The article proposes a technique for optimizing trihedral lattice tower structures according to the criterion of minimum mass, taking into account limitations in strength, ultimate slenderness of elements, stability, and the absence of resonant vortex excitation. A lattice tower with a cross section of elements in the form of round pipes, consisting of two sections, is considered. The variable parameters are the width of the tower, the height of the lower section, the outer diameters of the cross-section of the chords and gratings, the number of panels in the lower and upper sections. The solution of the nonlinear optimization problem is performed in the MATLAB environment using the Global Optimization Toolbox package. Determination of forces in the tower and frequencies of natural oscillations is performed by the finite element method using the subroutine for MATLAB developed by the authors. The influences on the tower are ice and wind loads, the dead weight of the tower, as well as the weight of the equipment. When calculating the effect of wind, the pulsation component is taken into account. The surrogate optimization method is used to solve the nonlinear optimization problem. In the initial approximation, the mass of the tower was 2 tons. As a result of optimization, the mass was reduced by more than 2 times.

Keywords: lattice towers, finite element method, surrogate optimization, resonant vortex excitation

The article discusses a new type of reinforced concrete columns with local prestressing of reinforcement. Such elements can be used for high flexibilities and eccentricities of the longitudinal force, for example, in the construction of industrial buildings. The derivation of resolving equations for determining the stress-strain state of the structures under consideration at the stage of prestressing is presented. Equations are obtained for calculating the level of prestresses in reinforcement, at which technological cracks are formed, expressions for determining stresses in concrete and reinforcement, as well as the deflection of the column at the manufacturing stage. The calculation algorithms are implemented numerically in the MATLAB environment. A comparison of the calculation by the author's method with finite element modeling in the LIRA software package in a three-dimensional setting is presented, taking into account the physical nonlinearity of concrete.

Keywords: reinforced concrete, columns, prestressing, stress-strain state, reinforcement, manufacturing stage, technological cracks, deflection

The relevance of modeling the temperature regime and the stress-strain state in the early period of the construction of massive monolithic reinforced concrete structures is shown. Some data are given on the temperature and time parameters of the formation of temperature fields in structures with a surface modulus from less than 1.1 to 2.4 from concrete classes from B25 to B70, both fast and slowly hardening. Based on the results of processing numerous data, the quantitative values ​​of the parameters of the heat release kinetics for the proposed dependence are substantiated. A simplified method for calculating thermal stresses is proposed, based on the proposed and substantiated dependences of concrete properties on its degree of maturity, which are confirmed by numerous experimental data, incl. obtained by other researchers. The calculated values ​​of stresses obtained during the construction of a temperature-shrinkage block 20x20x2 m from concrete of fast and slow hardening classes B25 and B45 were compared with some experimental results and modeling data. The conclusion is made about the inexpediency of using concrete of class B45 due to the high risk of cracking in the period of 1.5 - 3 days. When using concrete of class B25, preference should be given to fast-hardening.

Keywords: massive monolithic structures, thermal stresses, cracking, degree of concrete maturity, kinetics

The expediency of using modeling using the finite element method to study the influence of certain prescription-technological factors on the resulting temperature fields and temperature stresses during the construction of massive foundation slabs is substantiated. A simplified method for determining thermal stresses based on the reduction of a three-dimensional problem to a one-dimensional one based on the hypothesis of flat sections is considered. The dependence is proposed and the quantitative values ​​of the parameters for calculating the kinetics of heat release of concrete in the temperature-shrinkage block are substantiated. As a result of the implementation of a numerical experiment on the influence of the duration of breaks between overlapping layers, the temperature of the environment and the concrete mixture, the class and kinetics of concrete hardening, and heat transfer parameters, the dependences of the level of tensile stresses on these factors over time were obtained. It is shown that when developing technological regulations for concreting, the determination of technological parameters (the intensity of laying the mixture, the thermal resistance of the formwork, the arrangement of working joints, etc.) is impossible without taking into account the kinetics of concrete hardening, determined by the prescription features of concrete mixtures.

