Vol 19, No 5 (2023)

A systematic presentation of the modified classical semi-inverse SaintVenant method as an iterative one is given on the example of generating a solution to the differential equations of elasticity theory for a long layered strip. The firstorder differential equations of the plane problem are reduced to the dimensionless form and replaced by integral equations with respect to the transverse coordinate, just as it is done in the Picard method of simple iterations. In this case, a small parameter appears in the integral equations before the integral sign as a multiplying factor, which is used to ensure convergence of solutions in accordance with the Banach’s principle of compressed mappings. The equations and elasticity relations are converted to a form that enables to calculate the unknowns consecutively, so that the unknowns being calculated in one equation are the inputs for the next equation, and etc. Fulfillment of the boundary conditions at the long edges leads to ordinary differential equations for slowly and rapidly changing singular components of the solution with sixteen effective stiffness coefficients that are defined by integrals from the given ones as a stepped function of Young's moduli for each layer. Integrating of these ordinary differential equations makes it possible to obtain the formulas for all the required unknowns of the problem, including transverse stresses that are not defined in the classical theory of the beam and solutions of the edge effect type, and to fulfill all the boundary conditions for the elasticity theory problem. The solution of three boundary value problems of the strip elasticity theory is provided such as for a two-layer strip with layers of the same thickness and different thicknesses, and a strip with an arbitrary number of layers. Formulas for all unknowns of the problem are obtained.

An approach to the construction of equilibrium state diagrams is presented in order to reduce the sensitivity to initial imperfections for the problem of stability for reinforced plates (transfer of the bifurcation point corresponding to the wave formation of ribs and cladding). New ratios of geometric parameters for two variants of strengthened plates have been obtained, where the first critical load of the general form of stability loss is the first by value, and the next critical load corresponds to the local form of wave formation of ribs or cladding. The finite element complex MSC PATRAN - NASTRAN was used to solve the stated above problems. Flat four-node finite elements were applied for modeling. The calculations were performed with account of geometric nonlinearity. The material was considered to be absolutely elastic. Curves of critical load sensitivity to the amplitudes of the initial imperfections were generated. The results demonstrate that transposition of bifurcation points of wave formation in the plate or ribs enabled to obtain curves with less significant decrease of critical load as compared to the initial ones. Consequently, the presented algorithm for changing the geometric parameters of reinforced plates obtained in accordance with new equilibrium state diagrams implements the possibility of rational design of the specified thin-walled systems.

Relevance of the research. Numerical studies of structural frequency response of a large-span building with cylindrical-and-slab roof as a large mechanical system were carried out. Finite element model No. 1 “Superstructure-Fixed-end” . The purpose of the study was to develop the methodology for modal analysis of a large-span building structure with a cylindrical-and-slab roof as a mechanical system with a large number of degrees of freedom . Methods. Numerical analysis of the building dynamics was carried out with the use of the САЕ (Computer-aided engineering) software package Femap NX NASTRAN, which implements the finite element method. Results. The “dangerous” resonant frequencies and forms of harmonic oscillations of the structure were revealed, and the sensitivity of the buildings’ reactions to various structural changes was analyzed. Frequency analysis of harmonic response of the building allowed to obtain dependences of amplitude values of nodal displacements (accelerations) and stresses in finite elements from the frequency of the inducing external force. In the next article, it is proposed to conduct a dynamic analysis of a large-span building with a cylindrical-and-slab roof for seismic effects.

The subject of the study is the contact interaction of deformable elements of linear complementarity problem (LCP). To solve the linear complementarity problem, the Lemke method with the introduction of an increasing parameter of external loading is used. The proposed approach solves the degenerated matrix in a finite number of steps, while the dimensionality of the problem is limited to the area of contact. To solve the problem, the initial table of the Lemke method is generated using the contact matrix of stiffness and the contact load vector. The unknowns in the problem are mutual displacements and interaction forces of contacting pairs of points of deformable solids. The proposed approach makes it possible to evaluate the change in working schemes as the parameter of external load increases. The features of the proposed formulation of the problem are shown, the criteria for stopping the stepwise process of solving such problems are considered. Model examples for the proposed algorithm are given. The algorithm has shown its efficiency in application, including for complex model problems. Recommendations on the use of the proposed approach are given.

One of the promising objects for application in architectural and construction practice are analytically determined structural shapes in the form of thin elastic shells with a median surface in the form of algebraic ruled surfaces on a rhombic plan on the basis of various curves. In particular, this study considers three surfaces with identical framework forming lines of superellipses using framework curves that have the appearance of waterline, midships section, and main buttock lines - lines that have been initially generated and used in shipbuilding. The shapes of structures on a rhombic base were considered. The study contains geometric modeling of such structures, creation of finite element models and their computation. A comparison of the values characterizing the stress-strain state for three different shapes with the same span and lifting arm (variant designing with optimized choice) has been carried out. From the theoretical point of view, the possibility of generating three different surfaces on the same frame seems to be an interesting result. From the viewpoint of strength analysis, one of the three obtained shells was chosen as it has the most uniform stress distribution, which is the most economical in terms of material cost.

The issue of reducing costs for the maintenance of airfield coatings is particularly important nowadays due to the increase in the intensity of domestic air transportation. A significant part of the costs of the operational maintenance of airfields is spent on the purchase of deicing reagents (DIR) used to protect airfield pavements from icing. There is a possibility to reduce the required amount DIR by using of hydrophobizing impregnations (HPI) for cement concrete airfield pavements. The assumption about possibility to reduce costs for DIR by using HPI was proven by laboratory tests on specimens of cement concrete slabs. In the course of laboratory tests the process of airfield pavement icing and de-icing was modeled. According to the results of experimental studies it was determined that the consumption of DIR for cement concrete slabs specimens treated with HPI was reduced by 35% compared to similar specimens without HPI treatment. For the economic evaluation of cost reduction for the purchase of DIRs, the costs of applied DIRs used at civil airfields of the Russian Federation were analyzed, taking into account their location in different climatic zones. The assessment has revealed that the cost savings for the purchase of DIRs can be up to 29.1 %.

This study aims to investigate the effect of 3D-printed polymer shell reinforcemen ton ultra-high-performance concrete. The mechanical properties of ultra-high-performance polymer reinforced concrete have been investigated. At first, the 3D-printed shell reinforcements were designed using 3D Max and Rhino 6 software. Then, each was fabricated through the fused deposition modeling method and positioned into the cubic, cylindrical, and prismatic molds. In the next step, the prepared Ultra-High-Performance Concrete mixture was poured into the molds, and the samples were cured for 28 days. Finally, the compressive, tensile, and flexural strength tests were carried out on the samples. The results indicated that the compressive, tensile, and flexural strengths of reinforced samples were lower than that of the unreinforced ones, respectively. Although including 3D-printed reinforcement decreased the mechanical properties of the Ultra-High-Performance Concrete samples, it changed the fracture mechanism of concrete from brittle to ductile.