title: Ð£ÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ ÑÐ¾ÑÐ¼Ñ Ð¸Ð·Ð³Ð¸Ð±Ð° ÑÐ°ÑÐ½Ð¸ÑÐ½Ð¾-Ð¾Ð¿ÐµÑÑÐ¾Ð¹ Ð±Ð°Ð»ÐºÐ¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Stability of a flat form of bending of a hinged beam
Creators: name: ÐÐ²Ð¸Ð»Ð°, ÐÑÐ¼ÑÐµÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2022
Subjects: Ð±Ð°Ð»ÐºÐ°
ÑÐ¸ÑÑÑÐ¹ Ð¸Ð·Ð³Ð¸Ð±
ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸ ÑÐ¾ÑÐ½Ð°Ñ ÑÐµÐ¾ÑÐ¸Ñ ÑÑÐµÑÐ¶Ð½ÐµÐ¹
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Ð¿Ð¾ÑÐµÑÑ Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ ÑÐ¾ÑÐ¼Ñ ÑÐ°Ð²Ð½Ð¾Ð²ÐµÑÐ¸Ñ
ÑÐ»ÐµÐ´ÑÑÐ¸Ð¹ Ð¼Ð¾Ð¼ÐµÐ½Ñ
beam
pure bending
stability
geometrically exact theory of rods
critical load
loss of flat equilibrium
following moment

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description: The subject of the graduate qualification work is âStability of a flat form of bending of a hinged beamâ.The given work is devoted to studying a geometrically nonlinear articulated beam with pure bending. Tasks that were solved in the course of the study:Solution of the geometrically nonlinear problem of the statics of a hinged beam under pure bending;Solution of the problem of stability of a hinged beam under pure bending in the exact formulation;Solution of the problem of stability of a hinged beam under pure bending in a strongly linearized formulation;Obtaining a criterion for finding the critical moment.Â  Â  Â  Â The fulfilled work came out with a solution to the stability problem, to solve the problem of stability, a spatial model of the rod is used, which considers all types of deformation (tension, shear, bending, and torsion) and, for a complete understanding, various types of stiffness are considered. In this paper, a variational statement of the stability problem was applied, which is formulated as a search for the minimum point of the Lagrange functional. The stability functional is equal to the Lagrange function's second variation; in turn, the stability equation is the Euler equation for the stability function.Â  Â  Â  In this paper, a solution to the stability problem was obtained. As a result, a criterion for finding the critical moment is received in the form of a simple trigonometric equation. This equation is easy to solve by numerical methods using any software package, for this case Mathcad has been used. The solutions obtained in the thesis work can be used in the design of new structures, as well as in the reconstruction of structures for various purposes.