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5. Абрамов Л.М. О влиянии неравноупруго-сти на деформативность бетонного элемента при изгибе/ Л.М.Абрамов и др.//Технологии бетонов, 2016.-№1-2.-с.42-44.
Dyakov I.
Dept ofFoundations of Designing and Construction ofVehicles, Ulyanovsk State Technical NUMERICAL METHOD OF CALCULATION OF VEHICLES' UNDERCARRIAGE
ABSTRAKT
In this article, the features of use of numerical methods of calculation of thin-walled steel structures used for the design of vehicles have been analysed. Soma basic methods, trends and updating dynamics of the calculation by using the finite element in practice are demonstrated. The solution of the system of equalities has been realised by excitation of harmonic vibrations at different frequency values in operational range of vehicle undercarriage. The variety of software systems used for solving complex problems of double precision has been mentioned as well.
Keywords: finite element method, boundary elements, collocation method, boundary integral equation, potential of elasticity, orthotopic material.
State of the matter.
Intensive vehicles production has been driven by needs of calculation of bearing systems of thin-walled metal structures. High mechanical strength and ease of membranes provoke their wide use in aircraft structures, railway transport and earth-moving vehicles. In this regard, one of the main tasks of numerical methods of the calculation of thin-walled structures is improving the design of their complex shape under the influence of local and distributed loads. Due to various circumstances, the analytical solution of differential equations for the most practically important problems cannot be established. In this connection, the approximate numerical methods are the only possible approach to the study and obtaining acceptable results in the solution of practical problems in the field of vehicles [1 p. 60].
The most common numerical methods of calculation of plates and membranes are: the collocation method based on sufficiently fine division of the object being studied; finite difference method (FDM), based on the introduction of linear networks with unknown values of the variables at the nodes; different modifications of variational methods, as well as the method of boundary element method (BEM) based on numerical solution of boundary integral equations with the boundary of sampling and FEM based on simulation of the field by a large number of discrete elements of simple structure.
Calculation methods used.
In recent years to solve the problems of mechanics, the boundary integral equation methods (BIEM) or method of potentials has been effectively applied. BIEM solves not just initial differential equations describing the problem under consideration but appropriate to this problem boundary integral equation, which can be constructed with the existence of fundamental solutions for the study of differential operators and in conducting a detailed analysis of the limit relations of the integral representations that occur when moving through the circuit. By the BIEM solution some defini-
tive representation are described at the density boundary. In the numerical solution, discretisation is carried out not for the region but for its boundaries. This leads to a decrease in dimension per unit of the problem being solved.
The boundary element method (BEM) is a method of numerical solution of the boundary integral equation with discretisation of the boundaries region and the task of approximation of density functions on the boundary. From the computational point of view, BEM leads to the system of lower order rather than other numerical methods such as FEM and FDM in solving of the same problem. After solving the equations it is possible to find the solution in any point of the given region by virtue of analytical solutions which true everywhere in this area. Physical values related to derivatives can be obtained analytically by differentiating singular solutions and summarizing them, which also helps improve the accuracy since the numerical integration is always more stable and accurate process than numerical differentiation.
The main directions of the calculation.
Among the methods of BIEM construction two main directions can be distinguished: direct BEN based on the Somiliana's formula obtained from the Betti reciprocal work theorem where the unknown density in integral equation have real physical meaning. In the theory of shells, such quantities are moving, forces and moments. In indirect BEM kernel of integral equations represent a fundamental solution and its derivatives spread over the boundary of the area with some density. The density functions do not have any physical meaning but if they are defined the solution in the field will be determined by calculating the boundary integrals corresponding to the problem being solved.
Indirect BEM in the problems of plates bending is known as a method of compensating loads. The density functions are given the meaning of the loads applied to the infinite plate and distributed over the boundary region or some loop inside which there is a region. The problems of plates bending has been analysed first in
the works of B. G. Korenev, and further development of this method has been made in the works [2, p.141, 5, p. 34, 6, 7].
The following works [3, c.143, 4, c. 233, 7] study the problems of shallow membranes bending in the linear formulation. Using of BEM in problems of calculation membranes is associated with certain difficulties. This happens in many cases because of the lack of fundamental solutions in closed form. The work [6] is devoted to the use of research methods of deformation of plane and spatial bodies in statics. For the main types of boundary conditions at the boundaries discretisation and approximating densities, the transition from the integral relations to their algebraic counterparts has been made. The potential of elasticity method of calculating at the closed analytic expressions for the piecewise-lin-ear and spline approximations of density functions has been introduced. Special attention is paid to such issues as the formation of integral equations at the boundary conditions, analysis of the resulting singularities and the ways to overcome them. Considerable attention is paid to the boundary and discretisation approximation of desired boundary functions within individual boundary elements.
