"Вестник МГСУ"

The present article studies a procedure of calculating the strength of pipeline support constructions of the above-ground oil trunk pipeline system «Zapolyar'e — oil pumping station «Pur-pe». The calculations of the supports stress-strain state are performed with the use of computer complex Ansys v13, which applies the finite element method. The article provides a short description of the construction of fixed, linear-sliding and free-sliding supports of the oil pipeline of above-ground routing, developed for the installation in complex climatic and geologic conditions of the far north. According to the operation specification for design — the support constructions have to maintain the resistance power and bearing capacity under the influence of the pipeline stress without sagging and considering the possible sagging of the neighboring support. The support constructions represent space structures with a complex geometry. Together with the complex geometry, contacting elements are present in the construction of the supports. There is also an interaction of the pile foundation and the nonhomogeneous foundation. The enumerated peculiarities of the construction and operating conditions of the supports considerably complicate the strength calculations by engineering methods. The method of numerical modeling (finite element method) used in the article for the analysis of the supports’ operation under the stress is widely applied at the present time for calculations of space structures with a complex geometry. For the first time, while performing the supports’ strength calculations, the article considers the mutual deformation of the support, foundation grill and pile foundation in the ground, thus making it possible to consider real operation of the construction altogether. The main development stages of the calculation model “support — pile foundation — ground” in ANSYS, calculation and testing of the static strength of the support constructions are discussed in the article. The authors provide the calculation examples of the supports' stress-strain state for unfavorable combination of loads with maximum bending moment for a fixed support and maximum vertical force and maximum longitudinal-lateral displacement of the top part for a free-sliding support. The use of modern approaches to the operation modeling of the support constructions allows avoiding the excessive conservatism in estimating the stress-strain state of the supports and allows developing the construction optimal for metal intensity, while meeting the requirements for allowable stresses according to the actual normative documents.

Tower cranes are one of the main tools for execution of reloading works during construction. Design of tower cranes is carried out in accordance with RD 22-166-86 “Construction of tower cranes. Rules of analysis”, according to which to ensure stability it is required not to exceed the overturning moment upper limit. The calculation of these moments is carried out with the use of empirical coefficients and quite time-consuming. Moreover, normative methodology only considers the static position of the crane and does not take into account the presence of dynamic transients due to crane functioning (lifting and swinging of the load, boom turning) and the presence of the dynamic external load (e.g. from wind for different orientations of the crane). This paper proposes a method of determining the stability coefficient of the crane based on acting reaction forces at the support points - the points of contact of wheels with the crane rail track, which allows us, at the design stage, to investigate stability of tower crane under variable external loads and operating conditions. Subject: the safety of tower cranes operation with regard to compliance with regulatory requirements of ensuring their stability both at the design stage and at the operational stage. Research objectives: increasing the safety of operation of tower cranes on the basis of improving methodology of their design to ensure static and dynamic stability. Materials and methods: analysis and synthesis of the regulatory framework and modern research works on provision of safe operation of tower cranes, the method of numerical simulation. Results: we proposed the formula for analysis of stability of tower cranes using the resulting reaction forces at the supports of the crane at the point of contact of the wheel with the rail track.

Introduction. At present the urgent problem in hydraulic construction is establishing the causes of crack formation in seepage-control reinforced concrete faces at a number of rockfill dams. For solving this problem the studies are conducted of stress-strain state (SSS) of concrete-faced rockfill dams which are fulfilled by different methods. Materials and methods. Gives a review and analysis of the results of studies of stress-strain state of concrete-faced rockfill dams (CFRD) fulfilled by different authors over the last 15 years. The results of analytical, experimental and numerical studies are considered. Descriptions are given of the models used for simulation of non-linear character of rockfill deformation at numerical modeling of dam SSS. Results. Analysis showed that solving the problem of CFRD SSS causes a number of methodological difficulties. At present the only method permitting study of CFRD SSS is numerical modeling. The rest methods do not permit considering the impact of important factors on SSS. Large complications are caused by scarce knowledge of rockfill deformation properties in real dams. Conclusions. It was revealed that at present SSS of reinforced concrete faces has been studied insufficiently. The results of conducted studies do not give full and adequate understanding about operation conditions of reinforced concrete faces. Impact of various factors on the face SSS has not been studied. Besides, there are contradictions in the results of studies obtained by different authors. Differences in the results are based on objective and subjective reasons. A considerable obstruction for numerical studies is complicated modeling of rigid thin-walled reinforced concrete face behavior at large deformations inherent to rockfill. The obtained results of studies often do not permit conducting full analysis of SSS of concrete-faced rockfill dams.

