Мақаланы E-mail арқылы жіберу 
Determination of parameters of plastic deformation of elliptic membranes
- Авторлар: Galimov N.K1, Yakupov S.N2
-
Мекемелер:
- Institute of Mechanics and Engineering - subdivision of the Federal State Budgetary Institution of Science “Kazan Scientific Center of the Russian Academy of Sciences”
- Kazan State University of Architecture and Engineering
- Шығарылым: Том 15, № 2 (2019)
- Беттер: 90-95
- Бөлім: Analysis and design of building structures
- URL: https://journal-vniispk.ru/1815-5235/article/view/346260
- DOI: https://doi.org/10.22363/1815-5235-2019-15-2-90-95
- ID: 346260
Дәйексөз келтіру
Толық мәтін
Аннотация
Introduction. Thin-walled structural elements, combining lightness with high strength, are widely used in all industries. Widespread round design elements. However, based on the functional purpose, thin-walled structural elements of various shapes in plan are becoming more and more common. Methods. A technique has been developed for the study of thin elliptic membranes for the case of plastic deformation under the action of uniform pressure. The deflections of the membranes in the experiment are more than ten thicknesses. In this regard, to solve the problem, the following are used: geometric nonlinear relations for the deformations of the middle surface (according to Kh.M. Mushtari and K. Z. Galimov), relations for finite displacements and deformations for curvature expressions (according to K.Z. Galimov), physical relations (according to the theory of plasticity A.A. Ilyushin). Due to the smallness of the membrane thickness, only tensile membrane strains and forces are taken into account. The problem is solved by the Bubnov - Galerkin method and reduced to solving a nonlinear system of three algebraic equations. The “shooting” algorithm for solving the resulting system of equations is described. Results. The work on the assessment of the reliability of the results. To estimate the error, the comparison of the calculation results with the experimental results of G.D. Golovlev was also performed. An example of the calculation of an elliptical membrane is considered.
Авторлар туралы
Nail Galimov
Institute of Mechanics and Engineering - subdivision of the Federal State Budgetary Institution of Science “Kazan Scientific Center of the Russian Academy of Sciences”
Хат алмасуға жауапты Автор.
Email: tamas_86@mail.ru
PhD in Physical and Mathematical Sciences, leading researcher, Institute of Mechanics and Engineering - subdivision of the Federal State Budgetary Institution of Science “Kazan Scientific Center of the Russian Academy of Sciences”. Research interests: mechanics of thin-walled structures, mechanics of films and membranes, composite structures
PO Box 261, 2/31 Lobachevsky St., Kazan, 420111, Tatarstan, Russian FederationSamat Yakupov
Kazan State University of Architecture and Engineering
Email: tamas_86@mail.ru
SPIN-код: 7382-4759
PhD in Technical Sciences, senior researcher, Kazan State University of Architecture and Engineering. Research interests: structures of buildings and structures, mechanics of thin-walled structures, mechanics of films and membranes, composite structures, adhesion
1 Zelenaya St., Kazan, 420043, Tatarstan, Russian FederationӘдебиет тізімі
- Yakupov N.М., Yakupov S.N. (2009). Plenki neodnorodnoj struktury [Films of heterogeneous structure]. Structural Mechanics of Engineering Constructions and Buildings, (1), 60-70. (In Russ.)
- Yakupov S.N., Yakupov N.М. (2017). Tonkoslojnye pokrytiya [Thin coatings]. Structural Mechanics of Engineering Constructions and Buildings, (1), 6-14. (In Russ.)
- Smirnov-Alyaev G.А. (1939). Issledovanie plasticheskogo progiba tonkih plastinok (membran), zhestko zadelannykh po krugovomu konturu pod dejstviem gidrostaticheskogo davleniya [Investigation of plastic deflection of thin plates (membranes), rigidly set on a circular contour under the action of hydrostatic pressure]. Research on the theory of plasticity, (III), 28-52. (In Russ.)
- McPherson A.E., Ramberg W., Lery S. (1942). Normal pressure test of circular plates with clamped edges. NASA Report, (744), 269-285.
- ANALYSIS AND DESIGN OF BUILDING STRUCTURES Галимов Н.К., Якупов С.Н. Строительная механика инженерных конструкций и сооружений. 2019. Т. 15. № 2. С. 90-95
- Mahutov N.Ah. (2008). Strength and safety. Fundamental and applied research. Novosibirsk: Nauka Publ., 523. (In Russ.)
- Yakupov N.M. (2015). Mekhanika “lecheniya” konstrukcii [Mechanics of “treatment” of construction]. XI All-Russian Congress on Fundamental Problems of Theoretical and Applied Mechanics (Kazan, 20-24 August 2015), 4320-4322. (In Russ.)
- Yakupov N.M., Nurgaliyev A.R., Yakupov S.N. (2008). Metodika ispytaniya plenok i membran v usloviyah ravnomernogo raspredelennogo poverhnostnogo davleniya [The technique of test of films and membranes in the conditions of the uniform distributed superficial pressure]. Industrial laboratory. Diagnostics of materials, 74(11), 54-56. (In Russ.)
- Yakupov N.M. Galimov N.K., Leontiev A.A. (2000). Eksperimental'no-teoreticheskij metod issledovaniya prochnosti polimernyh plenok [Experimental-theoretical method for the study of the strength of polymer films]. Mechanics of composite materials and structures, 6(2), 238-243. (In Russ.)
- Galimov N.K., Yakupov N.M., Yakupov S.N. (2011). Eksperimental'no-teoreticheskij metod opredeleniya mekhanicheskih harakteristik sfericheskih plenok i membran so slozhnoj strukturoj [Experimentally-theoretical method for determining mechanical characteristics of spherical films and membranes with difficult structure]. Solid mechanics, (3), 58 (In Russ.)
- Weil N.A., Newmark N.M. (March, 1956). Large Deflections of elliptical Plates. Applied Mechanics, 23(1), 21-26.
- Gleyzal A. (1948). Plastic Deformation of a Circular Diaphragm under Pressure. J. of Applied Mechanics, Trans Asme, 70, 288-296.
- Mushtari Kh.M., Galimov K.Z. (1961). Nonlinear Theory of Thin Elastic Shells. 374.
- Galimov K.Z. (1951). K obshchej teorii plastin i obolochek pri konechnyh peremeshcheniyah i deformaciyah [On the general theory of plates and shells under finite displacements and deformations]. PMM, XV(6), 723-742. (In Russ.)
- Ilyushin A.A. (1948). Plastichnost' [Plasticity]. Moscow: Gostekhizdat Publ., 376. (In Russ.)
- Golovlev V.D. (1962). O sposobnosti metalla k glubokoj vytyazhke [On the ability of metal to deep drawing]. New processes of metal forming. Moscow: USSR Academy of Sciences, 135-143. (In Russ.)
Қосымша файлдар