It is used also a graphical output of results of calculation for example in the form of graphic lines of principal stresses on some elements of the design or buckling and modal in solving of relevant problems.
Definition of the forms, period of natural vibrations and dynamic loads is realised by the method of reduction. Definition of the nodes displacements is made by treating of the column of free terms of the system by Gaussian forward and backward substitutions. The calculation of the nodal forces is preceded by sorting of obtained nods movement of the structure.
The material selection is made on the characteristics of the hysteresis loop. At the same time, internal formats and corresponding calculated combinations of nodal forces for experiments or groups of standardized elements are sequentially reead. One of the most common large-scale foreign universal programs is "Automatic System of Kinematic Analysis (ASKA)" which is used in the nuclear, aerospace and machine building industries. ASKA modular structure can be developed by adapting it to meet of new challenges. Calculations on this complex program can be carried out with the usual precision partially with double one. Double precision is desirable to be used only when solving a system of linear equations of equilibrium. But in this case, the amount of RAM used and the time of decisions increase. In the kit of applications performing operations on matrices there is a sub soft named CONVT designed for converting the zero elements of the matrix of the normal into double-precision or from double-precision into usual one. In this sub soft one matrix contains elements in the form of single-precision numbers, and the other in the form of double-precision which is extremely irrational for computer memory: working memory array for solving the system of equations is increased by three times. Calculation accuracy can be improved if we solve the equilibrium equation with double precision. Depending on the type of the computer, it corresponds to the numbers representation to the
number of significant decimal digits. For the IBM computer compatible with PC the number of significant decimal digits Mantis of usual accuracy usually seven, in double one it is eleven.
It is proposed a more efficient algorithm for transforming the coefficients of the equations of normal precision into double one with which both matrix coefficients with the usual precision and double one match. The conversion is performed by means of computer external memory as follows.
Let the coefficient matrix of the system of linear equations form with a single-precision (each element of the matrix has 4 bytes) and written to the external memory in the NF direct access file on the equations of nodes, i.e, the number of entries is equal to KNY i.e. to the number of nodes of the model of structure, and the length of one recording is equal a NSLENTA. The conversion of coefficients matrix of the system of equations of a double-precision is performed by DFORM in which each entry in the external memory of NS LENTA length is converted into two entries, each of which has the length of NS LENTA but each element of the matrix is given by 8 bytes. Since the direct access file remains the same, the conversion is performed with the last file record and as a result, the number of entries in the file is doubled.
The conversion process is performed by DFORM sub soft as follows. In the cycle 1 FMG even elements of the array (of single-precision) is zeroed. In the cycle 2 (the number of nodes in KNY structure, i.e. by the number of entries) from the external memory to NF direct access file the last entry is read (conversion runs from the bottom) which elements are assigned to FMG even elements. Thus, each element of the FMG array is given 8 bytes of which the first 4 bytes is the actual value of the element and the following 4 bytes is set value of 0. Next, an array of FMG is recorded in the external memory. In the sub soft DFORM the FMG array is recorded in the external memory into the last two entries. It is possible to use one record but in this case the description of the NF direct access file the specification of the record length in bytes RECL will be determined as follows: RECL = LENTA-NS-8.
The approaches to study effect of edges and corner points on the boundary of the study area are being analysed. One of the tasks is dedicated to the thin plates bending both in direct and indirect version of the boundary element method. Each of these numerical methods of the theory of membranes is subject to the need of specific problems solution, and they have their own history of formation and subsequent stages of development in order to expand its scope. However, any of the numerical methods, having great advantages in terms of simplicity and efficiency has certain disadvantages often of basic character that determine the scope of its application.
Methods of structures calculation.
It is known that the calculation of various structures is reduced to the determination of stress-strain state, i.e. to solution of the problem of determining the unknown functions: displacements, strains and stresses and integral factors: linear forces and moments in plates
and membranes, internal force factors in sections rods and support reactions etc.