Keywords: massive monolithic structures, temperature fields and stresses, prescription-technological factors, heat release of concrete, stress-strain state

When accepting finished reinforced concrete structures, incl. monolithic, they are subject to requirements for strength, stiffness, crack resistance and durability. The quality of a monolithic reinforced concrete structure depends on the quality of work, the quality of materials, the quality of design solutions and the quality of regulatory documentation. According to SP 70.13330.2012, clause 5.18.1, "when accepting finished concrete and reinforced concrete structures ... you should check ... the quality of concrete for strength, and, if necessary, for frost resistance ...". Particular attention is required for massive monolithic reinforced concrete structures, during the construction of which, due to temperature-shrinkage deformations, it is possible to form an own stress field that exceeds its strength indicators at the stage of formation of the concrete structure, which may result in early cracking with subsequent development of cracks, which will not only negatively affect operational properties of the structure, but in principle can raise the question of the impossibility of its operation. The quality of concrete of a monolithic reinforced concrete structure is determined by both recipe and technological factors, the assessment of the degree of influence of which is an urgent task.

Keywords: massive monolithic reinforced concrete structures, crack resistance, durability, frost resistance, temperature-shrinkage deformation

The article deals with the transition from corrugated plates and shells to smooth structures of equivalent rigidity. An expression for the potential deformation energy of an infinitely small element of an equivalent smooth shell and formulas that establish a connection between internal forces and generalized deformations of a corrugated structure are given. A review of the formulas for the equivalent stiffness of the corrugated shell during bending, presented in the works of various authors, is carried out. In order to select the dependencies that provide the smallest error when replacing the corrugated shell with a smooth one, a numerical experiment is performed in the LIRA finite element complex. A corrugated plate hinged around the contour under the action of a uniformly distributed projective load is considered. The calculation of the structurally orthotropic construction is performed numerically by the finite difference method. It is also established that the monograph of S.G. Lekhnitsky contains an incorrect formula for the moment of inertia of a sinusoidal corrugation.

Keywords: corrugated structures, plates and shells, finite element method, finite difference method, orthotropy, equivalent stiffness

The article discusses the method for calculating beams with corrugated walls as three-layer structures of equivalent rigidity. The derivation of resolving equations for a one-dimensional finite element of a three-layer beam is given. A hypothesis is introduced that the shelves fully perceive normal stresses, and the wall only works on shear. When obtaining the basic equations, forced deformations are taken into account, which may include creep deformations, temperature deformations, shrinkage deformations, etc. The solution of the test problem for a beam hinged at the ends under the action of a load uniformly distributed over the length is presented. To control the reliability of the results, a finite element analysis was performed in a three-dimensional formulation in the LIRA software package. Shelves of the beam are modeled by flat triangular shell finite elements, and the wall is modeled by rectangular shell FE.

Keywords: corrugated wall beam, three-layer beam, finite element method, equivalent rigidity, stress-strain state

The technique of calculating the metal corrugated structures using the finite element method for an axisymmetric load is considered in the article. One-dimensional finite elements in the form of truncated cones are used. Calculations are performed using the program developed by the authors in the Matlab package. An example of calculation of a ground well rigidly clamped in the base under the action of ground pressure is given. The sinusoidal profile of the corrugation is considered. The graphs of changes in bending moments and ring forces are presented. For a smooth shell of the same thickness, the bending moment in the pinch was 30.3% higher compared to the corrugated, and the maximum value of the ring force was 15.7% higher.

Keywords: metal corrugated structures, cylindrical shell, finite element method, axisymmetric problem, soil well, shell theory, edge effect

Flat bending stability problem of constant rectangular transverse section wooden beam, loaded by a concentrated force in the middle of the span is considered. Differential equation is provided for the cases when force is located not in the center of gravity. The solution of the equation is generated numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the package Matlab. A relationship is obtained between the value of the critical force and the position of the load application point. For this dependence, a linear approximating function is chosen. A comparison of the results obtained by the authors with an analytical solution using the Bessel functions is performed.

Keywords: flat bending stability, secular equation, finite difference method, iteration process

Now elements of natural structures of the world surrounding us form a basis for loan by their architects and designers in their professional activity. It is caused not only by esthetic appeal of natural objects, but also big functionality of their form providing high degree of durability, reliability, adaptation to the changing external conditions, comforts of their use as inhabited and production rooms. In this work the analysis of the VAT of an oviform envelope under the influence of sole weight and intrinsic pressure is provided.

