Vol 17, No 1 (2021)

The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.

The seismic resistance of vibration-insulated turbine foundations is a complex and multifaceted problem that includes many aspects. The turbine foundation is a special building structure that unites parts of the turbine and generator unit into a single machine and it is used for static and dynamic loads accommodation. The number of designed and constructed power plants in high seismic level areas is large and steadily growing. In addition, engineers and designers deal with the issue of the frequency composition of the seismic impact influence on the seismic resistance of vibration-insulated turbine foundations. Dynamic calculations were performed in Nastran software using time history analysis and the finite element method. The main criteria for the seismic resistance of a vibration-insulated turbine foundation are the values of the maximum seismic accelerations in the axial direction at the level of the turbine installation and the values of vibration-insulated foundation maximum seismic displacements (deformations of vibration isolators). The results of the calculation experiments proved a significant effect of seismic action frequency composition on the behavior of the vibration-insulated turbine foundations. Calculations of foundations, taking into account earthquakes of the same intensity, but with different values of the prevailing frequencies of the impact, lead to the differing by several times values of the maximum seismic accelerations at the turbine level and seismic displacements.

The article is devoted to modeling and visualization of the formation of flat-nosed (snub-nosed) dodecahedron (snub dodecahedron). The purpose of the research is to model the snub dodecahedron (flat-nosed dodecahedron) and visualize the process of its formation. The formation of the faces of the flat-nosed dodecahedron consists in the truncation of the edges and vertices of the Platonic dodecahedron with the subsequent rotation of the new faces around their centers. The values of the truncation of the dodecahedron edges, the angle of rotation of the faces and the length of the edge of the flat-nosed dodecahedron are the parameters of three equations composed as the distances between the vertices of triangles located between the faces of the snub dodecahedron. The solution of these equations was carried out by the method of successive approximations. The results of the calculations were used to create an electronic model of the flat-nosed dodecahedron and visualize its formation. The task was generally achieved in the AutoCAD system using programs in the AutoLISP language. Software has been created for calculating the parameters of modeling a snub dodecahedron and visualizing its formation.

Nowadays there are various calculation methods for solving a wide range of problems in construction, hydrodynamics, thermal conductivity, aerospace research and many other areas of industry. Analytical methods that make up one class for solving problems, and numerical calculation methods that make up another class, including those implemented in computing complexes, are used for the design and construction of various thin-walled structures such as shells. Due to the fact that thin-walled spatial structures in the form of various shells are widely used in many areas of human activity it is useful to understand and know the capabilities of different calculation methods. Research works on the study of the stress-strain state of the torse shell of equal slope with an ellipse at the base are not widely available at the moment. For the first time the derivation of the differential equations of equilibrium of momentless theory of shells to determine the normal force Nu from the action of uniformly distributed load tangentially directed along rectilinear generatrixes to the middle surface of the torse of equal slope with a directrix ellipse is presented in this article. The parameters of the stress state of the studied torse are also obtained by the finite element method and the variational-difference method. The SCAD software based on the finite element method and the program SHELLVRM written on the basis of the variational-difference method are used. The numerical results of the parameters of the stress state of the studied torse are analyzed, and the advantages and disadvantages of the analytical method and two numerical calculation methods are determined.

Relevance. The load on a reinforced concrete slab with high strength lightweight aggregate concrete leads to increased brittleness and contributes to large deflection or flexure of slabs. The addition of fibers to the concrete mix can improve its mechanical properties including flexure, deformation, toughness, ductility, and cracks. The aims of this work are to investigate the flexure and ductility of lightweight expanded clay concrete slabs reinforced with basalt fiber polymers, and to check the effects of basalt fiber mesh on the ductility and flexure. Methods. The ductility and flexural/deflection tests were done on nine engineered cementitious composite (expanded clay concrete) slabs with dimensions length 1500 mm, width 500 mm, thickness 65 mm. These nine slabs are divided in three reinforcement methods types: three lightweight expanded clay concrete slab reinforced with basalt rebars ∅10 mm (first slab type); three lightweight expanded clay concrete slab reinforced with basalt rebars ∅10 mm plus dispersed chopped basalt fiber plus basalt fiber polymer (mesh) of cells 25×25 mm (second slab type); three lightweight expanded clay concrete slab reinforced with basalt rebars ∅10 mm plus dispersed basalt fiber of length 20 mm, diameter 15 µm (third slab type). The results obtained showed physical deflection of the three types of slab with cracks. The maximum flexural load for first slab type is 16.2 KN with 8,075 mm deflection, second slab type is 24.7 KN with 17,26 mm deflection and third slab type 3 is 32 KN with 15,29 mm deflection. The ductility of the concrete slab improved with the addition of dispersed chopped basalt fiber and basalt mesh.