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Calculation of deformations of a cantileverframe planar truss model with an arbitrary number of panelsстатья
Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из перечня ВАКДата последнего поиска статьи во внешних источниках: 23 сентября 2020 г.
- Авторы: Бука-Вайваде К., Кирсанов М.Н., Сердюк Д.О.
- Журнал: Вестник МГСУ
- Том: 15
- Номер: 4
- Год издания: 2020
- Первая страница: 510
- Последняя страница: 517
- DOI: 10.22227/1997-0935.2020.4.510-517
- Аннотация: Introduction. By method of induction using three independent parameters (numbers of panels) that characterize the proportions of the structure and its parts, formulas for deflection under different types of loading are derived. Curves based on the derived formulas are analyzed, and the asymptotics of solutions for the number of panels are sought. The frame is statically definable, symmetrical, with descending braces in a simple lattice of crossbars and consoles. The structure has movable and fixed supports. The problem of deflection under the action of a load evenly distributed over the nodes of the upper belt, a concentrated load in the middle of the span, and the problem of shifting the mobile support is considered. Materials and methods: the calculation of forces in the truss rods is performed in symbolic form using the method of cutting nodes and operators of the Maple computer mathematics system. The deflection is determined by the Maxwell-Mohr formula, taking into account only the compressive and tensile forces in the rods. Based on the results of a sequence of analytical calculations of trusses with different numbers of panels in the crossbar, consoles, and support trusses, the final calculation formulas for the deflection and displacement of the support are derived by induction. Operators of the special genfunc package of the Maple computer mathematics system are used for composing and solving homogeneous linear recurrent equations that satisfy sequences of coefficients of the required dependencies. The stiffness of all truss rods is assumed to be the same. Results: all the obtained dependencies have a polynomial form for the number of panels. To illustrate the obtained solutions and their qualitative analysis, curves of the deflection dependence on the number of panels are constructed. Conclusions. A scheme of a statically definable three-parameter truss is proposed that allows an analytical solution of the problem of deflection and displacement of the support. The obtained dependences can be used in engineering practice in problems of structural rigidity optimization and for evaluating the accuracy of numerical solutions.
- Добавил в систему: Кирсанов Михаил Николаевич
Прикрепленные файлы
| № | Имя | Описание | Имя файла | Размер | Добавлен |
|---|---|---|---|---|---|
| 1. | Полный текст | 1997-0935.2020.4.510-517.pdf | 1,3 МБ | 1 мая 2020 [KirsanovMN] |