In the calculation of complex engineering thin-walled structures considered as spatial shell-plate-core systems one must use the approximate methods for solving boundary problems in the mechanics of de-formable bodies, which lend themselves to better algorithms and therefore are more suitable for implementation into modern computers. For the study of stress-
strain state of the structures by means of computer the most suited methods are numerical methods in the matrix formulation. One of the universal methods of solving problems of mechanics of a deformable solid body is a FEM, which is presented, in the form of dynamic equilibrium. Conditions for dynamic balance finite element nodes are expressed as
-Bnkup - BU+( Ap+A+As+A+C-®2Jn )un - Bmus - Bntut
(1)
where Ank, Bnk — are matrices of dynamic stiffness; Cn — is a constant coefficient; n is the number of nodes inn the rod system; p, z, s, t are rods numbers adjacent to the node n ; U ,Us,Uz ,Ut,Un are corresponding displacement vectors; Rn concentrated loads vector in the node n ; J n is inertia matrix of n node.
Equation (1) has the symmetrical matrix is and it makes possible to find the natural frequencies and vibrations, and also solutions of the problems of forced oscillations of the system out of the resonance of complicated rod systems forms for example of cylinders
block, cabin frame, wing aircraft etc. The solution of the system of equations (1) is performed by excitation method of harmonic vibrations. Being given different values © in the range of operational values it is possible to get amplitude and frequency vibrations (characteristics) of the considered vehicle undercarriage before the production. For example, chassis frame (fig. 1) is divided into N = 1,2,. ..p — elements and n- nodes,
which bring into line with the system of equations (1) and direction cosines followed by drawing up of the matrix on the diagonal of which there are design characteristics of the elements' static stiffness of the chassis frame and on the lines and columns there are stiffness of the rods. The strength is in kN, torque kN-m.
Fig. 1. Model of structure of the UAZ chassis frame: by numerals (1, 2, ... n) are determined finite elements of side-members
The number of rows and columns corresponds to the number of elements. It should be noted that the use of the FEM solutions is associated with the appearance of errors, which depend on the type of element. Because of the accumulation of errors, it is difficult to get an accurate match of the calculation results with the experimental ones. The accuracy of solutions is affected by the discretisation error and rounding, and by increasing the number of elements first, it is possible to reduce the error and then increase it due to the rounding errors. Stiffness characteristics of the chassis elements are calculated according to the formulas set out in the work [4, p. 233]. All geometrical dimensions of the elements and load are given in meters MPa. The above mentioned
values of operating forces and moments for the elements located along the axis (Y) are not shown because their directions do not have a significant impact.
Below one can see an incomplete design matrix in general terms for the chassis of 18x18. All dimension are given in meters. Above mentioned values for the
elements located along the axis (Y) are not shown, as the direction of the acting forces and moments do not have a significant impact. The finite element's length
(l) is chosen in accordance with constant value of the
stiffness, absence of structural changes or of nodal points and crossings.
u u2 u3 etc.
ux A12 + A13 -B12 -B13
u2 - B12 0 =
u3 - B13 0 A31 + A35 + A34 etc.
u4 0 B42 -B43
u5 0 0 B53
etc.
B12 [U1 ] + B13 [u3 ] B12 [U1 ]+ B24 [u4 ]
B13 [U1 ]+ B34 [U4 ]
B42 [U4 ] + B34 [U4 ]+ B46 [
B53 [U5 ]+ B56 [U6 ]
etc.
where U — are displacement vectors of the start and end of the element correspondingly. Values of Ank, Bnk are given in the design matrix. Diagonally
the values AH/t are placed which are added by i, J .
' EF
where y . is the coefficient considering the energy dissipation in the material; matrix of the static stiffness Ank is given as follows
Ank -
l 0
0
0
0
0
0
12EJz
l3 0
0
0
66 l
0 0
12EJy
l2 0
6EJy
l2 0
0 0
0
GJ,
kp
l 0
0
0 0
6 EJy
l2 0
4EJy
l 0
0
6EJ,
l2 0
0
0
4EJ,
To the values B^ are also added B ~ Bst matrix of which is given as follows:
r EF
Bnk -
I 0
0
0
0
0
V
0
12J
l 0
0
0
6EJz ll
0 0
12EJy
l 0 6EJ
0 0 0
GJ,
kp
xy
ll
l 0
0
0 0
6EJy ll 0
2EJ„
0
l
0
6EJ,
l 0
0
0
2EJ
l
If the results are multiplied by © and then squared one will get a transfer function of the system
Wz (i©)| which is by multiplying by the spectral density of the bumps in the road allows to get
Sz (©) = (i©)|2 S#)COS©t,
where t driving time on uneven road on the basis of specified values.
