title: ÐÐ¾Ð»ÑÑÐ´Ð²Ð¸Ð³Ð¾Ð²Ð°Ñ ÑÐµÐ¾ÑÐ¸Ñ Ð.Ð. Ð¡Ð»Ð¸ÐºÐµÑÐ° Ð² Ð·Ð°Ð´Ð°ÑÐ°Ñ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÐ¾Ð½ÐºÐ¾ÑÑÐµÐ½Ð½ÑÑ ÑÑÐµÑÐ¶Ð½ÐµÐ¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Semi-shear theory V.I.Slivker's in problems of stability of thin-walled rods
Creators: name: ÐÐ·Ð°ÑÐ¾Ð², ÐÑÑÑÑ
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: 2019
Subjects: Ð¡ÑÐµÑÐ¶Ð½Ð¸ ÑÐ¾Ð½ÐºÐ¾ÑÑÐµÐ½Ð½ÑÐµ
Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¼Ð°ÑÑÐ¸ÑÐ° Ð¶ÐµÑÑÐºÐ¾ÑÑÐ¸
Ð¿Ð¾Ð»ÑÑÐ´Ð²Ð¸Ð³Ð¾Ð²Ð°Ñ ÑÐµÐ¾ÑÐ¸Ñ
ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð½Ð°Ð³ÑÑÐ·ÐºÐ°

description: ÐÐ¾ÑÐºÐ¾Ð»ÑÐºÑ Ð¿Ð¾ÑÐµÑÑ Ð½ÐµÑÑÑÐµÐ¹ ÑÐ¿Ð¾ÑÐ¾Ð±Ð½Ð¾ÑÑÐ¸ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ ÑÐ¶Ð°ÑÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð² ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹ Ð¸Ð· ÐÐ¡Ð¢Ð Ð¿ÑÐ¾Ð¸ÑÑÐ¾Ð´Ð¸Ñ Ð¿ÑÐ¸ Ð¾Ð±ÑÐµÐ¹ Ð¿Ð¾ÑÐµÑÐµ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¸ Ð´Ð»Ñ Ð½ÐµÐºÐ¾ÑÐ¾ÑÑÑ Ð¸Ð· Ð½Ð¸Ñ Ð½ÐµÑ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ, Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐµÑÑÑ Ð¾ÑÐ¾Ð±Ð¾ Ð¸Ð½ÑÐµÑÐµÑÐ½ÑÐ¼ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¸Ðµ Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¸ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÐµÐµ ÑÐµÑÐµÐ½Ð¸Ðµ. 
Ð Ð´Ð°Ð½Ð½Ð¾Ð¼ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð±ÑÐ»Ð¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ñ Ð¼Ð°ÑÑÐ¸ÑÑ Ð¶ÐµÑÑÐºÐ¾ÑÑÐ¸ Ð¸ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¶ÐµÑÑÐºÐ¾ÑÑÐ¸ Ð¿ÑÐ¸ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐ½Ð¾Ð¹ Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¸ Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ð¾Ð² Ð­ÑÐ¼Ð¸ÑÐ°, Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð¸ÑÑÑÑÐ¸Ñ ÑÑÐ½ÐºÑÐ¸Ð¸ ÑÐ³Ð»Ð° Ð·Ð°ÐºÑÑÑÐ¸Ð²Ð°Ð½Ð¸Ñ Ð¸ Ð´ÐµÐ¿Ð»Ð°Ð½Ð°ÑÐ¸Ð¸. ÐÐ¾Ð»ÑÑÐµÐ½Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ ÐºÑÐ¸ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð½Ð°Ð³ÑÑÐ·ÐºÐ¸ Ð¾Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÐÐ­ Ð´Ð»Ñ ÑÐ°Ð·Ð½ÑÑ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¸ ÐºÐ¸Ð½ÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð³ÑÐ°Ð½Ð¸ÑÐ½ÑÑ ÑÑÐ»Ð¾Ð²Ð¸Ð¹. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð° Ð½ÐµÑÐ¾ÑÑÐ¾ÑÑÐµÐ»ÑÐ½Ð¾ÑÑÑ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸Ð¸ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¼Ð¸ ÑÑÐ½ÐºÑÐ¸ÑÐ¼Ð¸ ÑÐ¾ÑÐ¼ Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ ÐºÐ²Ð°Ð´ÑÐ°ÑÐ¸ÑÐ½Ð¾Ð¹ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸ÐµÐ¹, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÐµÑÑÑ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð¹, ÑÐ°Ðº ÐºÐ°Ðº Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¸ ÑÑÐ°Ð·Ñ Ð´Ð¾ÑÑÐ¸Ð³Ð°ÐµÑ ÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ, Ð¿ÑÐ¸ Ð¸Ð·Ð³Ð¸Ð±Ð½Ð¾-ÐºÑÑÑÐ¸Ð»ÑÐ½Ð¾Ð¹ ÑÐ¾ÑÐ¼Ðµ Ð¿Ð¾ÑÐµÑÐ¸ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸. ÐÐ»Ñ ÑÐ¸ÑÑÐ¾ ÐºÑÑÑÐ¸Ð»ÑÐ½Ð¾Ð¹ Ð¸Ð»Ð¸ Ð¸Ð·Ð³Ð¸Ð±Ð½Ð¾Ð¹ ÑÐ¾ÑÐ¼Ñ Ð¿Ð¾ÑÐµÑÐ¸ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð°Ð¿Ð¿ÑÐ¾ÐºÑÐ¸Ð¼Ð°ÑÐ¸Ñ ÑÑÐ½ÐºÑÐ¸Ð¹ ÑÐ³Ð»Ð° Ð·Ð°ÐºÑÑÑÐ¸Ð²Ð°Ð½Ð¸Ñ Ð¸ Ð´ÐµÐ¿Ð»Ð°Ð½Ð°ÑÐ¸Ð¸ Ð¿ÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¿Ð¾Ð»Ð¸Ð½Ð¾Ð¼Ð°Ñ Ð­ÑÐ¼Ð¸ÑÐ° Ð½Ðµ Ð´Ð°ÐµÑ Ð±Ð¾Ð»ÐµÐµ Ð±ÑÑÑÑÐ¾Ð¹ ÑÑÐ¾Ð´Ð¸Ð¼Ð¾ÑÑÐ¸.
description: The loss of bearing capacity of some compressed Self-framing metal structures elements occurs with a general buckling and for some of them there is no analytical solution. That is why consideration of the problem variational statement and its numerical solution is particular interesting. In this study, the stiffness and geometric stiffness matrices were obtained for Hermite polynomials quadratic variation that approximate the functions of the twist angle and deplanation functions.
The dependences of the critical load on the number of finite elements for different geometric and kinematic boundary conditions are obtained. The inconsistency of the approximation by forms linear functions is shown in comparison with the quadratic approximation, which turns out to be optimal. The reason is that it almost immediately reaches the exact analytical solution, with a flexural-torsional form of buckling. For a purely torsional or flexural form of buckling, it is shown that functions of the twist angle and deplanation functions approximation for different Hermite polynomials does not give faster convergence.