plane stress, size effect, stability, surface stress",
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AU - Grekov, M. A.

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N2 - A system of von Karman equations for a nanoplate has been generalized by introducing effective tangential and flexural stiffnesses and elastic moduli, with regard to surface elasticity and residual surface stresses on the outer surfaces. A modified Kirsch problem was solved for the case of an infinite nanoplate with a circular hole under plane stress in terms of effective elastic moduli. Two forms of local stability loss in this problem and the corresponding critical load for two different elastic characteristics of all plate surfaces were determined numerically and analytically. The dependence of the effective stiffnesses and elastic moduli on the plate thickness, and of the critical load on the hole radius (size effect) was discussed.

AB - A system of von Karman equations for a nanoplate has been generalized by introducing effective tangential and flexural stiffnesses and elastic moduli, with regard to surface elasticity and residual surface stresses on the outer surfaces. A modified Kirsch problem was solved for the case of an infinite nanoplate with a circular hole under plane stress in terms of effective elastic moduli. Two forms of local stability loss in this problem and the corresponding critical load for two different elastic characteristics of all plate surfaces were determined numerically and analytically. The dependence of the effective stiffnesses and elastic moduli on the plate thickness, and of the critical load on the hole radius (size effect) was discussed.

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KW - Kirsch problem

KW - nanoplate

KW - plane stress

KW - size effect

KW - stability

KW - surface stress

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