Напружений стан гнучких пластин з отвором - Кривоблоцька, Л. М.; Kryvoblotska, L. (ЦНТУ, 2022)
Дана постановка і метод розв’язку класу задач з нелінійної механіки гнучких пластин з отвором; для цього сформульовані граничні умови; запропоновано метод розв’язку – розклад по безрозмірному параметру моментного навантаження; в результаті отримана послідовність ліній них граничних задач для визначення прогинів і функцій напружень для пластинки в довільному наближенні. Розв’язана неосесиметрична задача про згин гнучкої пластинки з отвором; одержано формули для обчислення прогинів і функції напружень. The article is dedicated to solving of problems of nonlinear mechanics of plates and shells – problems about stress-deformed state of flexible plates with hole under action of moment loading on “infinity”. Solve of problems is offered to find with method of expansion of parameter of the external loading. During the solving was determined, that the value of bending and power descriptions unlimitedly increase at breaking from the edge of hole. For elaboration of regularization methods was conducted the survey and analysis of problems from different fields of mechanics. On the basis of this survey was formed the new approach to the solving of problem of regularization: it is offered to change the usual notions about particular sum of series and methods of their summing. It is created such methods of linear and nonlinear summing, when in summable functions the arbitrary parameters and functions enter. On basis of this method was solved the new geometrical-nonlinear problems of plates and shells mechanics in nonaxes-symmetrical axes-symmetrical arrangement about bending on “infinity” with moment loading of plates with hole. It is established, that the finding numeral data, diagrams do not conflict with the usual notions about stress-deformed conditions of plates with hole; definite mechanical effects are got. The methods of regularization are approved on test problems. It is grounded mathematically, that the got solutions to equilibrium equations with some asymptotical exactness and exactly to the linear limit conditions, if the operators of initial problem will be polylinear.
Stress State of Flexible Plates with a Hole
Keywords: безрозмірний параметр; геометрична нелінійність; гнучка пластина з отвором; прогини; функція напружень; dimensionless parameter; geometric nonlinearity; flexible plate with a hole; deflections; stress function