Introduction. Reviewed the features of the work of the pile on Permian claystones with the help of numerical and field experiments, analytical calculations. Materials and methods. Numerical modeling was performed in the Plaxis 3D and Midas GTS NX software packages. Full-scale tests of driven piles are made in accordance with the requirements of GOST 20276-2012. The obtained results are compared with the results of analytical calculations according to SP 24.13330.2011. Results. The scientific novelty of the investigation consists in a comparative analysis of the results of numerical modeling of the interaction of a driving pile with claystones with the results of field tests and analytical calculations. Finite element analysis in software package Plaxis 3D using Hardening Soil model shows higher values of settlement (up to 6 times) in relation to stabilized settlement of full-scale pile tests. Calculations in the software package Midas GTS NX showed overestimated values of pile settlements in relation to full-scale pile tests (13-24 times). Analytical calculations in accordance with SP 24.13330.2011 also showed overestimated (up to 3 times) values of the maximum pile settlement in relation to the stabilized settlement during full-scale pile tests. Conclusions. The calculations by the finite element method in the package Plaxis 3D and Midas GTS NX, by the analytical method according to SP 24.13330.2011, show overestimated values of settlement in relation to the stabilized settlement of piles on claystones. Using the Linear-Elastic model for claystones in numerical calculations in Plaxis 3D provides a value close to the settlement of full-scale pile. However, the use of this model is not fully justified for claystones due to the presence of residual deformations and the nonlinear character of pile settlement during loading. Necessary to correct the existing numerical and analytical methods for calculating pile foundations on claystones. It is necessary to continue the work on the further generalization of the experience of arranging piles on weathered claystones in order to evaluate the long-term work of not only a single pile, but also a pile foundation.

The present article studies the order of performing low-cycle fatigue strength calculation of the elements of the full-scale specimen construction of the fixed support DN 1000 of the above-ground oil pipeline “Zapolyarye — Purpe” during rig-testing. The calculation is performed with the aim of optimizing the quantity of testing and, accordingly, cost cutting for expensive experiments. The order of performing the calculation consists of two stages. At the first stage the calculation is performed by the finite element method of the full-scale specimen construction’s stressed-deformed state in the calculation complex ANSYS. Thearticle describes the main creation stages of the finite element calculation model for the full-scale specimen in ANSYS. The calculation model is developed in accordance with a three-dimensional model of the full-scale specimen, adapted for rig-testing by cyclic loads. The article provides the description of the full-scale specimen construction of the support and loading modes in rig-testing. Cyclic loads are accepted as calculation ones, which influence the support for the 50 years of the oil pipeline operation and simulate the composite impact in the process of the loads’ operation connected to the changes in the pumping pressure, operational bending moment. They also simulate preloading in the case of sagging of the neighboring free support. For the determination of the unobservable for the diagnostic devices defects impact on the reliability of the fixed support and welding joints of the fixed support with the oil pipeline by analogy with the full-scale specimen, artificial defects were embedded in the calculation model. The defects were performed in the form of cuts of the definite form, located in a special way in the spool and welding joints. At the second stage of calculation for low-cycle fatigue strength, the evaluation of the cyclic strength of the full-scale specimen construction’s elements of the fixed support was performed in accordance with the requirements of Russian State Standard GOST R 52857.6—2007 on the basis of the overall and local stress condition, received according to the results of the calculation in ANSYS. In accordance with the results of the conducted work the conclusion was drawn about fulfilling the standard requirements for the low-cycle fatigue strength of the developed full-scale specimen of the support. Therefore, the application of the modern approaches to the numerical modeling of the fixed support construction operation allowed minimizing the quantity of full-scale tests of the specimen with the cyclic load, escaping the excessive conservatism in evaluation of the cyclic strength and developing of the optimal for the metal intensity construction.