The frequency © of vibrations of the chassis is given within the range from 1 to 14 Hz and corresponds to the vibrations caused by uneven road and shaft speed. With © = 0 obtained result expresses the value U of movement (stress) of the element under the static loading; and with © = 1,..., n it is possible to obtain these values under the dynamic loads of the chassis.
Fig. 2 shows the results of the calculation of bending and torsion stresses in the left and the right side member of the UAZ chassis.
uï 1J l/l l/l <L>
a
■s
-I—i
bfj
s
pq
120 100 30 60 40
j
1 20
20 40 60 -30
-100
/
/ I I * I A \ i k
J 1 w
Y Y My / \ A
V \
0 0,5 ] L I ,5 ; 1 2.5 l \ /\4 \ 4.
\ /
-
° st. the left O st. right
Ttor: the left
^ tor rigut
Frome length, m
Fig. 2. Diagrams of bending and torsion stresses under static load in the left and the right side members of UAZ
chassis
The calculation of the vehicle chassis bening in the horizontal plane was performed by lateral force Yr=1,84 kN which is determined by the method of the laboratory of chassis and on the basis of NAMI bodies: for 10 kN double weighting characteristics of the vehicle 1 kN is caused by lateral forces acting on the chassis of a ladder-type truck. Further, the calculated horizontal force is distributed over four nodes corresponding to the site of attachment of spring arms in the front suspension, and the same forces distributed in the rear suspension balance it. This definition of the calculated horizontal force acting on the chassis of the truck and its distribution is confirmed by road tests under different driving conditions ("Study of strength and stiffness of
the chassis of the family ZIL-169 vehicles," technical data report NAMI report, number 10430).
Vehicle undercarriage torsion calculation was carried out on the twist angle of the frame of 5 degrees along the length of wheelbase (skew-symmetric loading). The calculation results under symmetrical loading of the frame showed that the stress-strain state of the side member in practice does not affect the options of platform loading being considered. Deflection in the middle part of the side member in the vehicle base for all loadings options is up to 2 mm (Figure 3), and the total deflection (taking into account all parts of the side member), respectively, on loading options is 5.6; 5.8 and 5.9 mm.
Fig. 3. Deflection under the bending of undercarriage's side member UAZ-3303
According to the SAE recommendations for lorries the value of maximum deflection of the side member in the base of the vehicle shall not exceed 12.7 mm. Normal stresses caused by the weight of assemblies on the side member's top shelf reach up to 42 MPa at the front of the member side after the reaction and consequently for every loading options 53; 54 and 55 MPa. The structure of the source data includes information
on the geometry, boundary conditions, structure and physical and mechanical properties of the material. Calculation results such as displacement, force, design combinations, forms and periods of natural vibrations are given in tabular form having indexation familiar to engineers.
Particular attention is paid to the FEM algorithmi-zation problems: the structure of the original data, matrix forming, substructures stiffness, the introduction of boundary conditions of the problem, superelement forming, and resolving system of equations for finite element model-making hierarchy problem solving. FEM matrix machine is so general that theoretically it is possible to make a single computer program that can solve almost unlimited variety of tasks of mechanics of structures. Presented in the block diagram in Fig. 4 the four parts of the algorithm are practically common for all FEM programs of general purpose.
To extend the functionality of the program it is possible to introduce some additional computational procedures, for example, the definition of the hysteresis
loop area of each element, and from it one can predict resource of i structural element specifying the number of load-unload cycles. The value of external work as determined by the hysteresis loop area used for deformation of the material has the form
J = 2,723 • lO"6 K^^Vjsignk / 2TI, (3)
where Ar is hysteresis loop area; ,8) are scale factors for stress q and relative deformations 8
; K is the volume of the test material (element); 4 is the rate unit of the hysteresis loop area changes by i mode of loading.
Data input
+
Fig. 4. Block diagram of metal constructions analytical programs
In implementing of the method of super elements fort of all stiffness matrix are calculated, further from the stiffness matrix a system of linear algebraic equations for the equilibrium of the whole structure.
At the solution stage operations with previously built algebraic equations are realised i.e. the solution of linear algebraic equations with right-hand side already known. With the implementation of the super element, it is required to operate with the values that are applied to the substructure of the whole structure and to perform operations with the initial equations.
