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
CALCULATION OF COMPOSITE CYLINDRICAL SHELLS USING MULTIGRID ELEMENTS
А. D. Matveev1, A. N. Grishanov2
1Institute of Computational Modeling SB RAS 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation 2Novosibirsk State Technical University 20, K. Marksa Аv., Novosibirsk, 630073, Russian Federation
Calculating the three-dimensional elastic composite cylindrical shells with different coefficients of fullness that is reduced to the construction of discrete models consisting of complex curvilinear multi-grid finite elements has been proposed. The basis of such elements construction is curvilinear double-grid finite elements. Double-grid and complex multi-grid elements are designed based on the basic finite element models of composite shells which take into account their heterogeneous structure and have high dimension. Constructing the curvilinear double-grid and complex multi-grid elements in the local Cartesian reference systems has been shown. Displacement fields are interpolated by known degree polynomials of various orders, the stress state is described by the three-dimensional elasticity problem (without introduction of the simplifying hypotheses on the nature of the displacement fields, strain and stress distribution). Approximating polynomials and the equations of threedimensional elasticity problem are recorded in the local Cartesian reference systems. Advantages of the proposed elements are that they describe the three-dimensional stress state in composite shells, take into account their heterogeneous structures, complex fixing and generate multi-grid discrete models with a small number of nodal unknowns. The dimensions of multi-grid discrete shell models are by several orders less than the dimensions of the basic ones. Time spending of the finite element method (FEM) realization on a computer for discrete models of multi-grid composite shells is significantly less than for the basic models. A complex multi-grid element of the 3rd order to calculate the composite cylindrical shells is proposed. The FEM calculation example of cantilever sandwich shell using complex multi-grid elements of the 3rd order has been given. Shell calculation results show the high efficiency of the proposed complex elements.
Keywords: composites, elasticity, cylindrical shell, finite element method, complex multigrid curvilinear finite elements.
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Matveev Aleksandr Danilovich – Cand. Sc., docent, senior researcher, Institute of Computational Modeling SB

RAS, docent, Siberian Federal University. E-mail: mtv@icm.krasn.ru.

Grishanov Alexandr Nikolaevich – competitioner, Department of the strength of aircrafts, Novosibirsk State

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