Abstract

The paper compares analytical and numerical solutions for 2-D problems of an elastic body with a nanometer surface relief that arises on a free planar boundary of a solid and on a free surface of a nearly circular hole. Analytical results are based on simplified Gurtin - Murdoch's surface elasticity theory and first-order boundary perturbation procedure. Finite element method is used to get numerical results for both types of the periodic nanometer relief.

Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018
EditorsT.E. Simos, T.E. Simos, T.E. Simos, T.E. Simos, Ch. Tsitouras, T.E. Simos
PublisherAmerican Institute of Physics
ISBN (Electronic)9780735418547
DOIs
Publication statusPublished - 24 Jul 2019
EventInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018 - Rhodes
Duration: 13 Sep 201818 Sep 2018

Publication series

NameAIP Conference Proceedings
Volume2116
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2018, ICNAAM 2018
CountryGreece
CityRhodes
Period13/09/1818/09/18

Fingerprint

elastic bodies
relief
modeling
elasticity (mechanics)
finite element method
elasticity
elastic properties
perturbation
methodology

Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology
  • Plant Science
  • Physics and Astronomy(all)
  • Nature and Landscape Conservation

Cite this

Vakaeva, A. B., Shuvalov, G. M., Kostyrko, S. A., & Grekov, M. A. (2019). The finite element modeling of an elastic body with a nanometer surface relief. In T. E. Simos, T. E. Simos, T. E. Simos, T. E. Simos, C. Tsitouras, & T. E. Simos (Eds.), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018 [290008] (AIP Conference Proceedings; Vol. 2116). American Institute of Physics. https://doi.org/10.1063/1.5114300
Vakaeva, Aleksandra B. ; Shuvalov, Gleb M. ; Kostyrko, Sergey A. ; Grekov, Mikhail A. / The finite element modeling of an elastic body with a nanometer surface relief. International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018. editor / T.E. Simos ; T.E. Simos ; T.E. Simos ; T.E. Simos ; Ch. Tsitouras ; T.E. Simos. American Institute of Physics, 2019. (AIP Conference Proceedings).
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abstract = "The paper compares analytical and numerical solutions for 2-D problems of an elastic body with a nanometer surface relief that arises on a free planar boundary of a solid and on a free surface of a nearly circular hole. Analytical results are based on simplified Gurtin - Murdoch's surface elasticity theory and first-order boundary perturbation procedure. Finite element method is used to get numerical results for both types of the periodic nanometer relief.",
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Vakaeva, AB, Shuvalov, GM, Kostyrko, SA & Grekov, MA 2019, The finite element modeling of an elastic body with a nanometer surface relief. in TE Simos, TE Simos, TE Simos, TE Simos, C Tsitouras & TE Simos (eds), International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018., 290008, AIP Conference Proceedings, vol. 2116, American Institute of Physics, Rhodes, 13/09/18. https://doi.org/10.1063/1.5114300

The finite element modeling of an elastic body with a nanometer surface relief. / Vakaeva, Aleksandra B.; Shuvalov, Gleb M.; Kostyrko, Sergey A.; Grekov, Mikhail A.

International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018. ed. / T.E. Simos; T.E. Simos; T.E. Simos; T.E. Simos; Ch. Tsitouras; T.E. Simos. American Institute of Physics, 2019. 290008 (AIP Conference Proceedings; Vol. 2116).

Research outputpeer-review

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AB - The paper compares analytical and numerical solutions for 2-D problems of an elastic body with a nanometer surface relief that arises on a free planar boundary of a solid and on a free surface of a nearly circular hole. Analytical results are based on simplified Gurtin - Murdoch's surface elasticity theory and first-order boundary perturbation procedure. Finite element method is used to get numerical results for both types of the periodic nanometer relief.

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Vakaeva AB, Shuvalov GM, Kostyrko SA, Grekov MA. The finite element modeling of an elastic body with a nanometer surface relief. In Simos TE, Simos TE, Simos TE, Simos TE, Tsitouras C, Simos TE, editors, International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2018. American Institute of Physics. 2019. 290008. (AIP Conference Proceedings). https://doi.org/10.1063/1.5114300