At the output stage, it is given information about the stress-strain state of the finite-element model of the problem, the knowledge of which allows to determine the structure and proportions of various issues to resolve during designing. Usually the solution as an outputted to print array of nodes displacement in the design scheme and arrays of internal forces factors and the stresses calculated at predetermined nodes, or related to the corresponding used FE. Based on the values hysteresis loop area is calculated which is proportional to the energy costs.
Since some of the energy is expended in the destruction of the crystal lattice, its value can be expressed as
Л/раз = 2,723-10"6 FnAs, /2л, (4)
where FN is the amount of force expended in the deformation of the material; As is increment of microcracks.
To obtain the equations describing the growth of micro-cracks it is necessary to consider the damage and destruction of the structural elements that fall in the crack front. In general, the task is complicated by the need to consider the stress concentration zone and plastic deformation covering a large number of structural elements, which are located near the front cracks.
Using external equilibrium conditions (3) and internal (4) power consumption in the first approximation one can obtain the equality
it follows that
M = ArM-(oq>fignKVu IFn >
taking into account than VM = Ao6lo6, where
Ao6 is the cross-section area of the element; lo6
length of the element. Then
M = 4/oS^cpf'teH/a-i > (5)
where — is the tensile strength of a material
under cyclic loading.
The expression (5) will allow finding the equation of the intensity of the growth of micro-cracks of a certain number of load cycles
As 4 lR
-— = — My —
AN N (o<p) ^
ц
ц
G
—1
In general, the rate of growth of micro-cracks can be described as the multiplication of two functions, one
of which f (J) — depends on the level of energy
consumed and the other f (AJpa3) only on increment of micro-crack. Because of experiments, one obtain the following relationship:
Av = /i(/)/2(A/pa3),
Assuming that a failure occurs at the time of achieving the maximum permissible level of energy
for resource definition we ob-
consumption ^A/pa3 J tain the next expression
KA/pJ/Av.
Here the rate of change of external energy is a random variable with a given probability distribution function, which implies that the resource is a function of a random parameter depending on the number of load cycles (./(A''|( j ). In accordance with the methods of
determining the law of probability distribution of random argument, the distribution function can be expressed as uptime elements:
R (t ) = 1 - fk
p33 ]'
As
v /
Technical condition of the structure for which residual life is predicted can be characterized by an average power consumption, depending on the number of
load cycles / ( ) . By increasing the stress in the
concentrator zone the yield strength is obtained earlier than in other places. Thereby the residual life is defined
R (t) = / (N)-/(N') K,
V /OCT ^
where Kr is effective stress concentration factor.
Effective stress concentration factor is defined as follows:
k = /(Ar)* r /(Ar)r,
where J(A^k is the cost of energy on deformation of the part with concentrator; J(Ar)r energy cost on finite element deformation without stress concentrators.
Conclusion.
However, application of FEM in calculation of complex engineering structures, regarded as the spatial models formed by a set of a large number of different FE results great difficulties. A major disadvantage is the considerable expenditure of time and effort in preparation of background information for the realization of the finite element method. Background information of universal systems is very complex as a rule in the process of describing of the structure (topological and geometric characteristics of the structure). The complexity of the preparation of the topological characteristics is rational for universal software systems with a large library of different FE types, which allows one to perform practically any design calculation as required from these software systems. In addition to the universal software systems, they create special purpose systems for solving various problems arising in the design and evaluation of the stress-strain state of concrete structures i.e. object-oriented systems, which are more convenient to use. Object-oriented systems for determination of stress-strain state of structures are usually
built on a modular principle, which, in turn, may consist of one or more sub softs.
The main modules include the following: initial data input, formation of matrix rigidity, input of kinematic problem for fixing conditions, solution of linear equilibrium equations, calculations of the internal forces and stresses. Solution module of linear system of equations of equilibrium should contain a procedure of calculating of residual, which can be used not only to obtain refined solution of the system, but also to use the very residual for the calculation of rounding errors. In addition, one shall provide the possibility of solving a system of linear equations of equilibrium in double precision. In the process of object-oriented complex programs development it is necessary to use structure features to simplify the preparation of background information and input it into a computer, in particular, the topological characteristics of the structure. However, the complexes must have the program which will generate geometric (design scheme nodes of the problem with their coordinates) and topological characteristics of the structure (matrix of node types or matrix codes for CE) for use them in the preparation of the initial data of finite element structural model with a sufficiently large number of nodes and FE. The complex may contain other various auxiliary programs. For example, in the calculation of the rods structure of vehicles one of the preparation stages of the initial data is calculation of geometric characteristics of thin-walled section, which requires certain skills and causes certain difficulties, i.e. there must be an additional soft for calculation of the geometric characteristics of arbitrary sections of thin-walled rods. This approach in the development of object-oriented software complex for a variety of metal structures allows organise in a standard (similar) form the input background information and display the results of calculation.
