Сибирский журнал науки и технологий
ISSN 2587-6066

Vestnik sibsau
Vestnik sibsau
Vestnik sibsau
Vestnik sibsau

UDK 519.6; 539.3 Doi: 10.31772/2587-6066-2018-19-3-423-431
EFFICIENT METHOD OF CALCULATING LAYERED CONICAL SHELLS WITH LAGRANGE MULTIGRID ELEMENTS USE
G. I. Rastorguev, A. N. Grishanov , А. D. Matveev*
Novosibirsk State Technical University, 20, Karl Marx Av., Novosibirsk, 630073, Russian Federation; Institute of Computational Modeling SB RAS, 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation. *E-mail: mtv241@mail.ru
The increased requirements for strength calculations of space-rocket and aviation technology designs cause the need for the development and improvement of approximate solutions for elasticity theory tasks with small error algorithms. The article considers the numerical method of calculating elastic layered conical shells (LCS) of various thickness under static loading which are widely used in space-rocket technology. The suggested method uses three-dimensional curvilinear Lagrange multigrid finite elements (MGFE). A system of nested grids is used for MGFE constructing. The fine grid is generated by the basic partition that takes into account MGFE heterogeneous structure. The basic partition dimensionality is reduced with the help of large grids which leads to the system of linear algebraic equations of the small dimension finite elements method. Three-dimensional elasticity theory equations use allows to apply MGFE for calculating LCS of any thickness. Displacements in MGFE are approximated by Lagrange polynomials which, in contrast to power polynomials, gives the opportunity to design big size three-dimensional thin shell elements. Lagrange polynomials nodes coincide in shell thickness with the nodes of MGFE large grids which lie on the shared borders of multi-module layers. The efficiency of the presented method is that the suggested MGFE generate small dimension discrete models that require 103–107 times less electronic computing machine (ECM) memory than basic models. The suggested law of discrete models grinding generates uniform and fast convergence of numerical solutions which allows to make solutions with the specified (small) error. Examples of LCS calculating (whole ones as well as with holes) under axisymmetric and local loading are given. Comparative analysis of solutions obtained with the help of MGFE, single-grid finite elements and the program complex ANSYS has been conducted.
Keywords: elasticity, conical shell, composites, Lagrange polynomials, multigrid finite elements.
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Rastorguev Gennadii Ivanovich – Dr. Sc., professor, First Vice-rector, Novosibirsk State Technical University. Е-mail: rastorguev@ adm.nstu.ru.

Grishanov Alexander Nicolaevich – applicant of Department of Aircraft strength, Novosibirsk State Technical University. Е-mail: a_grishanov@ngs.ru.

Matveev Aleksandr Danilovich – Cand. Sc., Docent, senior research fellow, Institute of Computational Modelling SB RAS. Е-mail: mtv241@ mail.ru.


  EFFICIENT METHOD OF CALCULATING LAYERED CONICAL SHELLS WITH LAGRANGE MULTIGRID ELEMENTS USE