Approximate analytical solutions in the analysis of elastic structures of complex geometry

Dmitriy Goloskokov, A. Matrosov

Research output

1 Citation (Scopus)

Abstract

A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

Original languageEnglish
Title of host publicationEIGHTH POLYAKHOV'S READING
Subtitle of host publicationProceedings of the International Scientific Conference on Mechanics
EditorsElena V. Kustova, Gennady A. Leonov, Mikhail P. Yushkov, Nikita F. Morosov, Mariia A. Mekhonoshina
PublisherAmerican Institute of Physics
Number of pages7
ISBN (Electronic)9780735416604
DOIs
Publication statusPublished - 2 May 2018
EventВосьмые Поляховские чтения: международная научная конференция по механике - Старый Петергоф, Saint Petersburg
Duration: 29 Jan 20182 Feb 2018
Conference number: 8
https://events.spbu.ru/events/polyakhov_readings
http://nanomat.spbu.ru/en/node/175
http://nanomat.spbu.ru/ru/node/192
http://spbu.ru/news-events/calendar/viii-polyahovskie-chteniya

Publication series

NameAIP Conference Proceedings
Number1
Volume1959
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Scientific Conference on Mechanics - Eighth Polyakhov's Reading
CountryRussian Federation
CitySaint Petersburg
Period29/01/182/02/18
Internet address

Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Goloskokov, D., & Matrosov, A. (2018). Approximate analytical solutions in the analysis of elastic structures of complex geometry. In E. V. Kustova, G. A. Leonov, M. P. Yushkov, N. F. Morosov, & M. A. Mekhonoshina (Eds.), EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics [070013] (AIP Conference Proceedings; Vol. 1959, No. 1). American Institute of Physics. https://doi.org/10.1063/1.5034688
Goloskokov, Dmitriy ; Matrosov, A. / Approximate analytical solutions in the analysis of elastic structures of complex geometry. EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. editor / Elena V. Kustova ; Gennady A. Leonov ; Mikhail P. Yushkov ; Nikita F. Morosov ; Mariia A. Mekhonoshina. American Institute of Physics, 2018. (AIP Conference Proceedings; 1).
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abstract = "A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.",
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Goloskokov, D & Matrosov, A 2018, Approximate analytical solutions in the analysis of elastic structures of complex geometry. in EV Kustova, GA Leonov, MP Yushkov, NF Morosov & MA Mekhonoshina (eds), EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics., 070013, AIP Conference Proceedings, no. 1, vol. 1959, American Institute of Physics, Saint Petersburg, 29/01/18. https://doi.org/10.1063/1.5034688

Approximate analytical solutions in the analysis of elastic structures of complex geometry. / Goloskokov, Dmitriy; Matrosov, A.

EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. ed. / Elena V. Kustova; Gennady A. Leonov; Mikhail P. Yushkov; Nikita F. Morosov; Mariia A. Mekhonoshina. American Institute of Physics, 2018. 070013 (AIP Conference Proceedings; Vol. 1959, No. 1).

Research output

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T1 - Approximate analytical solutions in the analysis of elastic structures of complex geometry

AU - Goloskokov, Dmitriy

AU - Matrosov, A.

PY - 2018/5/2

Y1 - 2018/5/2

N2 - A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

AB - A method of analytical decomposition for analysis plane structures of a complex configuration is presented. For each part of the structure in the form of a rectangle all the components of the stress-strain state are constructed by the superposition method. The method is based on two solutions derived in the form of trigonometric series with unknown coefficients using the method of initial functions. The coefficients are determined from the system of linear algebraic equations obtained while satisfying the boundary conditions and the conditions for joining the structure parts. The components of the stress-strain state of a bent plate with holes are calculated using the analytical decomposition method.

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KW - BIHARMONIC PROBLEM

KW - EQUILIBRIUM

KW - RECTANGLE

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DO - 10.1063/1.5034688

M3 - Conference contribution

T3 - AIP Conference Proceedings

BT - EIGHTH POLYAKHOV'S READING

A2 - Kustova, Elena V.

A2 - Leonov, Gennady A.

A2 - Yushkov, Mikhail P.

A2 - Morosov, Nikita F.

A2 - Mekhonoshina, Mariia A.

PB - American Institute of Physics

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Goloskokov D, Matrosov A. Approximate analytical solutions in the analysis of elastic structures of complex geometry. In Kustova EV, Leonov GA, Yushkov MP, Morosov NF, Mekhonoshina MA, editors, EIGHTH POLYAKHOV'S READING: Proceedings of the International Scientific Conference on Mechanics. American Institute of Physics. 2018. 070013. (AIP Conference Proceedings; 1). https://doi.org/10.1063/1.5034688