Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 539.3; 519.6 Doi: 10.31772/2587-6066-2019-20-2-174-182
MULTI-GRID FINITE ELEMENTS IN CALCULATIONS OF MULTILAYER OVAL CYLINDRICAL SHELLS
Pustovoi N. V., Grishanov A. N., Matveev А. D.
Novosibirsk State Technical University, 20, Karl Marx Av., Novosibirsk, 630073, Russian Federation; 2Institute of Computational Modeling SB RAS, 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
The method of finite elements (FEM) is actively used in calculations of composite shell constructions (rotation shells, circle and oval cylindrical shells), which are widely used in space-rocket and aviation equipment. To calculate multi-layer oval cylindrical shells three-dimensional curvilinear Lagrange multi-grid finite elements (MGFE) are suggested. When building a k-grid finite element (FE), k nested grids are used. The fine grid is generated by the basic split of MGFE that takes into account its complex heterogeneous structure and shape. On k-1 large grids the move functions used for decreasing MGFE dimension are determined. The stress-strain state in MGFE is described by the elasticity theory three-dimensional task equations (without introduction of additional hypotheses) in local Cartesian coordinates systems. The procedure of building shell-type Lagrange MGFE with the use of Lagrange polynomials presented in curvilinear coordinate systems is demonstrated. With the size reduction of discrete models MGFE have constant thickness equal to the thickness of the shell. The Lagrange polynomials nodes coincide in thickness with the MGFE large grid nodes and are located on the shared borders of different module layers. The use of such MGFE generates approximate solutions sequences that uniformly and quickly converge to precise solutions. The main advantages of MGFE are as follows: they form discrete models with the dimension 102–106 times smaller than the basic models dimension and they generate small error solutions. Examples of calculations are given for four- and three-layer oval shells of various thickness and shape under both uniform and local loading with the use of 3-grid FE. Comparative analysis of the obtained solutions with the solutions built with the help of the software package ANSYS shows high efficiency of the suggested MGFE in calculations of multi-grid oval shells.
Keywords: elasticity, composite, oval cylindrical shell, multi-grid finite elements, Lagrange polynomials, convergence of the solution sequence, software package ANSYS.
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Pustovoi Nikolai Vasilevich – Dr. Sc., Professor; Novosibirsk State Technical University. E-mail: pla@craft.nstu.ru.

Grishanov Aleksandr Nikolaevich – applicant of the Department of aircraft strength; Novosibirsk State Technical University. Е-mail:a_grishanov@ngs.ru.

Matveev Aleksandr Danilovich – Cand. Sc., senior researcher; Institute of computational modeling SB RAS. Е-mail: mtv241@mail.ru.


  MULTI-GRID FINITE ELEMENTS IN CALCULATIONS OF MULTILAYER OVAL CYLINDRICAL SHELLS