
№ 4, 2017

C o n t e n t s and A b s t r a c t s
Reviewandanalytical information 

Krivoshapko S.N. On application of parabolic shells of revolution in civil
engineering in 20002017. Summary Dome is often used by architects for cover of large spans. Only spherical, conical, elliptical, parabolic, and hyperbolic surfaces of revolution among tens of the wellknown surfaces of revolution can be taken for middle surfaces of domes. Spherical domes have the most spread in modern building due to simplicity of their form in comparison with other shells of double curvature. But researches of paraboloidal domes do not end. Some new information on strength analysis of parabolic shells, on determination of the frequencies of their natural vibrations and the examples of application of paraboloid of revolution in civil engineering in 1900=2017 are presented in this review paper.
The main presented bibliography was published in XXI century.
Key words: paraboloid of revolution, parabolic dome of revolution, examples of application of parab0oloid of revolution.

4 
Geometrical investigations of middle surfaces of thin shells 

Berestova S.A, Misyura N.E., Mityushov E.A. Geometry of selfbearing covering on rectangular plan. Summary An algorithm for constructing an unlimited set of velaroid surfaces theoretically suitable for the formation of selfsupporting spatial structures on ectangular plane is given. The general form of the equation of the velaroidal surface is given using two even functions satisfying special boundary conditions. The continuum capacity of the set of these surfaces is proved.
KEY WORDS: velaroidal surfaces, selfsupporting coatings, spatial constructions.

15 
Theory of elasticity 

Hasanov Sh.H. Cracking in sheet structural element under nonuniform stress field. SummaryWe give a mathematical description of calculation model for cracking in sheet structural element under a nonuniform stress field. The model of prefracture zones in state of plastic flow under constant stresses was accepted. The boundary value problem for interaction of zones of weakened interparticle material bonds in the sheet structural element under influence of the inhomogeneous stress field is reduced to a system of singular integral equations. The integral equations further reduce to a system of nonlinear algebraic equations for solution of which we use the method of successive approximations. Sizes of the prefracture zones and limit value of external loads at which in the sheet structural element the cracking occurs are found.
KEY WORDS: sheet structural element, nonuniform stress field, prefracture zone in a state of plastic flow, cracking.

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Kolmogorov G.L., Melnikova T.E., Azina E.O. Application of the BubnovGalerkin method for assessment of stability of nonisotropic plates. Summary The technique of assessment of stability of nonisotropic plates based on application of the BubnovGalerkin method is offered. As an example, the problem of analysis of stability of an orthotropic rectangular plate, by the hinge opera on a contour, under action in a median surface of compression load is considered.
KEW WORDS: anisotropy, stability, plate, critical load, the BubnovGalerkin method, compression. 
29 
Analysis and design of building structures 

Turusov R.A., Andreev V.I., Tsybin N.Yu. General solution of bending of
multilayer beams in Fourier series. Summary The article deals with the solution of the problem of bending of a hinged multilayer beam under the normal uniformly distributed load and induced axial forces. The interaction between layers is accomplished by the contact layer in which the substances of adhesive and substrate are mixed. We will consider the contact layer as the transversal anisotropic medium with such parameters that it can be represented as a set of short elastic rods, which are not connected to each other. The solution is obtained in the form of decomposition into Fourier series of sines. There is an example of the calculation of a threelayer beam. The convergence of the obtained solution is analyzed according to the number of accounted members of the decomposition 
34 
Razzakov S.J., Kholmirzaev S.A. Influence of frame work strengthening on the stressstrain state of twostorey buildings of lowstrength materials. Summary On the basis of the spatial model, the researches of stressstrain state of a twostory building from lowstrength material for substantiate the effectiveness of the installation frame were fulfilled. The frame helps to reduce the stress and strain in the loadbearing structures and ensures reliable operation housing in areas with high seismicity. The choice of physicalandmechanical characteristics for the material of brickwork is realized on the basis of natural experiments. Two models are considered: with strengthening and without strengthening of the walls by the frame. Analysis of a boxtyped structure is carried out numerically by FEM.
Keywords: spatial model, the stressstrain state, the frame, the elasticity, the horizontal brace, strength, stability, dynamic characteristics, finite element method.

43 
Buckling analysis of reticulated shells 

Trushin S.I., Petrenko Ph.I. Influence of physical nonlinearity on the calculated indicators of stability of reticulated onesheet hyperboloid of revolution with different forms of generatrixes. Summary The article contains a comparative stability analysis of initial equilibrium forms of reticulated onesheet hyperboloids of revolution. The calculations are performed taking into account the geometric and the dual (geometric and material) nonlinearities. The influence of the shape of generatrix onesheet hyperboloid of rotation on shells stability in these formulations of the problem is considered. The equilibrium curves of shells with load acting on the upper base are shown.
KEY WORDS: onesheet hyperboloid of rotation, reticulated shell, equilibrium curves, stability, geometrical nonlinearity, physical nonlinearity, straight generatrix, generatrixhyperbola.

50 
Analysis of underground structures 

Golik V.I., Razorenov Yu.I., Lyashenko V.I. The strength of rock structures in underground mining. Summary Questions of the mechanics of rock massif with use resulting in destroyed rocks structures with dynamically occurring in the underground workings of the processes are considered. The ability of natural and technologically disturbed species to maintain stable structure during the interaction in the array is gravitytectonicstructural field is investigated. The model definition elements of the control array is given. It is shown that the rock supporting structure within the covered portions of the crust allows the use of a minimized the cost of labor and materials and construction elements of underground Geotechnology.
Keywords: Mechanics, rock mass, rock, design, management, array, construction Geotechnology.

57 
Strength of flying apparatus 

Firsanov V.V., Gavva L.M. The investigation of the bending form of buckling for structurallyanisotropic panels made of composite materials in operating MATLAB system. Summary The mathematical model relations for buckling investigation of structurallyanisotropic panels made of composite materials are presented. The mathematical model of stiffening rib being torsioned under oneside contact with the skin is refined. One takes into account the influence of panel production technology: residual thermal stresses and reinforcing fibers preliminary tension. The resolved eight order equation and natural boundary conditions are obtained with variation Lagrange method. Computer program is developed using operating MATLAB system. The influence of the structure parameters on the level of critical buckling forces for bending form has analyzed.
Key words: panels made of composite materials, uncentric longitudinal and lateral set, thinwalled rib, nonsymmetric package structure, force and technology temperature action, variation Lagrange method, buckling, bending form, MATLAB.

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Grishmanov A.I. ‘ Prize. 
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