References
1. I.F. Dyakov. Matrix form of integration method for random diagrams // Current scientific and technical problems of transportation: proceedings of III international scientific technical conference, Ulyanovsk, UlSTU, 2005 - p. 60-62.
2. I.F. Dyakov. Calculation of geometric characteristics of thin-walled sections // Mathematical methods and models in applied science and technology: proceedings of international conference "Continual algebraic logic, calculation and neuroinformatics in science and technology" (KLIN-2006), chief editor L. I. Vol-gina. Ulyanovsk, UlSTU, 2006. Volume 4, - p. 141142.
3. I.F. Dyakov. Formation of resolving equations in finite element method // Mathematical methods and models in applied science and technology: proceedings of international conference "Continual algebraic logic, calculation and neuroinformatics in science and technology" (KLIN-2006), chief editor L. I. Volgina. Ulyanovsk, UlSTU, 2006. Volume 4. - p. 143-146.
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5. P. P. Kapusta A. N. Veres, I. A. Slabko Experimental study of fatigue resistance and development of
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6. Certificate of the Russian Federation on the official registration of computer
7. soft № 2006611602. Static of random spatial thin-walled rod system / S. A. Chernov, I. F. Dyakov. The applicant and right holder is UlSTU, №
2006610839, application number 9.12.2005, registered in the Record of computer soft 12.05.2006.
8. Certificate of the Russian Federation on the official registration of computer soft № 2006610930. Plane and axisymmetric problem of elasticity theory / S. A. Chernov, I. F. Dyakov. The applicant and right holder is UlSTU, № 2006610046, application number 10.01.2006, registered in the Record of computer soft 9.03.2006.
Leonov V.Ye.
Doctor of Technical Science, Professor, Member of International Academy «EcoEnergy», Kherson State
Maritime Academy, Ukraine.
THE WAYS OF INCREASING ENVIRONMENTAL-ECONOMIC EFFICIENCY OF TECHNOLOGICAL SYSTEMS (BASED ON MARINE TRANSPORT)
ABSTRACT
The modern industrial systems are selectively developing on one vector - economic efficiency, profits - to the damage of the second vector - environmental safety. This gives rise to the World Global problems:
1) limitations and depletion of non-renewable nature resources;
2) environmental issues to the environment, biosphere and human life.
For the operating conditions of marine transport there are considered the ways of solving environmental and economic problems of unidirectional action.
As a result of conducted scientific and experimental researches, the technology, that allows to increase economic efficiency and environmental safety of shipping, is developed.
Relatively to a particular ship, techno-economic performance of the suggested technology is calculated, the absolute and prevented environmental and economic damage to the air are defined, the layout for installation of the complex systems on board is designed.
It should be noted, that the proposed concept of the unidirectional action, that consists of the two main vectors - economic and environmental - can be used in other technological systems as well.
Keywords: technological systems, raw material resources of non-renewable nature, sea transport, economic efficiency, environmental safety, absolute, prevented damage, installation, vessel, concept.
The era of non-renewable hydrocarbons passed its "peak" and maximum in the 70-ies of the 20th century and steadily goes to its end.
The area of gas and oil production moves to Maritime shelves, deep sea developments, the Arctic latitudes. Production of the shale oil, gas and processing of bituminous sand are developing quiet fast and productively.
In article [4] the World's reserves of oil and natural gas, their duration of work and operation are characterized.
At the General Assembly of the United Nations (29.09.2015) the idea of an uncontested transition to non-hydrocarbon raw materials was promoted by the
heads of the major leading world countries to meet the growing needs of technological systems.
In article [4], the conceptual problems of the transfer of technological systems from hydrocarbon to non-hydrocarbon, a hypothetical strategy of gradual transition to non-hydrocarbon raw materials are proposed and a model of obtaining non-hydrocarbon energy, using raw materials with a large number of stock that is available and cheap is developed.
At the International Energy Congress in Turkey (Istanbul, 10.10.2016) the current structure of the distribution of the World's energy resources is given (Fig.1).
