Volodymyr Shvabyuk’s research while affiliated with Lutsk National Technical University and other places

Most refined bending models of medium-thick plates, which consider transverse shear and partial compression deformations, differ little. However, despite a significant increase in the order of the governing differential equations, the results obtained from their equations give mainly a small increase in accuracy compared to the existing theories. On the other hand, such an increase in the order of the constructed systems of differential equations requires a significant increase in the effort required to solve them, complicates their physical interpretation, and narrows the range of people who can use them, primarily engineers and designers. Therefore, developing a plate-bending model that incorporates all the above factors and is on par with previously applied theories regarding the complexity of the calculation equations remains relevant. For example, most of the applied theories that do not consider transverse compression cannot be used to solve problems of contact interaction with rigid and elastic dies and bases because it is impossible to satisfy the conditions at the contact boundary of the outer surface of the plate, as well as the boundary conditions at the edges of the plate. Therefore, to provide guaranteed accuracy of the results, some researchers of these problems have introduced such a concept as “energy consistency” between the functions of representation of the displacement vector components, their number, the order of equations, and the number of boundary conditions. The authors, based on the developed version of the model of orthotropic plates of medium thickness, investigate the problem of taking into account the so-called “energy consistency” effect of the bending model, depending on the order of the design equations and the number of boundary conditions, as well as its usefulness and disadvantages in practical calculations. The equations of equilibrium in displacements and expressions for stresses in terms of force and moment forces are recorded. For rectangular and circular plates of medium thickness, test problems are solved, and the numerical data are compared with those obtained using spatial problems of elasticity theory, as well as the refined Timoshenko and Reissner theories. An analysis of the obtained results is provided.

The research of the influence of technological modes has been carried out and the negative influence of contaminating impurities on the lead iodide crystallization process has been grounded. The new technological approach to PbI2 single crystals growth has been proposed, which, unlike traditional methods, is based on increasing of the purity of the source components at the initial stage of technological process. The comparative analysis of the proposed growth technique with other known methods has been made, the efficiency of the purification operation of the Pb and I2 source components for the obtention and properties of PbI2 single crystals has been determined. The main types of defects during PbI2 crystallization from the melt have been analyzed and technological approaches for elimination of the structural violations have been proposed.

Specified calculation of steady-state oscillations of circular transtropy plates of medium thickness was performed. The calculation considers transverse displacement deformation and transverse compression effect. Compared to other plate models, such clarifications highly increase calculation accuracy of their stress-strain state. While considering the influence of tangential loads and inertia forces, they do not change equations structure nor increase their order. Obtained equations deal with specification via certain parameters, which depend on characteristics of plate anisotropy and geometry. The calculation order of the equations remains the same, stresses and forces stay similar as in other plate models. At the same time, their accuracy highly increases and becomes close to the results of elasticity theory spatial problem. In case of hinged round plate, the solutions for the free oscillation frequencies are found. Obtained numeric results are compared with corresponding results of classic theory of Kirchhoff’s thin plates. On the basis of these comparisons, the conclusions about significant influence of transverse displacement and compression effects on the magnitude of oscillation frequencies in the direction of their significant decrease are made. This effect is especially noticeable at low transverse physical characteristics of the plate. This conclusion coincides with corresponding results, which were obtained in the monograph of V.T. Grinchenko for a thick plate in a spatial setting.