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 DoI: 10.31772/2587-6066-2018-19-1-27-36
MULTIGRID FINITE ELEMENTS IN THE CALCULATIONS OF MULTILAYER CYLINDRICAL SHELLS
А. D. Matveev1*, A. N. Grishanov2
1Institute of Computational Modeling 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation 2Novosibirsk State Technical University 20, Karl Marx Av., Novosibirsk, 630073, Russian Federation *E-mail: mtv241@mail.ru
An effective numerical method for calculating linearly elastic multilayer cylindrical shells under static loading implemented on the basis of Finite Element Method (FEM) procedures using the multilayer curved Lagrangian multigrid finite elements (MFE) of the shell type was proposed. Such shells are widely used in rocket-space and aircraft engineering. MFE are developed in local Cartesian coordinate systems based on small (basic) shell partitions that take into account their heterogeneous structure, irregular shape, combined loading and fixing. The stress strained state (SSS) in the MFE was described by the equations of the three-dimensional elasticity problem without using the additional kinematical and static hypotheses, which allow one to use MFE for the shells of various thicknesses to be calculated. The procedure of constructing the Langrage polynomials in local curvilinear coordinate systems used to develop the shell MFE is presented. The displacements in the MFE were approximated by the power and Lagrange polynomials of different orders. When constructing a n -grid finite element (FE), n ≥ 2, n-nested grids were used. The fine grid was generated by the basic partition of the MFE; the other (coarse) grids were used to reduce its dimension. According to the method, the nodes of the coarse MFE grids are located on the common boundaries of the different modular layers of the shell. The proposed law of the expansion in the number of discrete models using MFE with a constant thickness, multiple of the shell thickness, provides a uniform and rapid convergence of approximate solutions, allowing one to frame solutions with a small error. Multigrid discrete models have 103…106 times less unknown MFE than the basic ones. The implementation of the MFE for multigrid models requires 104…107 times less computer storage space than for the reference models, which allows one using the proposed method to calculate some large shells. An example of calculating a multilayer cylindrical local loading shell of irregular shape was given. In the calculation, three-grid shell – type FE, developed on the basis of the reference models having from 2 million to 3.7 billion of the nodal MFE unknowns were used. To study the approximate solution convergence and error, a well-known numerical method was used.
elasticity, cylindrical shells, composites, multigrid finite elements of shell type, Lagrange polynomials, small error.
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Matveev Aleksandr Danilovich – Cand. Sc., Docent, senior researcher, Institute of Computational Modelling SB

RAS. E-mail: mtv@icm.krasn.ru.

Grishanov Alexandr Nikolaevich – competitor, Department of Aircrafts strength, Novosibirsk State Technical

University. E-mail: a_grishanov@ngs.ru.


  MULTIGRID FINITE ELEMENTS IN THE CALCULATIONS OF MULTILAYER CYLINDRICAL SHELLS