Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole

Aleksandra B. Vakaeva; Gleb M. Shuvalov; Sergey A. Kostyrko

doi:10.1063/5.0026622

Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole

Aleksandra B. Vakaeva, Gleb M. Shuvalov, Sergey A. Kostyrko

Research output › › peer-review

Abstract

In this paper, we discuss two approaches to study the stress concentration and distribution around a cylindrical nanohole with undulated surface profile based on the first-order boundary perturbation technique and finite element method, respectively. To describe the effect of surface elasticity, the simplified formulation of Gurtin - Murdoch model neglecting the surface tension is used. Taking into account the plane strain conditions, the corresponding boundary value problem is formulated for a 2-D infinite domain with a nearly circular hole. The detailed numerical investigations are given to compare the first-order boundary perturbation and finite element solutions.

Original language	English
Title of host publication	International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
Editors	Theodore E. Simos, Charalambos Tsitouras
Publisher	American Institute of Physics
ISBN (Electronic)	9780735440258
DOIs	https://doi.org/10.1063/5.0026622
Publication status	Published - 24 Nov 2020
Event	International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 - Rhodes Duration: 23 Sep 2019 → 28 Sep 2019

Publication series

Name	AIP Conference Proceedings
Volume	2293
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
Country	Greece
City	Rhodes
Period	23/09/19 → 28/09/19

Scopus subject areas

Physics and Astronomy(all)

Access to Document

10.1063/5.0026622

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1 выступление с устной презентацией

Two Approaches to Study Stress Concentration and Distribution in an Elastic Body with a Nearly Circular Nanohole
Александра Борисовна Вакаева (Keynote speaker), Глеб Михайлович Шувалов (Speaker) & Сергей Алексеевич Костырко (Speaker)
23 Sep 2019 → 28 Sep 2019
Activity

Cite this

Vakaeva, A. B., Shuvalov, G. M., & Kostyrko, S. A. (2020). Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole. In T. E. Simos, & C. Tsitouras (Eds.), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019 [360008] (AIP Conference Proceedings; Vol. 2293). American Institute of Physics. https://doi.org/10.1063/5.0026622

Vakaeva, Aleksandra B. ; Shuvalov, Gleb M. ; Kostyrko, Sergey A. / Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole. International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. editor / Theodore E. Simos ; Charalambos Tsitouras. American Institute of Physics, 2020. (AIP Conference Proceedings).

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title = "Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole",

abstract = "In this paper, we discuss two approaches to study the stress concentration and distribution around a cylindrical nanohole with undulated surface profile based on the first-order boundary perturbation technique and finite element method, respectively. To describe the effect of surface elasticity, the simplified formulation of Gurtin - Murdoch model neglecting the surface tension is used. Taking into account the plane strain conditions, the corresponding boundary value problem is formulated for a 2-D infinite domain with a nearly circular hole. The detailed numerical investigations are given to compare the first-order boundary perturbation and finite element solutions.",

author = "Vakaeva, {Aleksandra B.} and Shuvalov, {Gleb M.} and Kostyrko, {Sergey A.}",

note = "Funding Information: The research was supported by the Russian Science Foundation (project no. 19-71-00062). Publisher Copyright: {\textcopyright} 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 ; Conference date: 23-09-2019 Through 28-09-2019",

year = "2020",

month = nov,

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doi = "10.1063/5.0026622",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

editor = "Simos, {Theodore E.} and Charalambos Tsitouras",

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Vakaeva, AB , Shuvalov, GM & Kostyrko, SA 2020, Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole. in TE Simos & C Tsitouras (eds), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019., 360008, AIP Conference Proceedings, vol. 2293, American Institute of Physics, International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019, Rhodes, 23/09/19. https://doi.org/10.1063/5.0026622

Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole. / Vakaeva, Aleksandra B.; Shuvalov, Gleb M.; Kostyrko, Sergey A.

International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. ed. / Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics, 2020. 360008 (AIP Conference Proceedings; Vol. 2293).

Research output › › peer-review

TY - GEN

T1 - Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole

AU - Vakaeva, Aleksandra B.

AU - Shuvalov, Gleb M.

AU - Kostyrko, Sergey A.

N1 - Funding Information: The research was supported by the Russian Science Foundation (project no. 19-71-00062). Publisher Copyright: © 2020 American Institute of Physics Inc.. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/11/24

Y1 - 2020/11/24

N2 - In this paper, we discuss two approaches to study the stress concentration and distribution around a cylindrical nanohole with undulated surface profile based on the first-order boundary perturbation technique and finite element method, respectively. To describe the effect of surface elasticity, the simplified formulation of Gurtin - Murdoch model neglecting the surface tension is used. Taking into account the plane strain conditions, the corresponding boundary value problem is formulated for a 2-D infinite domain with a nearly circular hole. The detailed numerical investigations are given to compare the first-order boundary perturbation and finite element solutions.

AB - In this paper, we discuss two approaches to study the stress concentration and distribution around a cylindrical nanohole with undulated surface profile based on the first-order boundary perturbation technique and finite element method, respectively. To describe the effect of surface elasticity, the simplified formulation of Gurtin - Murdoch model neglecting the surface tension is used. Taking into account the plane strain conditions, the corresponding boundary value problem is formulated for a 2-D infinite domain with a nearly circular hole. The detailed numerical investigations are given to compare the first-order boundary perturbation and finite element solutions.

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U2 - 10.1063/5.0026622

DO - 10.1063/5.0026622

M3 - Conference contribution

AN - SCOPUS:85097983617

T3 - AIP Conference Proceedings

BT - International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019

A2 - Simos, Theodore E.

A2 - Tsitouras, Charalambos

PB - American Institute of Physics

T2 - International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019

Y2 - 23 September 2019 through 28 September 2019

ER -

Vakaeva AB , Shuvalov GM , Kostyrko SA. Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole. In Simos TE, Tsitouras C, editors, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019. American Institute of Physics. 2020. 360008. (AIP Conference Proceedings). https://doi.org/10.1063/5.0026622

Two approaches to study stress concentration and distribution in an elastic body with a nearly circular nanohole

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Two Approaches to Study Stress Concentration and Distribution in an Elastic Body with a Nearly Circular Nanohole

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