Keywords: intense strained state, finite element method, oviform envelope, sole weight, intrinsic pressure, analysis, efforts, deformation

The general equations of the moment theory of a circular cylindrical shell with creep are considered: static, geometric and physical. We solve the problem of determining the stress-strain state of a shell rigidly clamped in the base when an internal hydrostatic pressure acts on it. The problem has reduced to a linear nonhomogeneous differential equation of the fourth order with respect to deflection. The solution was performed numerically by the finite difference method in the Matlab software package. As a law of connection between creep strains and stresses, the generalized nonlinear Maxwell-Gurevich equation was used. To determine the creep strains, a linear approximation of the first time derivative was used. The shell was made from secondary PVC, and as a result, it was found that in the process of creep in the shell, the circumferential stresses increase by 15%.

Keywords: cylindrical shell; creep; moment theory; polymers; finite difference method

The article proposes the derivation of resolving equations for the bending of triangular finite element of plate with regard to creep. In deriving of the equations we use Lagrange variational principle. The problem is reduced to a system of linear algebraic equations. Creep contributes only to the right side of the system of equations. These equations allow to calculate the plates of arbitrary shape, taking into account the viscoelastic properties of the material. An example of the calculation for a rectangular plate of a secondary polymeric PVC, hinged along the contour and loaded uniformly distributed over the area load is presented. As a law establishing a link between stress and creep deformation we used nonlinear equation of Maxwell-Gurevich. Calculations were performed in Matlab software package. The graphs of change in time of deflection and stresses are presented. Stress during creep vary slightly, a difference between the stresses at the beginning and end of creep process does not exceed 6%. The result of numerical calculation of the maximum deflection value at the end of creep is different from the theoretical on 0.26%.

Keywords: creep, finite element method, bending of plates, polymers, Maxwell-Gurevich equation, long cylindrical rigidity

We investigated the creep of concrete arches based on the following theories: the theory of linear creep by Harutyunyan-Maslov, kinetic theory, the theory of flow, theory of aging, and nonlinear theory of Y. Gurieva. We considered viscoelastic model of the concrete, ie total strain was represented as the sum of elastic strain and creep strain. Solution of the problem was carried out by finite element method. We considered the arch rigidly clamped at the ends and loaded with a uniformly distributed load. Graphs of growth of deflection and stress distribution in the reinforcement and concrete are represented. We obtained the substantial redistribution of stress between the reinforcement and the concrete during creep: in reinforcement stresses increased and in concrete stresses decreased. The strongest redistribution occurs on the theory Y. Gureva.

Keywords: reinforced concrete arch, creep theory of heredity, aging theory, the theory of flow, kinetic theory, finite element method, stress-strain state

The stationary heat conduction problem for radiation-heat shield of the reactor nuclear power plant based on domestic sources of heat was solved. We took into account the dependence of the thermal conductivity of the concrete on the temperature, which leads to nonlinear problem. The solution is performed using the finite element method in combination with the method of successive approximations. We used the simplex triangular elements. The problem was solved in axisymmetric formulation. As a design scheme we used a rigidly clamped at the base thick-walled cylinder. It was found that the inclusion of thermal conductivity depending on the temperature leads to a slight (2.5%) increase of temperature in core of the construction.

Keywords: thermal conductivity, finite element method, the steady-state temperature field, radiation-heat shield, thick-walled cylinders

The article presents basic equations for reinforced concrete elements that are experiencing bending moment and axial force, taking into account the creep of concrete. The stress-strain state of reinforced concrete statically determinate three–hinged arch is investigated on the basis of these equations. Also for this task we gained the resolving equations of finite element method and compared the numerical-analytical calculation with the numerical performed using the finite element method to the arch loaded with a uniformly distributed load and having the shape of a circular arc. The calculations used viscoelastic model, according to which the total deformation is the sum of concrete elastic deformation and creep. We consider a rectangular cross section with symmetrical reinforcement. It is shown that because of creep stress redistribution between concrete and reinforcement arises.

Keywords: finite element method, the creep of concrete, viscoelasticity, reinforced concrete arch, the stress–strain state.