izvestswsuИзвестия Юго-Западного государственного университетаProceedings of the Southwest State University2223-15602686-6757ЮЗГУ10.21869/2223-1560-2023-27-3-21-33izvestswsu-1184Research ArticleСтроительствоConstructionsНапряженно-деформированное состояние пологой оболочки на упругом основании с переменными прочностными характеристикамиStress-Strain State of Shallow Shell in an Elastic Foundation with Variable Strength Characteristicshttps://orcid.org/0000-0001-7874-3646КолесниковА. Г.KolesnikovA. G.

Колесников Александр Георгиевич, кандидат технических наук, доцент, кафедра уникальных зданий и сооружений,  

ул. 50 лет Октября, д. 94, г. Курск 305040.

Alexander G. Kolesnikov, Cand. of Sci. (Engineering), Associate Professor,

50 Let Oktyabrya str. 94, Kursk 305040.

ag_kolesnikov@mail.ruhttps://orcid.org/0009-0002-8564-5790ИвановА. А.IvanovA. A.

Иванов Андрей Александрович, аспирант,

ул. 50 лет Октября д. 94, г. Курск 305040. 

Andrey A. Ivanov, Post Graduate Student,

50 Let Oktyabrya str. 94, Kursk 305040.

Юго-Западный государственный университетSouthwest State University2023040220242732133Copyright © Колесников А.Г., Иванов А.А., 20242024Колесников А.Г., Иванов А.А.Kolesnikov A.G., Ivanov A.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://izvestswsu.elpub.ru/jour/article/view/1184

Целью исследования является исследование изменения напряженно-деформированного состояния конструкций пологих оболочек на упругом основании при изменении его прочностных характеристик.

Методы

Методы. Методом Бубнова-Галеркина решается система дифференциальных уравнений состояния пологих оболочек на упругом основании с учетом геометрической нелинейности работы материала конструкции. Аппроксимирующая функция позволяет моделировать различные условия опирания конструкции на основание.

Результаты

Результаты. В аналитическом виде получены выражения для определения напряжений и критической нагрузки в изотропных пологих оболочках, покоящихся на упругом основании с учетом геометрической нелинейности работы конструкции. Прочностные характеристики основания заданы функцией, что позволяет моделировать различные грунты и их распределение под подошвой конструкции. Приведены графики возможного распределения коэффициента, характеризующего быстроту затухания осадок в глубине основания под подошвой фундамента. Показано несколько вариантов резкого уменьшения прочностных характеристик основания под частью конструкции. Приведены зависимости критической нагрузки для пологой оболочки от изменения форм и величин участков упругого основания с пониженными прочностными характеристиками. Показаны сравнительные графики напряжений и критической нагрузки для конструкций фундаментов зданий и сооружений в виде плит и пологих оболочек на упругом основании.

Заключение

Заключение. Приведенные аналитические уравнения для определения напряжений и критической нагрузки позволяют проектировать и исследовать фундаменты зданий и сооружений в виде плит и пологих оболочек на упругом основании. Показанные зависимости помогают подобрать рациональные геометрические характеристики конструкций, позволяющие сохранить несущую способность при изменении прочностных характеристик основания под частью конструкции

Purpose of research

Purpose of research. Changes in the stress-strain state of structures of shallow shells on an elastic foundation with a change in its strength characteristics investigation.

Methods

Methods. To solve a system of differential equations of state for shallow shells in an elastic state the BubnovGalerkin method is used. Geometric non-linearity of work material of construction is taken into account. The approximating function allows you to simulate various conditions for supporting a structure on a foundation.

Results

Results. Expressions are obtained for determining the stresses and critical load in isotropic shallow shells resting on an elastic foundation in analytical form. The geometric nonlinearity of the structure taking into account. The strength characteristics of the base are given by a function, which allows modeling various soils and their distribution under the base of the structure. Graphs of the possible distribution of the coefficient characterizing the rate of sediment attenuation in the depth of the foundation under the base of the foundation are given. Several variants of a sharp decrease in the strength characteristics of the base under a part of the structure are showт. Dependences of the critical load for a shallow shell on the shapes and sizes of sections of the elastic foundation with reduced strength characteristics are given. Comparative graphs of stresses and critical load are shown for the foundation structures of buildings and structures in the form of slabs and shallow shells on an elastic foundation.

Conclusion

Conclusion. Analytical equations for stresses and critical loads determining make it possible to design and investigation the foundations of buildings and structures in the form of slabs and shallow shells on an elastic foundation. The dependencies lets to select rational geometric characteristics of structures, allowing maintaining the bearing capacity when changing the strength characteristics of the base under a part of the structure.

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The authors declare that there are no conflicts of interest present.