Registration Number
0224U001963,
(0122U201064)
, R & D reports
Title
Development and application of mathematical methods for the study of applied problems
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Створення математичного апарату для розв’язання прикладних задач
Head
Nikolaiev Oleksii H., Доктор фізико-математичних наук
Registration Date
02-02-2024
Organization
National Aerospace University "Kharkiv Aviation Institute"
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Development and application of mathematical methods for studying the problems of mathematical physics and mechanics of deformed solids, mechanics and optimization of multilayer structures, theory of atomic functions and their application, systems analysis and mathematical modeling.
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The construction of the Green's functions of the first and second boundary value problems for Laplace's equation in space with a spherical segment in analytical form, as well as the numerical analysis of these functions, were studied. The study of the stress state in a transversely isotropic space with two parallel circular cracks was carried out. Further development of the generalized Fourier method for compressed spheroidal coordinate systems with origins was carried out. A local stationary model of the thermoelastic state of the porous material was constructed. The problem of topological optimization of a symmetric two-piece connection has been solved. The proposed mathematical model of a joint of variable thickness is a generalization of the classic Holland-Reissner model. The results were compared with the results of finite element modeling. A constructive mathematical tomic-function apparatus was obtained for solving problems of signal and image processing, as well as for solving boundary value problems for equations with partial derivatives of mathematical physics. The Birkhoff interpolation apparatus using tomic-function has also been developed. A set of modifications is proposed to reduce the spatial complexity of the DAC algorithm. Also proposed is a procedure for partitioning blocks to reduce the size of buffer matrices and a progressive coding scheme for quantized DAT coefficients. A stochastic approach to the analysis of discrete linear exchange models is considered. These models are described by Markov chains using the Z-transformation, which allows to obtain an analytical form of problem solving. The stability conditions for the equilibrium of a double pendulum with an imperfect (non-tangent) trailing force for undetermined values of mass, damping and stiffness coefficients are obtained and analyzed. The cases of undamped and weakly damped systems are considered.
Product Description
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Barakhov Kostiantyn P.
Brysina Iryna V.
Holovchenko Oleksandr V.
Kuznichenko Volodymyr M.
Kuriennov Serhii S.
Makarichev Viktor O.
Nikolaev Oleksii G.
Polyakov Oleksandr G.
Rvachov Volodymyr O.
Rvachova Tatiana V.
Savchenko Nina V.
Tomilova Eugenia P.
Ukrayinets Natalia A.
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2024-02-02