The superelement of a column of rectangular section made of homogeneous material and intended for linear analysis, developed by authors earlier on the basis of the three-dimensional theory of elasticity, is updated with reference to static analysis of reinforced concrete columns with account for geometrical nonlinearity. In order to get the superelement the column is divided on sections and longwise into eight-node solid finite elements modelling the concrete and two nodes rod elements modelling reinforcement. The elements are connected with one another in the nodes of finite element mesh that provides joint operation of concrete and reinforcement. The internal nodes of the obtained finite element mesh are excluded at the stage of stiffness matrix and load vector of a column calculation. Formulas for calculation of linearized stiffness matrix of a superelement and a vector of the nodal forces statically equivalent to internal stresses are received. The element is adjusted to the computer program PRINS, and can be used for geometrically nonlinear analysis of complex structures containing reinforced concrete columns of rectangular section. Separately standing reinforced concrete column was calculated on longitudinal-transverse bending for the verification of the received superelement. The critical load was determined according to the results of calculation. The determined critical force value corresponds to the theoretical value. Thus, the proposed method of accounting for the geometric nonlinearity in the analysis of reinforced concrete columns can be recommended for practical use.

Application of flexible-walled beams is rather effective because the reducing of wall thickness compared to ordinary welded beams leads to substantial reduction of metal expenditure for the walls and its more rational use. The operation experience of such beams shows that the loss of local stability of a wall takes place near bearing cross section with characteristic diagonal type of half waves, indicating, that the reason for the stability loss is in shear deformation. In plate girder with slender web big transverse forces appear, which leads to its buckling as a result of shear. One of the ways to increase stability of the parts of web near supports is to install stiffeners. In the given work the task of finding critical stresses of fixed square plate with installed inclined stiffener is considered. Investigations were performed with the help of finite element method and were experimentally checked. Recommendations were given on the choice of optimal size of the stiffener.

In this paper the author offers is the classification of the formulae of Finite Element Method. This classification help to orient in a huge number of published articles, as well as those to be published, which are dedicated to the problem of enhancing the efficiency of the most commonly used method. The third part of the article considers the variation formulations of FEM and the energy principles lying in the basis of it. If compared to the direct method, which is applied only to finite elements of a simple geometrical type, the variation formulations of FEM are applicable to the elements of any type. All the variation methods can be conventionally divided into two groups. The methods of the first group are based on the principle of energy functional stationarity - a potential system energy, additional energy or on the basis of these energies, which means the full energy. The methods of the second group are based on the variants of mathematical methods of weighted residuals for solving the differential equations, which in some cases can be handled according to the principle of possible displacements or extreme energy principles. The most widely used and multipurpose is the approach based on the use of energy principles coming from the energy conservation law: principle of possible changes in stress state, principle of possible change in stress-strain state.

Solid eight-node finite elements are widely used in practical design in spite of the fact that numerous curvilinear finite elements having multiple nodes are developed. This element is suitable for nonlinear calculations if characteristics of a structure are subject to numerous alterations. Therefore, it is preferable that all calculations were simple. An eight-node element meets this requirement. A standard linear shape function is used by many software programmes to construct this element. Strains and stresses remain constant within the limits of the above element.The authors have developed and implemented a solid eight-node isoparametric finite element using PRINS software. The element developed by the authors has improved bending properties. A quadratic out-of-node shape function was used to improve the bending properties of the element. Principal formulas and testing results are provided. Numerical results confirm the accuracy and effectiveness of the element developed by the authors.

The superelement of the rectangular cross section column designed by the authors earlier for the linear analysis purposes is now applied to analyze the same column with account for the geometric nonlinearity. The superelement is composed of eight solid finite elements. The stiffness matrix technique, the initial stress matrix and the analysis of the vector of unbalanced nodal forces are described.The procedure for excluding internal degrees of freedom of a superelement, using the layer-by-layer reduction method, is described in detail. All calculation formulas are provided in the article. The element, developed by the authors, was adapted to PRINS finite element software; therefore, it can be used to perform the nonlinear analysis of building structures. The console beam, having a rectangular cross section, was analyzed in transverse longitudinal bending to verify the developed element. The comparison of the theory and calculations using PRINS software proved the accuracy of the proposed technique.

The authors consider a dynamic problem solving procedure based on the theory of elasticity in the Cartesian coordinate system. This method consists in the development of the pattern of numerical solutions to dynamic elastic problems within any coordinate system and, in particular, in the polar coordinate system. Numerical solutions of dynamic problems within the theory of elasticity are the most accurate ones, if the boundaries of the areas under consideration coincide with the coordinate lines of the selected coordinate system.The first order linear system of differential equations is converted into an implicit difference scheme. The implicit scheme is transformed into the explicit method of numerical solutions. Using the Galerkin method, the authors obtain formulas for the calculation of both the points of the computational domain and the boundary points.Difference ratios similar to those obtained for a discrete rectangular grid and derived in this paper are suitable to design any geometry, which fact significantly increases the value of the methods considered in this paper.As a test case, the problem of diffraction of a longitudinal wave in a circular cavity, where maximum stresses are obtained analytically, was considered by the authors. The proposed method demonstrated sufficient accuracy of calculations and convergence of numerical solutions, depending on the size of discrete steps. The problem of diffraction of longitudinal waves in a circular cavity was taken for example; however, the proposed method is applicable to any problems within any computational domain.The polar coordinate system is the best one for any research into the diffraction of plane longitudinal waves in a circular cavity, since the boundaries of the computational domain coincide with the coordinate lines of the selected system.

