title: ÐÑÐ±Ð¾Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸Ð·Ð³Ð¸Ð±Ð° ÑÑÐµÑ ÑÐ»Ð¾Ð¹Ð½Ð¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ð² Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¾Ñ ÑÐ¿ÑÑÐ³Ð¸Ñ Ñ Ð°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº ÑÐ»Ð¾ÐµÐ²
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: The choice of a bending model of a three-layer plate depending on the elastic characteristics of the layers
Creators: name: ÐÐ¸ÐºÐ¾Ð»Ð°ÐµÐ², ÐÐ°Ð½Ð¸Ð¸Ð»
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: 2024
Subjects: ÑÐ¾Ð»Ð½ÐµÑÐ½ÑÐµ Ð¿Ð°Ð½ÐµÐ»Ð¸
ÑÑÐµÑ ÑÐ»Ð¾Ð¹Ð½ÑÐµ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ
Ð¿Ð»Ð°ÑÑÐ¸Ð½Ð° ÐÐ¸ÑÑ Ð³Ð¾ÑÐ°-ÐÑÐ²Ð°
Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ñ Ð½ÐµÐ·Ð°Ð²Ð¸ÑÐ¸Ð¼ÑÐ¼Ð¸ ÑÐ»Ð¾ÑÐ¼Ð¸
solar panels
three-layer plates
Kirchoff-Love plate
plate model with independent layers

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÑÑÑ Ð¸Ð·Ð³Ð¸Ð± Ð¿ÑÑÐ¼Ð¾ÑÐ³Ð¾Ð»ÑÐ½Ð¾Ð¹ ÑÑÐµÑÑÐ»Ð¾Ð¹Ð½Ð¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ ÑÐ¸Ð¼Ð¼ÐµÑÑÐ¸ÑÐ½Ð¾Ð¹ ÑÑÑÑÐºÑÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸ÑÐµÐ»ÑÐ½Ð¾ Ðº ÑÐ¾Ð»Ð½ÐµÑÐ½ÑÐ¼ Ð¿Ð°Ð½ÐµÐ»ÑÐ¼. Ð¦ÐµÐ»ÑÑ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¾ÑÐ½Ð¾Ð²ÑÐ²Ð°ÐµÑÑÑ Ð½Ð° Ð³Ð¸Ð¿Ð¾ÑÐµÐ·Ðµ ÐÐ¸ÑÑÐ³Ð¾ÑÐ°-ÐÑÐ²Ð°, Ð¸ ÑÑÐ¾ÑÐ½ÐµÐ½Ð½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸ Ð¿ÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÑÐ°Ð·Ð¼ÐµÑÐ°Ñ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ð² Ð¿Ð»Ð°Ð½Ðµ. Ð¡ÑÑÐ¾Ð¸ÑÑÑ ÑÐµÑÐµÐ½Ð¸Ðµ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸. ÐÐ»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð´ÐµÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐµÑÑÐ»Ð¾Ð¹Ð½Ð¾Ð¹ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑÑÑ Ð¿Ð¾Ð»ÑÐ´Ð¸ÑÐºÑÐµÑÐ½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´ ÐÐ°Ð½ÑÐ¾ÑÐ¾Ð²Ð¸ÑÐ° Ð¸ ÑÐµÑÐµÐ½Ð¸Ðµ ÐÐ°Ð²ÑÐµ. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ ÑÑÐ°Ð²Ð½Ð¸Ð²Ð°ÑÑÑÑ Ñ ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½ÑÐ¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼ Ð² CAE ÑÐ¸ÑÑÐµÐ¼Ðµ Ansys, Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ Ð¾Ð±Ð»Ð°ÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð³Ð¸Ð¿Ð¾ÑÐµÐ·Ñ ÐÐ¸ÑÑÐ³Ð¾ÑÐ°-ÐÑÐ²Ð° Ð·Ð° ÑÑÐµÑ Ð²Ð°ÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ¿ÑÑÐ³Ð¸Ñ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº ÑÐµÑÐµÐ´Ð¸Ð½Ð½Ð¾Ð³Ð¾ ÑÐ»Ð¾Ñ Ð¿ÑÐ¸ Ð½ÐµÐ¸Ð·Ð¼ÐµÐ½Ð½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ñ Ð²Ð½ÐµÑÐ½Ð¸Ñ ÑÐ»Ð¾ÐµÐ². Ð¡Ð¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÐµÐ½Ð½Ð¾ Ð² Ð¼Ð¾Ð´ÐµÐ»ÑÑ, Ð³Ð´Ðµ ÑÐ°Ð½ÐµÐµ Ð¿ÑÐ¸Ð½ÑÑÐ°Ñ Ð³Ð¸Ð¿Ð¾ÑÐµÐ·Ð° Ð½Ðµ Ð²ÑÐ¿Ð¾Ð»Ð½ÑÐµÑÑÑ, Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ ÐºÐ¾ÑÑÐµÐºÑÐ½Ð¾ÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÑÐ¾ÑÐ½ÐµÐ½Ð½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¿Ð»Ð°ÑÑÐ¸Ð½Ñ Ñ Ð½ÐµÐ·Ð°Ð²Ð¸ÑÐ¸Ð¼ÑÐ¼Ð¸ ÑÐ»Ð¾ÑÐ¼Ð¸. ÐÑÐ¸Ð¼ÐµÐ½ÑÑÑÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ»Ð¾Ð¹Ð½ÑÑ Ð¿Ð»Ð°ÑÑÐ¸Ð½, ÑÐµÑÐµÐ½Ð¸Ðµ ÐºÐ¾ÑÐ¾ÑÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐµÑÐµÐ½Ð¸Ñ ÐÐ°Ð²ÑÐµ. ÐÐ»Ð°Ð²Ð½ÑÐ¼ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð¼ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ðµ Ð´Ð»Ñ ÑÐ°Ð·Ð½ÑÑ ÑÐ°Ð·Ð¼ÐµÑÐ¾Ð² Ð¿Ð»Ð°ÑÑÐ¸Ð½ Ð³ÑÐ°Ð½Ð¸ÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð³Ð¸Ð¿Ð¾ÑÐµÐ·Ñ ÐÐ¸ÑÑÐ³Ð¾ÑÐ°-ÐÑÐ²Ð° Ð¸ ÑÑÐ¾ÑÐµÐ½Ð½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸.
description: In this paper, the bending of a rectangular three-layer plate of a symmetrical structure is considered in relation to solar panels. The aim of the work is to determine the applicability of the classical theory, which is based on the Kirchhoff-Love hypothesis, and the refined theory for different plate sizes in plan. The solution is constructed using classical theory. To study the deformation of a three-layer plate, a semi-discrete Kantorovich method and a Navier solution are used. The results obtained are compared with the finite element solution contained in the Ansys CAE system, and the scope of the Kirchhoff-Love hypothesis is determined by varying the elastic characteristics of the middle layer with unchanged parameters of the outer layers. Accordingly, in models where the previously accepted hypothesis is not fulfilled, the correctness of using the refined theory is determined based on the plate model with independent layers. The equations of multilayer plates are applied, the solution of which is obtained using the Navier solution. The limits of applicability of the Kirchhoff-Love hypotheses and the refined theory are determined for different plate sizes. The main result of the work is to obtain for different plate sizes the limits of applicability of the Kirchhoff-Love hypothesis and the refined theory.