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Название Stress-strain state of elastic shell based on mixed finite element // Magazine of Civil Engineering. – 2023. – № 4 (120). — С. 12003
Авторы Klochkov Yu. V. ; Pshenichkina V. A. ; Nikolaev A. P. ; Vakhnina O. V. ; Klochkov M. Yu.
Выходные сведения 2023
Коллекция Общая коллекция
Тематика Техника ; Сопротивление материалов ; mixed finite elements ; elastic shells ; stress-strain state ; shell-type constructions ; compliance matrix (copromat) ; four-node finite elements ; смешанные конечные элементы ; упругие оболочки ; напряженно-деформированное состояние ; конструкции оболочечного типа ; матрица податливости (сопромат) ; четырехузловые конечные элементы
УДК 539.3/6
ББК 30.121
Тип документа Статья, доклад
Тип файла PDF
Язык Английский
DOI 10.34910/MCE.120.3
Права доступа Свободный доступ из сети Интернет (чтение, печать, копирование)
Ключ записи RU\SPSTU\edoc\71905
Дата создания записи 09.10.2023

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In a mixed formulation, a four-node finite element was developed, which is a fragment of the middle surface of the elastic shell. Longitudinal forces and bending moments, as well as displacements and their first derivatives with respect to curvilinear coordinates, were taken as nodal unknowns. To obtain the compliance matrix, the Reissner functional was used, in which the stresses, when using the direct normal hypothesis, are represented by dependences on the forces and bending moments of the middle surface, the approximation of which was carried out by bilinear functions. In the interpolating expressions for the kinematic sought quantities, Hermite polynomials of the third degree were used. As a result of minimizing the transformed functional with respect to the force and kinematic nodal unknowns, the compliance matrix of the accepted discrete element was formed. Verification of the developed discrete element in a mixed formulation was carried out on the examples of calculations of cylindrical shells with circular and elliptical cross sections. The values of the force parameters found using the developed algorithm adequately satisfied the conditions of static equilibrium (the calculation error was less than 0.5 %). An analysis of the obtained finite element solutions showed the effectiveness of the developed algorithm and made it possible to note the possibility of its use in calculations of thin-walled structures made of incompressible materials.

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  • Stress-strain state of elastic shell based on mixed finite element
    • 1. Introduction
    • 2. Materials and Methods
    • 3. Results and Discussion
    • 4. Conclusions

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