The authors present numerical results of the asymptotic homogenization method for elastoplastic bending of the plate. The plate is supposed to be laminated and exposed to the transversal load. Stresses and displacements in the cylindrical bending problem are compared with those calculated using the 2D finite element method. The new trend in the mathematical simulation of structures, made of composite materials, contemplates accurate consideration of their nonlinear properties (for instance, plasticity or damage) on the micro-structural level of materials. The homogenization method provides for the coupling between the microstructural level and the level of the entire structure. The authors have developed a numerical implementation of this coupling. It represents a combination of the homogenization method and linearization with account for the loading parameter. The approach was implemented as a parallel algorithm and applied to the plastic bending simulation of the FGM plate. The parallel algorithm is based on the overlapping subdomain decomposition method and the Euler explicit and implicit integration methods. MPI was used for software development purposes.In this paper, the authors provide a concise description of the proposed method applied to the 3D boundary-value problem. The authors compare numerical solutions obtained through the application of the homogenization approach and the finite element method. Two types of laminated plates are taken as an example. Three-layered plate was exposed to uniformly distributed transversal loading. The second five-layered plate, that was a lot thinner than the first one, was exposed to piecewise constant transversal loading. All layers of both plates are homogenous; they are supposed to be elastic or bilinearly plastic. It was discovered that the asymptotic homogenization technique provides a more accurate solution for the five-layered plate than for the three-layered one. Edge effects near the edges of the plates are smaller for the thin five-layered plate if compared with the thick three-layered plate. The edge effect appears due to the large value of the plate height-to-length ratio. Nevertheless, the first order asymptotic homogenized method provides sufficient accuracy in both cases.

It is well known, that buildings and their bearing structures are subject to ageing, including corrosion, deterioration, etc. When faults in bearing structure are detected, disposal-at-failure maintenance should be made. But before that, it is necessary to assess the rate of deterioration.The author suggests to use finite element method for calculation of the safety margin of reinforced concrete bearing structures, because the finite element method is widely used in engineering practice of structural design. In the process of engineering inspection of reinforced concrete structures all defects of the inspected structure should be clearly specified. The article suggests to create the FEM-Model of the inspected structure in view of the fact that this structure is defected. In order to achieve this effect, the stiffness matrix of some finite elements should be changed and the FEM-Model must be created of volumetric finite elements (the article speaks about eight-node parallelepiped elements).At first the FEM-Model will be created of eight-node parallelepiped elements with standard descriptions for the reinforced concrete; then finite elements in damage area must be changed. On the basis of integral estimation of the mode of deformation, deformation ratio will be calculated, which is essential for the description assignment of the changes in stiffness matrix. The formulation of the deformation ratio includes all the possible defects of structure through indexes, which must be analytically calculated depending on the concrete defect.The method described in the article is useful in the process of engineering inspection of the reinforced concrete structures. Using this method can sufficiently specify the safety margin of a defected structure and forecast the future operational integrity of this structure under the acting load.

