Stability of a compressed-tensioned rod of variable cross-section with combined loading

Author:

Kulterbaev H. P.1,Payzulaev M. M.2

Affiliation:

1. North Caucasus Federal University

2. Daghestan State Technical University

Abstract

Objective. The purpose of the study is to determine the stability of a straight rod of variable cross-section under combined axial loading. Method. The longitudinal bending of the rod is described by the classical theory using Bernoulli’s hypothesis, and the critical forces are determined from the Euler problem with appropriate assumptions. Result. An algorithm for a numerical method for solving the problem of determining the eigenvalues of the differential equation for longitudinal bending of a rod is proposed. External loads are considered “dead”. The functions of changing the variable cross-sectional area, variable stiffness and distributed load are considered given. The curved axis of the rod after bifurcation is described using a linear ordinary differential equation. Conclusion. The implementation of the numerical method was carried out by the finite difference method using numerical methods and modern computer software.

Publisher

FSB Educational Establishment of Higher Education Daghestan State Technical University

Reference15 articles.

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2. Samarsky A.A., Gulin A.V. Numerical methods. M.: Nauka, 1989; 432. (In Russ)

3. Ilyin V.P., Karpov V.V., Maslennikov A.M. Numerical methods for solving problems of structural mechanics. – M.: Publishing house ASV; St. Petersburg: SPbGASU, 2005; 425. (In Russ)

4. Baragunova L.A. Determination of the critical force of a compressed rod by the finite difference method. Nalchik: Bulletin of Kabardino-Balkarian State University. 2000; 13. (In Russ)

5. Kulterbaev K., Lafisheva M., Baragunova L. (2022). Solving the Euler Problem for a Flexible Support Rod Base on the Finite Difference Method. In: Tchernykh, A., Alikhanov, A., Babenko, M., Samoylenko, I. (eds) Math-ematics and its Applications in New Computer Systems. MANCS 2021. Lecture Notes in Networks and Systems, vol 424. Springer, Cham.

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