The use of a solid analog and the involvement of an appropriate theory of stability made it possible to perform mathematical modeling and determine the parameters of the critical state of cylindrical mesh shells depending on the geometric characteristics and the number of half-waves of the shape of the loss of stability. The values of the critical load of cylindrical mesh shells are determined taking into account geometric and force factors. According to the results of calculations, the patterns of changes in the number of half-waves of the form of loss of stability and obtaining the minimum value of the critical load under the condition of maximum approximation of flexural and membrane stiffness are revealed and analyzed. A numerical example is shown in which the values of critical load and stiffness are determined, taking into account possible forms of loss of stability. The patterns of changes in these indicators for a given number of half-waves are established and analyzed.

Keywords: cylindrical mesh shells, mathematical modeling, critical load, stability, stiffness, number of half-waves

The article is devoted to the development of a nodal joint for assessing the level of rigidity of a cylindrical mesh shell. Practical recommendations on the assembly of the tightening unit are proposed and the design of the screw coupling for the adjustable tension process is presented. The rational locations of the nodal joints on the lower belts of the support faces are determined. Numerical studies of possible schemes were carried out and the regularity of changes in the vertical movements of nodes from the end to the center was established. The positive contribution of reinforcing elements was revealed and the rigidity of the shell was determined. It is shown that the introduction of puffs with a developed node increases the level of resistance to operational loads and significantly reduces deformations in characteristic zones.

Keywords: nodal connection, cylindrical mesh shell, tightening, screw coupling, reinforcement, stiffness

Studies of a circular cylindrical mesh shell with additional rods and increased rigidity of the supporting ribs were carried out. As part of the search for the optimal design, the criterion of rational material consumption was used. According to the results of the conducted studies, the regularities of the distribution of force factors and deformation parameters were revealed. An assessment of the degree of activity of the work and vulnerability to deformations was carried out. Dangerous areas of surfaces are analyzed, mosaics of forces and displacements are obtained. The contribution of reinforcing elements is determined and the influence of the stiffness of the supporting ribs is revealed. A significant unloading of the spatial structure was achieved and a high level of impact resistance was recorded. A significant decrease in calculated indicators was obtained.

Keywords: cylindrical mesh shell, reinforcement with rods, stiffness of support ribs, optimization, forces, displacements, material consumption

The influence of the location of reinforcing bonds on the general condition of cylindrical mesh shells is investigated. Cruciform core elements made of tubular profiles were used as reinforcing structures. The number of reinforcing elements is 8 (4 on each panel). Opposite nodes of adjacent faces are connected by cross-shaped elements in the direction of the arc. The expediency of placing reinforcement elements inside each of the two middle panels and at a distance of one panel from the middle of the length is checked. As a result of the conducted studies, the regularities of the stress-strain state and dangerous areas of the shell were determined. When using cruciform joints, a decrease in the forces in the elements and a decrease in the movements of the nodes were revealed. A redistribution of internal force factors and a decrease in the number of typical sizes of elements were recorded. A rational scheme of reinforcement of the structure is obtained.

Keywords: cylindrical mesh shell, reinforcement, cross-shaped elements, forces, displacements

The article considers the method of applying dynamic effects on cylindrical mesh roofs. The necessity of taking into account oscillatory processes from operating devices and in case of mechanical failure of the attached equipment is justified. The features of the construction of structures and the location of static loads are taken into account. A specific numerical example is given in the framework of application software application. A rational grid shape with a diagonal element in the middle is adopted and acceptable ratios of geometric parameters are obtained. The defining mathematical dependencies are indicated and the dynamic load modeling process is shown. Direct integration of the equations of motion is carried out. The regularities of the influence of oscillatory processes on the operation of the roof are revealed and a visual visualization of the results is obtained. Extreme values of force factors and parameters of deformation of the structure at a given time interval are recorded.

