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Документ Analysis of free vibration of porous power-law and sigmoid functionally graded sandwich plates by the R-functions method(Shahid Chamran University of Ahvaz, 2023) Kurpa, Lidiya; Shmatko, Tetyana; Awrejcewicz, Jan; Timchenko, Galina; Morachkovska, IrynaInvestigation of free vibration of porous power and sigmoid-law sandwich functionally graded (FG) plates with different boundary conditions is presented in this paper. The FG sandwich plate includes three layers. The face layers are fabricated of functionally graded material (FGM) and middle layer (core) is isotropic (ceramic). Imperfect sigmoid FG sandwich plates with even and linear-uneven porosities and nonporous core layer are studied. Developed approach has been realized in the framework of a refined theory of the first-order shear deformation theory (FSDT) using variational methods and the R-functions theory. The analytical expressions are obtained for calculating the elastic characteristics with the assumption that the values of Poisson's ratio are the same for constituent FGM materials. For rectangular plates, the obtained results are compared with known results and a good agreement is obtained. Vibration analysis of a complex-shaped porous sandwich plate made of FGM has been performed. The effect of various parameters on the dynamic behavior of the plate, such as the type and values of porosity coefficients, power index, lay-up scheme, types of FGM, has been studied.Документ The problem of selecting and structuring of educational material in english when teaching students of technical specialities(Полтавський національний педагогічний університет ім. В. Г. Короленка, 2022) Ponomarenko, Natalia; Ponomarenko, Vitaliy; Neustroieva, Gelena; Timchenko, GalinaThe article deals with the scientifically substantiated methods of selecting and organizing educational material based on its didactic significance, taking into account the characteristics of perception, preservation and forgetting of educational information by students of technical specialities, the peculiarities of the educational process of higher education from the point of view of the influence of educational material on the formation of professional qualities of a future specialist.Документ Research of elasto-plastic bending of thin shells and plates by the R-fanctions method(NTU "KhPI", 2016) Morachkovska, Irina; Timchenko, Galina; Lyubitska, KaterynaThe effective method basing on theory of R-functions and variational structural method is developed for solving non-linear boundary problems. Elastic-plastic bending of thin shallow shells is considered. The problems are reduced to finding stationary points of suggested mixed variational functionals according to the initial linearization due to usage of subsequent loading and Newton-Kantorovich jointly with method of varying elastic parameters. The method is used for automatic calculations in "POLE" programming system for investigations of shell structural elements. The numerical justification of the method is given. New laws of non-linear deformation of shallow shells and plates with complex shapes in plane are established.Документ Research of Nonlinear Vibrations of Laminated Shallow Shells with Cutouts by R-functions Method(NTU "KhPI", 2016) Kurpa, Lidiya; Timchenko, Galina; Osetrov, Andriy OlexandrovichIn present work an effective method to research geometrically nonlinear free vibrations of elements of thin-walled constructions that can be modeled as laminated shallow shells with complex planform is applied. The proposed method is based on joint use of R-functions theory, variational methods and Bubnov-Galerkin procedure. It allows reducing an initial nonlinear system of motion equations of a shallow shell to the Cauchy problem. The mathematical formulation of the problem is performed in a framework of the refined first-order theory. The appropriate software is created within POLE-RL program system for polynomial results and using C++ programs for splines. New problems of linear and nonlinear vibrations of laminated shallow shells with cutouts are solved. To confirm reliability of the obtained results their comparison with the ones obtained using spline-approximation and known in literature is provided. Effect of boundary condition on cutout is studied.Документ Applicatin of R-functions Theory to Nonlinear Vibration Problems of Laminated Shallow Shells with Cutouts(NTU "KhPI", 2016) Kurpa, Lidiya; Timchenko, Galina; Osetrov, AndreyIn present work an effective method to research geometrically nonlinear free vibrations of elements of thinwalled constructions that can be modeled as laminated shallow shells with complex planform is applied. The proposed method is based on joint use of R-functions theory, variational methods and Bubnov-Galerkin procedure. It allows reducing an initial nonlinear system of motion equations of a shallow shell to the Cauchy problem. The mathematical formulation of the problem is performed in a framework of the refined first-order theory. The appropriate software is created within POLE-RL program system for polynomial results and using C+ + programs for splines. New problems of linear and nonlinear vibrations of laminated shallow shells with cutouts are solved. To confirm reliability of the obtained results their comparison with the ones obtained using spline-approximation and known in literature is provided. Effect o f boundary condition on cutout is studied.Документ Application of the Variational-Structural Method to Investigate the Elasto-Plastic Bending of Thin Shells and Plates(NTU "KhPI", 2016) Morachkovska, Irina; Timchenko, Galina; Lyubitska, KaterynaThe effective method basing on theory of R-functions and variational structural method is developedfor solving non-linear boundary problems. Elastic-plastic bending of thin shallow shells is considered. The problems are reduced to finding stationary points of suggested mixed variational functionals according to the initial linearization due to usage of subsequent loading and Newton-Kantorovich jointly with method of varying elastic parameters. The method is used for automatic calculations in «POLE» programming system for investigations of shell structural elements. The numerical justification of the method is given. New laws of nonlinear deformation of shallow shells and plates with complex shapes in plane are established.