Nonlinear Dynamics : міжнародна конференція
Постійне посилання на розділhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24521
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Документ Structural Modeling of Elastoplastic Deformation Processes of the Bodies of Non-classical Shape(NTU "KhPI", 2016) Sizova, N. D.An approach based on the theory of small elastoplastic deformations is proposed to study the aims of the stress-strain state determining of finned cylindrical and conical bodies of finite sizes. We consider small elastoplastic deformations described by the nonlinear equations system, for linearization of which the variable elastic parameters method is applied. Approximate solution of the linearized elasticity problem at each k-th iteration is made with the use of the R-functions theory in the form of a single analytical expression. Determination of the stress-strain state, the plasticity areas and analysis of the results obtained has been performed with the POLE software package.Документ R-functions in Development of Analytical Identification of Geometrical Objects(NTU "KhPI", 2016) Sheiko, Tetyana I.; Litvinova, Yulia S.; Maksymenko-Sheiko, Kyrylo V.In this paper for mathematical and computer modeling of fractal geometry objects, machine parts and building structure the R-functions theory is applied. The mathematical tools of the R-functions theory are very convenient for the fractal geometry objects description. The equations of the Levi fractal, Pythagoras's tree, Koch's curve, cross and snowflake, Menger's sponge (also known as the Menger universal curve), Sierpinski's carpet, etc. have been constructed. The techniques using both the equations of three-dimensional primitives, and information about the equations of boundaries of sections of reset object have been developed. The equations of the automobile body surface, the bearing sleeve, the stepped shaft having two cogged pulleys, the rotary valve, the revolver drum, the screw having the shaped head, cut and lock surface, the cutter lift, the oil filter arm, etc. were constructed. The equations of the hexahedral cartridge having 91 fuel elements have been constructed using only two R-operations.Документ Application of the R-Functions Method for Nonlinear Bending of Orthotropic Shallow Shells on an Elastic Foundation(NTU "KhPI", 2016) Kurpa, Lidiya; Lyubitska, KaterynaGeometrically nonlinear behavior of orthotropic shallow shells subjected to the transverse load and resting on Winkler’s foundation is investigated. On base of the R-function theory and variational methods problem's solution for shells with complex plan form is proposed. The algorithm to finding upper and lower critical loads is developed. The stress-strain state of shallow shells with the complex planform is investigated including different boundary conditions, properties of material and elastic foundation.Документ R-Functions and WA-Systems of Functions in Modern Information Technologies(NTU "KhPI", 2016) Kravchenko, Victor F.; Kravchenko, Oleg V.; Konovalov, Yaroslav Yu.; Pustovoit, Vladislav I.; Churikov, Dmitry V.The review report consists of five parts. It describes the main physical applications of atomic, WA-systems and R-functions.