Research article Vol. 21 No. 3 (2025): International Journal for Computational Civil and Structural Engineering

THE MODIFIED METHOD OF SEQUENTIAL LOADS FOR THE ANALYSIS OF SLENDER SHALLOW SHELLS

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THE MODIFIED METHOD OF SEQUENTIAL LOADS FOR THE ANALYSIS OF SLENDER SHALLOW SHELLS

Authors

  • Vladilen Petrov Yuri Gagarin State Technical University of Saratov, Saratov, RUSSIA
  • Olga Gorbacheva Yuri Gagarin State Technical University of Saratov, Saratov, RUSSIA

DOI:

https://doi.org/10.22337/2587-9618-2025-21-3-201-208

Keywords:

geometric nonlinearity, zero approximation selection, collocation method, collocation node selection, golden ratio, solution residual, critical load

Abstract

This study discusses specific features of analyzing shallow shells using a modified sequential load method and a collocation method. This combination shows a rapid rate of convergence when the golden section principle is used to select the collocation node system.

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References

Petrov, V.V. Nonlinear Structural Mechan-ics, second edition, expanded: textbook / V.V. Petrov. – Moscow: ASV Publishing House, 2024. – 504 p.

Zenkevich, O. The Finite Element Method in Engineering. Moscow: Mir Publishing House, 1975. 541 pp.

Ilyin, V.P., Karpov, V.V., Maslennikov, A.M. Numerical Methods for Solving Prob-lems in Structural Mechanics. Moscow: ASV Publishing House, 2005. 425 p.

Volmir, A.S. Slender Plates and Shells / A.S. Volmir. Moscow: Gostekhizdat, 1956. 419 p.

Petrov V.V. Nonlinear Structural Analysis Based on the Modified Sequential Load Method / V. V. Petrov // International Jour-nal for Computational Civil and Structural Engineering. – 2021. – Vol. 17, No. 4. – P. 146-152.

Petrov, V. V. Modified method of sequen-tial loads in nonlinear structural mechanics / V. V. Petrov, R. V. Mishchenko, O. A. Gorbacheva // Fundamental, exploratory, and applied research by the RAASN on sci-entific support for the development of archi-tecture, urban planning, and the construction industry in the Russian Federation in 2021: Collection of scientific works by the RAASN / Russian Academy of Architecture and Construction Sciences. Volume 2. – Moscow: ASV Publishing House, 2022. – Pp. 339-349.

Petrov V.V. The method of sequential loads in nonlinear plate and shell theory / Saratov: Saratov University Press, 1975. – 119 p.

Gorbacheva O.A. On the calculation of plates using the collocation method / O.A. Gorbacheva // Expert: Theory and Practice. – 2023. – No. 1(20). – P. 69-72.

Petrov V.V., Gorbacheva O.A. Calculation of a plate made of nonlinearly elastic mate-rial using the collocation method // Bulletin of the Volga Regional Branch of the Russian Academy of Architecture and Construction Sciences: Collection of scientific papers. – Nizhny Novgorod: Nizhny Novgorod State University of Architecture and Civil Engi-neering, 2023. – Pp. 124-128.

Korobko V.I. , Korobko G.N. The Golden Ratio and Man, second edition, supplement-ed and revised. – Moscow: ASV Publishing House, 2002. – 394 p.

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Published

2025-09-29

How to Cite

Petrov, V., & Gorbacheva, O. (2025). THE MODIFIED METHOD OF SEQUENTIAL LOADS FOR THE ANALYSIS OF SLENDER SHALLOW SHELLS. International Journal for Computational Civil and Structural Engineering, 21(3), 201-208. https://doi.org/10.22337/2587-9618-2025-21-3-201-208

Keywords

geometric nonlinearity, zero approximation selection, collocation method, collocation node selection, golden ratio, solution residual, critical load

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