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Stability and bifurcations of eccentrically reinforced compound shell structures by means of computer algebra

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Parent Category: 2026

Category: Content №4 2026

Created on 24 August 2026

Last Updated on 24 August 2026

Published on 30 November -0001

Written by D. V. Hryshchak, V. Z. Gristchak, N. M. Dyachenko, V. O. Kuprikov

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Authors:

D. V. Hryshchak, orcid.org/0009-0009-8428-6520, Pivdenne State Design Office named after M. K. Yangel, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V. Z. Gristchak*, orcid.org/0000-0001-8685-3191, Dnipro University of Technology, Dnipro, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

N. M. Dyachenko, orcid.org/0000-0001-5284-4502, Zaporizhzhia National University, Zaporizhzhia, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

V. O. Kuprikov, orcid.org/0009-0008-3221-582X, Zaporizhzhia National University, Zaporizhzhia, Ukraine, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2026, (4): 077 - 088

https://doi.org/10.33271/nvngu/2026-4/077

Abstract:

Purpose. To develop an analytical-numerical approach and algorithms for applying a computer algebra system (CAS) to analyze the influence of the arrangement of reinforcing load-carrying elements on the stability of compound orthogonally stiffened shell structures under combined external loading. Achieving this objective involves deriving governing stability equations and developing algorithms for studying the dependence of critical loads on geometric and stiffness parameters of compartments, the arrangement of reinforcing structural elements, and the character of external loading

Methodology. A methodology for deriving the governing equations using the Maple system is proposed, along with an algorithm for numerical solution of the stability problem by the finite-difference method with computer visualization of bifurcation modes for the compartments and the compound shell system.

Findings. Based on computer algebra systems, an approach to solving the stability problem of a compound stiffened “cone–cylinder” shell system under combined external loading taking into account specific stiffness characteristics of the compartments is proposed. Algorithms are proposed for studying the influence of eccentricity of the reinforcing system, discrete arrangement of ring stiffeners, and visualization of the investigated processes with determination of characteristic bifurcation modes and construction of boundary curves separating the stability domain of the investigated structure under dominant external pressure.

Originality. The influence of eccentricity of reinforcing load-carrying elements relative to the midsurface of a compound shell structure under two-parameter loading by axial compressive forces and external pressure is established. Specific features of the influence of stiffness characteristics of the reinforcing system are identified based on the proposed algorithm for automated derivation of governing differential equations using computer algebra systems. Numerical results for critical loads of a “cone-cylinder” type system are presented.

Practical value. The conducted analysis makes it possible to identify the influence of the arrangement and stiffness characteristics of reinforcing load-carrying elements on the load-bearing capacity of compound “cone–cylinder” shell systems. The interaction of local and global bifurcation modes under combined loading is taken into account. The application of computer algebra systems enables the construction of boundary curves separating the stability region of the investigated system depending on the arrangement and configuration of stiffening ribs. The obtained results enable the design of structures that are rational with respect to the critical state.

Keywords: computer algebra, compound shell, stiffening elements, eccentricity, stability equations, bifurcation modes

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