title: ÐÐ¾Ð¸ÑÐº ÑÐ¼Ð¿Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð´Ð¾Ð¿Ð¾Ð»Ð½Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÑÐ»Ñ ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸ ÐºÑÐ¸Ð²Ð¾Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð³Ð¾ ÑÑÐµÑÐ¶Ð½Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ¾Ð²
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: Search for an empirical expression to determine the additional modulus of elasticity of a curvilinear rod based on numerical experiments
Creators: name: Ð¨Ð¸Ð±Ð°ÐµÐ², Ð¡ÑÐµÐ¿Ð°Ð½
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: 2023
Subjects: Ð¡ÑÐµÑÐ¶Ð½Ð¸ ÐºÑÐ¸Ð²Ð¾Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÐµ
ÐÐ°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ

description: Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÑÐ»Ñ Ð32 Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½ÑÐ¼ ÑÐ°Ð½ÐµÐµ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼, Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿Ð¾Ð»ÑÑÐ°ÐµÐ¼ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹, Ð° Ð¸Ð¼ÐµÐ½Ð½Ð¾ Ð¸Ñ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑ Ð¾Ñ Ð´ÑÑÐ³Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¸ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÑ ÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²ÐºÐ¸ Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ñ Ð´Ð»Ñ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð32. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. Ð¢ÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð¹ ÑÐ°Ð½ÐµÐµ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÑÐ»Ñ Ð32 Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¾Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð¸ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¹. 2. ÐÐ¾Ð´Ð³Ð¾ÑÐ¾Ð²ÐºÐ° Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐ¸Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ¾Ð² Ð² ÐºÐ°ÑÐµÑÑÐ²Ðµ ÑÐµÑÐµÐ½Ð¸Ñ ÑÑÐµÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸. 3. ÐÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ðµ Ð¸ÑÐºÐ¾Ð¼Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÑÐ»Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð´Ð°Ð½Ð½ÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ¾Ð². 4. ÐÐ½Ð°Ð»Ð¸Ð· Ð¿Ð¾Ð»ÑÑÐ°ÐµÐ¼ÑÑ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ð¹ Ð¸ Ð¿Ð¾Ð¸ÑÐº Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐµÐ¹ (Ð²ÑÑÐ°Ð¶ÐµÐ½Ð¸Ñ). ÐÑÐ»Ð° Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° ÑÐµÑÐ¸Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÐºÑÐ¿ÐµÑÐ¸Ð¼ÐµÐ½ÑÐ¾Ð² Ñ ÐºÑÐ¸Ð²Ð¾Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¼Ð¸ ÑÑÐµÑÐ¶Ð½ÑÐ¼Ð¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ Ð¿ÑÑÐ¼Ð¾ÑÐ³Ð¾Ð»ÑÐ½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹, Ð¸ÑÐ¿ÑÐ¾Ð±Ð¾Ð²Ð°Ð½Ñ Ð´Ð²Ðµ Ð¼ÐµÑÐ¾Ð´Ð¸ÐºÐ¸ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¸ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ð³Ð¾ ÑÐ°ÑÑÐµÑÐ°. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ»Ð¸ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ñ Ð¼Ð¾Ð´ÑÐ»Ð¸ Ð32 Ð´Ð»Ñ ÑÑÐµÑÐ¶Ð½ÐµÐ¹ ÑÐ°Ð·Ð»Ð¸ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ, Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ñ Ð¼Ð¾Ð´ÑÐ»ÐµÐ¼ Ð¶ÐµÑÑÐºÐ¾ÑÑÐ¸ Ð½Ð° Ð¸Ð·Ð³Ð¸Ð± Ð¡2. ÐÑÐ»Ð¾ Ð¾ÑÐ¼ÐµÑÐµÐ½Ð¾ Ð²ÑÑÐ¾ÐºÐ¾Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ðµ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð¹ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸, Ð¸ ÑÐ´ÐµÐ»Ð°Ð½Ð¾ Ð·Ð°ÐºÐ»ÑÑÐµÐ½Ð¸Ðµ Ð¾ ÑÐ¾Ð¼, ÑÑÐ¾ ÑÐ»Ð¾Ð¶Ð½Ð¾ Ñ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½Ð¾Ð¹ ÑÑÐµÐ¿ÐµÐ½ÑÑ Ð´Ð¾ÑÑÐ¾Ð²ÐµÑÐ½Ð¾ÑÑÐ¸ ÑÐ´ÐµÐ»Ð°ÑÑ Ð¾Ð±Ð¾Ð±ÑÐ°ÑÑÐµÐµ Ð·Ð°ÐºÐ»ÑÑÐµÐ½Ð¸Ðµ Ð¾ ÐºÐ¾Ð½ÐºÑÐµÑÐ½Ð¾Ð¼ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½ÑÐµ Ð¿ÑÐ¾Ð¿Ð¾ÑÑÐ¸Ð¾Ð½Ð°Ð»ÑÐ½Ð¾ÑÑÐ¸. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½Ñ Ð¿Ð¾Ð»ÑÑÐ¸Ð»ÑÑ ÑÐ°Ð²ÐµÐ½ 0,7.
description: The paper presents the results of the calculation of the modulus B32 by the previously proposed method, the analysis of the values obtained, namely their dependence on other parameters and the possibility of formulating an expression for determining B32. Tasks that were solved in the course of the study: 1. Theoretical analysis of the previously proposed method for determining the B32 module based on a comparison of three-dimensional and one-dimensional theories. 2. Preparation and conduct of appropriate numerical experiments as a solution to the three-dimensional problem. 3. Calculation of the modulus based on data from numerical experiments. 4. Analysis of the obtained values and search for dependencies (expressions). A series of numerical experiments with curvilinear rods of various rectangular cross-sections was carried out, two integration methods were tried when processing the results of finite element calculation. As a result of the study, the B32 moduli for rods of various cross-sections were calculated, and a comparison was made with the C2 bending stiffness modulus. The high influence of numerical error was noted, and it was concluded that it was difficult to make an overall conclusion about a specific proportionality coefficient with a sufficient degree of reliability. In this work, the coefficient turned out to be equal to 0.7.