Vol 19, No 6 (2023)

This study considers a plane statically determinate truss with double lattice structure and without a lower chord. Well-known versions of this design are Fink and Bollman trusses. Two methods are used to derive the analytical relationship of the lower limit of the fundamental frequency with the number of panels in the periodic structure. It is assumed that mass of the truss is concentrated at its joints (nodes). The nodes vibrate vertically, and the number of degrees of freedom coincides with the number of nodes. The stiffness analysis of the truss is performed using the Maxwell - Mohr method. The forces in the elastic elements and the reactions of the roller and pin supports are calculated by the method of joints depending on the size of the truss and its order of periodicity. The system of linear equations is solved using the inverse matrix method. The Dunkerley method of partial frequencies is used to calculate the lower limit of the fundamental frequency. For a series of solutions obtained for trusses with different number of panels, the common term in the sequence of solution formulas is found by induction using Maple software. The solution coefficients have polynomial form in the number of panels of order not higher than the fifth. The solution is compared with an approximate version of the Dunkerley method, in which the sum of the terms corresponding to partial frequencies is calculated using the mean value theorem. The closeness of the frequency obtained by the two analytical methods to the numerical frequency spectrum solution is shown by particular examples. An approximate version of the Dunkerley method has a simpler form and an accuracy comparable to the original Dunkerley method.

Known methods and approaches are ineffective or not applicable at all in the study of mechanical characteristics and adhesion of coatings of complex structure, initially formed on non-planar surfaces. A device has been developed that includes fragments of spherical substrates with rings for mounting along the contour, a pressure source of the working medium with a pressure gauge, a line with a valve for supplying the working medium, a measuring complex and a line for etching the working medium. In a fragment of a spherical substrate there is a small diameter hole, in the area of which a cover is formed according to a given technology. The working medium is fed through a small hole in the tray. A segment of the coating detached from the substrate forms a dome in the form of an ellipsoid fragment. A numerical model of deformation of a coating fragment in the form of a spherical segment with a complex contour is being developed using well-known software complexes. At each step of loading by the “targeting” method, varying the modulus of elasticity and the Poisson’s ratio, we approach the parameters of the experimental dome and determine the actual mechanical and stiffness properties of the coating under study. We calculate the normal separation forces through the radial forces determined by the current numerical model, and then determine the coupling stresses. The developed experimental-theoretical method is an effective tool for evaluating the mechanical properties and stiffness of coatings of complex structure, as well as the adhesion of the coating to a spherical substrate.

Conical shells and their panels are important elements of building structures, but have not been studied sufficiently. This paper explores buckling of truncated steel conical panels reinforced with an orthogonal grid of stiffener plates. The panels are simply supported and are subjected to external uniformly distributed transverse load acting normal to the surface. A geometrically nonlinear mathematical model that takes into account lateral shearing is used. Two options of describing the effect of stiffener plates are considered: the refined discrete method and the method of structural anisotropy (the stiffness of the plates is “smeared”). The computational algorithm is based on the Ritz method and the method of continuing the solution using the best parameter. The algorithm is implemented using Maple analytical computing software. The values of critical buckling loads were obtained for two cases of conical panels with different stiffener options. The load-deflection curves are presented. The convergence of the methods for describing the effect of stiffeners with the increase in their number is discussed. It was found that for conical panels, when choosing a small number of unknown coefficients in the approximation, the value of the critical load may be “overshot”, and it is necessary to select a larger number of unknowns compared to cylindrical panels or flat shells of double curvature.

The solid finite element has been developed for the calculation of massive reinforced concrete structures with cracks. When constructing a finite element in the compression-compression-compression mode, the Willam & Warnke failure criterion was used. The tensile behavior of concrete was assumed to be linear before the crack initiation. Modern building codes require non-linear calculations of concrete and reinforced concrete structures, taking into account the real properties of concrete and reinforcement. In this regard, a technique has been developed and a solid finite element has been built, adapted to the PRINS software, which makes it possible to perform calculations of massive reinforced concrete structures, taking into account their actual work. Development of a method for calculating reinforced concrete structures under conditions of a three-dimensional stress state, taking into account the brittle fracture of compressed concrete and cracking in tensile concrete. Based on this technique, the implementation of a solid finite element in the PRINS software. To verify the developed finite element, a series of test calculations of a beam under three-point bending conditions was carried out. Comparison of the calculation results with the data of experiments by the authors confirmed the high accuracy and reliability of the results obtained. The developed solid finite element included in the PRINS software can be effectively used by engineers of design and scientific organizations to solve a wide class of engineering problems related to the calculations of massive reinforced concrete structures.

The study analyzed the structural characteristics of carbon nanomaterials obtained at different time parameters of the synthesis based on X-ray diffractometry, Raman spectroscopy, and scanning microscopy. According to the Raman spectroscopy and X-ray scattering data, the crystallite size of nanotubes is estimated to be in the range from 9 to 38 nm. With the synthesis time of 90 minutes, the nanotube crystallite size remains minimal in comparison with other samples, which is confirmed, among other things, by various diagnostic methods. Based on the X-ray diffraction data, the Lc and La crystallite sizes (longitudinal and perpendicular to the direction of the carbon layers) were calculated using the Selyakov-Scherrer formula. The sizes of nanotube crystallites as a result of increasing the synthesis time are in the range of 9-12 nm in the longitudinal direction and 22-38 nm in the perpendicular direction. The diffraction patterns of the samples do not reflect the presence of a significant amount of graphite; the intensity structure is predominantly in the (002) and (004) peaks, which are characteristic of nanotubes. As a result of the use of nanotubes as a modifier component with a synthesis duration from 40 to 90 minutes, an increase in the performance of the composite up to 20-25 % relative to the control sample is observed.