In the article the finite elements were developed that allow to take into consideration the design features of structures and the specific deformation of reinforced concrete without complicating the design scheme. The results of flat structures calculation under different types of loading are presented.The flat finite elements, which are used today in most widespread software systems for the calculation of the majority of buildings and structures, have significant drawbacks due to the peculiarities of the finite element method computational model. The two major drawbacks are: first, stiffness characteristics are specified as for rectangular cross-section and, second, constant stiffness characteristics over the entire area of finite elements is presupposed.These drawbacks are particularly evident in the process of calculating reinforced concrete structures and they significantly complicate the support systems design of multi-storey buildings. The simplifications used by the calculators are dangerous, as it is practically impossible to evaluate the resulting inaccuracies.The calculation model of the finite element method can be represented as a collection of nodes connected in one system with the help of finite elements, which conditionally replace the corresponding parts of a structure.Elasticity theory problems are solved with the help of finite elements of the shells and spatial finite elements. Here the accuracy of the results increases with the increase in breakdown frequency, and one of the main criteria for evaluating the effectiveness of discrete models is their convergence: the worse is the convergence — the higher breakdown frequency is needed to achieve the required accuracy of homogeneous structures calculations.In order to consider the factors affecting the calculations accuracy without increasing the complexity of making the design scheme, it is advisable to arrange a more detailed structure discretization on the stage of developing computational model. This concept is implemented in the discrete-braced computational model, which supposes replacement of the structure sections by the discreet braces combined in nodal points. The main advantages of discrete-braced model are determined by the possibility of multilevel discretization of a structure, achieved in terms of geometrical dimensions and in terms of the direction of digital communication, components of the stressstrain state, stiffness characteristics of digital communications, variable along the longitudinal axis and changing layer by layer in cross section.The basic diagram of the discrete-braced model is: the calculated structure is conditionally replaced by a set of nodes located at the layout grid lines crossing and linked in pairs by the discrete braces, which limit the mutual displacement of the nodal points for all the considered degrees of freedom.The stiffness characteristics of braces are set independently for each brace and each type of deformation on the basis of geometrical and deformational characteristics of the construction sections replaced by braces.In order to determine these sections, conventional boundary lines are traced on the structure, that are located between the grid lines. It is believed that these lines demarcate the structure sections that influence the stiffness parameters of the neighboring connections of one direction. Thus each out-of-node structure point belongs simultaneously to two sections. Stress-strain state of the structure, stiffness characteristics of the braces along the X and Y axes are defined independently of one another. The distributed internal forces arising in front sections of the braces are brought to concentrated generalized forces transmitted through the nodes between the braces in both directions.In the general case, each node of the obtained flat system has six degrees of freedom — three linear and three angular. Generalized displacements inside connections are described by linear functions. Each connection resists six types of deformations — tension and compression, shear in plane of the structure, shear out of the plane, torsion, rotation (bending in plane) and bending out of the plane. In the process of braces deformation, the efforts relevant to deformations appear in them: axial force , two shear forces, torque and two bending moments, and the stress-strain states during deformation of braces in plane and out of plane of the structure are independent from one another.It is offered to determine stress-strain state of the obtained discrete braced-noded system using the method of shifts by means of composing and solving the system of 6n linear algebraic equations (n — the number of nodes ).The accuracy and convergence of the calculation results for discrete-braced model of structural homogeneous isotropic elements is not inferior, and in some cases exceeds the accuracy and convergence of the finite element method results. The use of discretebraced model provides additional opportunities, in particular for non-linear calculations of reinforced concrete structures, which can significantly simplify the numerical schemes used, and thus significantly reduce the calculation complexity.

This summary report is based on the experimental and numerical research of thin-walled cross-section’s compression resistance carried out in St. Petersburg State Polytechnical University. Current situation on the Russian market concerning the usage of cold-formed thin walled cross-sections is aimed at finding out a base foundation to start up a stipulation of the elements under discussion in the building industry. Some questions about the compression resistance of such cross-sections were raised at different conferences by scientific community and such companies as Arsenal ST, Baltprofile (Russia) and Rautaruukki Oyj (Finland). In this field a number of Doctoral theses have been defended during recent years in Russia (A.R. Tusnin, G.I. Belyy, I.V. Astakhov, D.V. Kuz'menko). Steel galvanized Cand U-profiles and thermo-profiles are the types of thin-walled cross-sections are normally used in small houses construction. Thermo-profiles have slots in webs that decrease the thermal flow through the web, but have negative effect on strength of the profiles. Reticular-stretched thermo-profile is a new type of thin-walled cross-sections that found its place on Russian market. These profiles were an object of the research. The carried out investigations included tests to prove the compression resistance of the thin-walled cross-sections. The compression tests as a result showed the behavior of stud’s profile under critical load. The specimen was compressed under various loads and deformation was recorded. In order to get buckling force a load-deformation diagram was plotted and analyzed. Analytical modeling of thin-walled cross-sections was done with contemporary analysis software (SCAD Office) using finite element method (FEM). During the modeling process the thin-walled profile based on shelland bar-elements were created and buckling analysis task showed good results.

