Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and BuildingsСтроительная механика инженерных конструкций и сооружений1815-52352587-8700Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)2707110.22363/1815-5235-2021-17-2-99-111Analysis and design of building structuresРасчет и проектирование строительных конструкцийResearch ArticleThe method of compensating loads for solving of problems of cyclic symmetrical flexure of anisotropic plates, resting on an elastic subgradeМетод компенсирующих нагрузок для решения задач о циклически симметричном изгибе анизотропных пластин, контактирующих с упругим основанием8804-7930KorenevaElena B.КореневаЕлена Борисовна

Professor of the Department of General Engineering Disciplines, Doctor of Technical Sciences

профессор кафедры общетехнических дисциплин, доктор технических наук

elena.koreneva2010@yandex.ruMoscow Higher Combined Arms Military Command School Holding the Order of Lenin, the Order of the October Revolution nd the Order of the Red BannerМосковское высшее общевойсковое командное орденов Ленина и Октябрьской Революции Краснознаменное училище20072021172VOL 17, NO2 (2021)ТОМ 17, №2 (2021)9911120072021Copyright ©; 2021, Koreneva E.B.Copyright ©; 2021, Коренева Е.Б.2021Koreneva E.B.Коренева Е.Б.http://creativecommons.org/licenses/by/4.0https://journals.rudn.ru/structural-mechanics/article/view/27071

The purpose of the study - receiving of exact analytical solutions of statics problems of anisotropic plates, resting on an elastic subgrade and subjected to an action of cyclic symmetrical loads. The method of compensating loads is used for solving of the formulated problems. The basic and the compensating solutions are determined. The new approach, connected with the use of Nielsen’s equation for receiving of the solutions, is applied. For the first time by means of the method of compensating loads the exact analytical solutions of the cycle symmetric flexure of anisotropic circular plates, resting on the elastic subgrade, are received. Various boundary conditions and the loads, distributed along circumferences and over ring surfaces, are considered. The problem of anisotropic infinite plate with the circular opening, resting on the elastic subgrade, is also examined. All the solutions are obtained in the closed form and expressed in terms of Bessel functions.

Цель исследования - построение точных аналитических решений задач статики анизотропных пластин, находящихся под действием циклически симметричных воздействий и лежащих на упругом основании. Для решения поставленных в работе задач используется метод компенсирующих нагрузок, определяются основное и компенсирующие решения. Для нахождения решений используется новый прием, связанный с применением уравнения Нильсена. С помощью метода компенсирующих нагрузок впервые получены точные аналитические решения для задач об анизотропных пластинах, очерченных круговым контуром, лежащих на упругом основании при различных условиях опирания и при действии циклически симметричных нагрузок, распределенных вдоль окружности и по площади кольца. Также рассматривается задача о расчете неограниченной пластины, лежащей на упругом основании и имеющей круговое отверстие. Решения получены в замкнутом виде и выражены в функциях Бесселя.

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