Keywords: cylindrical mesh roof, direct integration of equations of motion, dynamic impact, force factor, deformation parameter

As part of the optimization of the design solution, studies of a cylindrical rod roof with increased rigidity of the support ribs and taking into account the reinforcement of the system with puffs were carried out. The required distance between the tension elements along the length of the structure is determined and the dimensions and shape of the section of the lower ribs are proposed. An optimality criterion with control parameters has been developed and three standard sizes of rods for the greatest efforts have been taken into account. Internal force factors and node movements with and without reinforcement are obtained. A positive redistribution of efforts on the surface and a decrease in the deformability of the roof were revealed. The dependence of the main geometric parameters on the mass is established.

Keywords: cylindrical rod roof, stiffness of support ribs, reinforcement by tightenings, optimization, forces, displacements, mass

The optimal ratio of geometric parameters is found, taking into account the rational distribution of forces on the surface and the minimal change in the shape of the cylindrical mesh shell. As part of the increase in overall dimensions to determine the bearing capacity of the structure, a research program was compiled, an experimental installation was designed and tests were carried out on a physical model. According to the results of the conducted studies, the necessary parameters of the stress-strain state of the shell were determined. The effectiveness of the methods of strengthening the system supports using puffs and horizontal trusses was tested. The regularities of the shell behavior under conditions of full and unilateral application of loads are established. The influence of reinforcement methods on the general condition of the mesh surface is investigated. The degree of unloading of the rod system in the case of horizontal trusses was determined and a significant increase in the load-bearing capacity of the structure was established due to the use of tightening in the support zone.

Keywords: cylindrical mesh shell, geometric parameter, reinforcing element, tightening, horizontal truss

The problem of optimal control synthesis is formulated and the matrix and vector components in the Riccati system are taken into account. Bellman's dynamic programming method was used to determine the patterns. A specific mathematical model of the oscillatory process is considered and its properties are numerically investigated. Examples of linear and quasi-linear problems are given and the minimum possible value of the quality criterion is determined. The corresponding graphical dependencies are constructed and with the help of optimal control tools, the state of the object is transferred from one point to another. Based on the use of the Zubov power series method, optimal control is revealed. Numerical calculations are carried out and Riccati functions are obtained in a nonlinear system with concentrated parameters.

Keywords: synthesis tasks, optimal control, matrix and vector components, Ricatti system, oscillatory process, quality criteria

The condition of a metal cylindrical mesh shell with external horizontal trusses is investigated. The basic principles of forming the structure are considered, taking into account the use of a support rib to align the faces of a mesh surface. The analysis of important force factors and deformation parameters of the reinforced shell is carried out taking into account all possible combinations of loads. The regularities of the system operation are determined and the influence of the location of the support trusses on the behavior of the structure is estimated. Vulnerable areas with maximum longitudinal forces in the elements and the greatest displacements of nodes were identified. An increase in stiffness outside the shell plane in the transverse direction was obtained and a positive redistribution of forces over the surface was recorded. An acceptable result was established from the point of view of ensuring the stability of the structure and the increased resistance of the shell to deformation was noted.

Keywords: cylindrical mesh shell, side elements, horizontal trusses, design parameters, forces, displacements

Studies of a cylindrical mesh shell using the method of decomposition into flat faces and the LIRA application software package have been carried out. The assessment of the possibility of using the considered approaches in the analysis of specific sites and in the case of a complete study of the mesh surface is carried out. The necessary indicators of inclusion in the work of the design, reliability, accuracy and speed of calculation of design parameters are determined. The characteristics of the stress-strain state of the system are revealed, which made it possible to recommend an approximate calculation method for quickly determining preliminary results. Methods of obtaining calculated data in all zones of the shell on a cylindrical surface are analyzed. With the help of application software, a high degree of information about the forces, displacements and mass of the spatial structure was obtained. The simplicity and clarity of visualization of the obtained schemes in accordance with the design requirements are noted.

Keywords: cylindrical mesh shell, approximate method, computer approach, calculated parameters, forces, displacements, mass