In the article, the authors consider some classes of problems of geomechanics that are resolved through the application of SIMULIA ABAQUS software. The tasks associated with the assessment of the zone of influence of structures produced on surrounding buildings and structures in the dense urban environment, as well as the tectonic and physical simulation of rifts with the purpose of identification of deformations of the Earth surface and other defects of lithospheric plates. These seemingly different types of tasks can be grouped together on the basis of common characteristics due to the complexity of numerical modeling problems of geomechanics and geophysics. Non-linearity of physical processes, complexity of the geological structure and variable thickness of layers, bed thinning layers, lenses, as well as singular elements, make it hard to consolidate different elements (for example, engineering and geological elements and associated structures of buildings) in a single model. In this regard, software SIMULIA ABAQUS looks attractive, since it provides a highly advanced finite-element modeling technique, including a convenient hexahedral mesh generator, a wide range of models of elastic and plastic strain of materials, and the ability to work with certain geometric areas that interrelate through the mechanism of contacting surface pairs that have restrictions. It is noteworthy that the research also facilitates development of personal analytical methods designated for the assessment of physical and mechanical properties of heterogeneous materials as well as new solutions applicable in the vicinity of singular elements of the area that may be used in modeling together with ABAQUS software.

The equations of the finite element method for calculation of sandwich shells taking into account creep were obtained. The shell is represented as a set of flat triangular elements. The thickness of the carrier layers is supposed to be small compared to the total thickness of the shell. It is assumed that the outer layers perceive normal stresses, and the average layer perceives the shear forces. In the derivation of governing equations we used variational Lagrange principle. According to this principle, the true moves of all the possible ones satisfying the boundary conditions, are the ones that give a minimum of the total energy. Total energy is the sum of the strain energy and the work of external forces. The problem is reduced to a system of linear algebraic equations. On the right side of this system there is the vector of the sum of the external nodal forces and the contribution of creep strains to the load vector. The calculations were performed in mathematical package Matlab. As the law for description of the relationship between stress and creep strain, we used linear creep theory of heredity. If the core of creep is exponential, the creep law can be written in differential form. This allows the calculation by step method using a linear approximation of the time derivative. The model problem has been solved for a spherical shell hinged along the contour. The relationship between the curvature of shell and the growth of deflections was analyzed. It was found out that for the shells of large curvature the creep has no appreciable effect on the deflections.

The theory of plates and shells is the most important application of the theory of elasticity. Rectangular slabs of average thickness are quite widely in construction, engineering and other fields of modern technology. Calculation of such structures cannot be conducted on the basis of the classical theory of bending of thin plates. In order to obtain a reliable picture of stress-strain state of a plate with average thickness, it is necessary to use different versions of improved theories. The aim of this work is the use generalized equations of the finite difference method (FDM) to calculate the dynamic loads of the plates average with thickness basing on the Reissner theory. On the basis of the developed algorithms computer programs have been worked out for calculating the dynamic load of bending plates of average thickness. The algorithm of calculating the dynamic load of bending plates of average thickness according to generalized equations of FDM can be recommended for practical use in frames of studying process.

In the Soviet Union a lot of residential buildings with wooden window systems were built. In the last 15 years the requirements to heat protection of buildings have strengthened and the technologies of window systems production have developed. New window constructions appeared, in which window frames of PVC profiles are used. So now double-casement windows with glass are replaced by single-casement with glass units. The replacement of windows is associated with a number of specific problems. The authors analyzed the quantitative parameters of the heat losses in the claddings of brick buildings. It was revealed that significant heat leakage occurs in the joint areas of window frame with the wall, at the junction of slopes. The authors offer a quantitative calculation of heat losses in these units in case of two-dimensional heat flux based on thermal conductivity matrix taking into account the convective heat transfer. On the basis of this calculation a computer program was developed that allows pinpointing the most problematic areas for choosing rational actions for elimination of cold bridges.

At the present time a great number of works have been published, in which the problems of numerical solution of geometrical nonlinear tasks of calculating different types of structures are considered. Nevertheless the problem of the certainty of the numerical solution of geometrical nonlinear tasks of rod structures deformation (large displacements) still provokes great interest. The quality of the solution for a certain task is proved only by the coincidence of the results obtained before using two different methods or with the experiment. The authors consider the numerical solution algorithm of geometrical nonlinear tasks of the deformation of hinged-rod systems (large displacements and turns) both in case of high and gentle loading basing on the finite element method in the form of classical mixed method being developed by the authors. Solving the problem of static deformation of a flat mechanical hinged-rod system consisting of two linear-elastic rods the authors show the simplicity and efficiency of the algorithm when finding all the range equilibrium system states. The quality of the solution is proved by the coincidence of the results in case of gentle and heavy loading of the system and with the results of other investigations.