### 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 language | English |
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Title of host publication | EIGHTH POLYAKHOV'S READING |

Subtitle of host publication | Proceedings of the International Scientific Conference on Mechanics |

Editors | Elena V. Kustova, Gennady A. Leonov, Mikhail P. Yushkov, Nikita F. Morosov, Mariia A. Mekhonoshina |

Publisher | American Institute of Physics |

Number of pages | 7 |

ISBN (Electronic) | 9780735416604 |

DOIs | |

Publication status | Published - 2 May 2018 |

Event | Восьмые Поляховские чтения: международная научная конференция по механике - Старый Петергоф, Saint Petersburg Duration: 29 Jan 2018 → 2 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

Name | AIP Conference Proceedings |
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Number | 1 |

Volume | 1959 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | International Scientific Conference on Mechanics - Eighth Polyakhov's Reading |
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Country | Russian Federation |

City | Saint Petersburg |

Period | 29/01/18 → 2/02/18 |

Internet address |

### Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*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

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*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.

Research output

TY - GEN

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.

KW - INITIAL FUNCTIONS

KW - BIHARMONIC PROBLEM

KW - EQUILIBRIUM

KW - RECTANGLE

UR - http://www.scopus.com/inward/record.url?scp=85047183221&partnerID=8YFLogxK

U2 - 10.1063/1.5034688

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

ER -