DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

BILAYER DIFFERENCE SCHEME OF A NUMERICAL SOLUTION TO TWO-DIMENSIONAL DYNAMIC PROBLEMS OF ELASTICITY

Vestnik MGSU 8/2012
  • Nemchinov Vladimir Valentinovich - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Professor, Department of Applied Mechanics and Mathematics, Mytischi Branch 8 (495) 583-73-81, Moscow State University of Civil Engineering (MGSU), 50 Olimpiyskiy prospekt, Mytischi, Moscow Region, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 104 - 111

Numerical modeling of dynamic problems of the theory of elasticity remains a relevant task.
A complex network of waves that propagate within solid bodies, including longitudinal, transverse,
conical and surface Rayleigh waves, etc., prevents the separation of wave fronts for modeling purposes.
Therefore, it is required to apply the so-called "pass-through analysis".
The method applied to resolve dynamic problems of the two-dimensional theory of elasticity
employs finite elements to approximate computational domains of complex shapes, whereby the
software calculates the speed and voltage in the medium at each step. Preset boundary conditions
are satisfied precisely.
The resulting method is classified as explicit bilayer difference schemes that form special
relationships at the boundary points.
The method is based on an implicit bilayer time-difference scheme based on a system of
dynamic equations of the theory of elasticity of the first order, which is converted into an explicit
scheme with the help of a Taylor series in time, while basic relations are resolved with the help of
the Galerkin method. The author demonstrates that the speed and voltage are calculated with the
same accuracy as the one provided by the classical finite element method, whereby determination
of stresses has to act as a numerically differentiating displacement.
The author identifies the relations needed to calculate both the internal points of the computational
domain and the boundary points. The author has also analyzed the accuracy and convergence
of the resulting method having completed a numerical simulation of the well-known problem
of diffraction of a longitudinal wave speed in a circular aperture. The problem has an analytical
solution.

DOI: 10.22227/1997-0935.2012.8.104 - 111

References
  1. Baron M.L., Matthews. Difraktsiya volny davleniya otnositel’no tsilindricheskoy polosti v uprugoy srede [Diffraction of a Pressure Wave with Respect to a Cylindrical Cavity in an Elastic Medium]. Prikladnaya mekhanika [Applied Mechanics]. A series, no. 3, 1961, pp. 31—38.
  2. Klifton R.Dzh. Raznostnyy metod v ploskikh zadachakh dinamicheskoy uprugosti [Difference Method for Plane Problems of Dynamic Elasticity]. Mekhanika [Mechanics]. 1968, no. 1 (107), pp. 103—122.
  3. Musaev V.K. Primenenie metoda konechnykh elementov k resheniyu ploskoy nestatsionarnoy dinamicheskoy zadachi teorii uprugosti [Application of the Finite Element Method to Solve a Transient Dynamic Plane Elasticity Problem]. Mekhanika tverdogo tela [Mechanics of Solids]. 1980, no. 1, p. 167.
  4. Musaev V.K. Vozdeystvie prodol’noy stupenchatoy volny na podkreplennoe krugloe otverstie v uprugoy srede [Impact of the Longitudinal Steo-shaped Wave on a Supported Circular Hole in an Elastic Medium]. All-Union Conference “Modern Problems of Structural Mechanics and Strength of Aircrafts.” Collected abstracts. Moscow Institute of Aviation, 1983, p. 51.
  5. Sabodash P.F, Cherednichenko R.A. Rasprostranenie uprugikh voln v polose, sostavlennoy iz dvukh raznorodnykh materialov [Propagation of Elastic Waves in a Band Composed of Two Dissimilar Materials]. Collected works on “Selected Problems of Applied Mechanics” dedicated to the 60th Anniversary of Academician V.N. Chelomey. Moscow, VINITI, pp. 617—624.
  6. Clifnon R.J. A Difference Method for Plane Problems in Dynamic Elasticity. Quart. Appl. Mfth. 1967, vol. 25, no. 1, pp. 97—116.

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Calculation of spiral turbine cases according to the equations of flow caused by vortex discharge - circle

Vestnik MGSU 11/2015
  • Mikhaylov Ivan Evgrafovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, Department of Hydraulics and Water Resources, Moscow State University of Civil Engineering (National Research University) (MGSU), ; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Alisultanov Ramidin Semedovich - Moscow State University of Civil Engineering (National Research University) (MGSU) postgraduate student, Assistant Lecturer, Department of Engineering Geodesy, Moscow State University of Civil Engineering (National Research University) (MGSU), ; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 142-156

The authors considered the issues of spiral turbine cases calculation with the help of the equations of fluid flow line of a potential flow induced by vortex discharge-circle situated on an infinite impenetrable cylinder in infinite space filled with ideal (nonviscous) fluid and the characteristics of the flow in spiral cases. It was established that: 1) the stated equations allow calculating the spiral cases, which differ in constructive parameters and the direction of the flow at the entry to the stator of the turbine; 2) slope angle of spiral cones and the direction of the flow at the entry into the stator significantly influence the dimensions of the spiral case; 3) the shape of the cross-sections of the spiral differs from the T-shaped and circle ones usually applied today; 4) the height of the cross-sections is greater than their width. This difference grows in the direction from the entry section to the tooth of the spiral case; 5) the dimensions of the calculated spiral cases are smaller than the dimensions of the cases with round cross sections and bigger than the ones with T shape. It was stated that the theoretical characteristics of the floe formed by spiral case calculated according to the equations of the potential flow induced by vortex discharge-circle situated on an infinite impenetrable cylinder are in good agreement with the experimental characteristics and are favourable for flow-around of stay vanes and guide vanes of turbines.

DOI: 10.22227/1997-0935.2015.11.142-156

References
  1. Mikhaylov I.E., Alisultanov R.S. Vikhrevoy stok — okruzhnost’, raspolozhennyy na beskonechnom nepronitsaemom tsilindre [Vortex Discharge — Circle Situated on Infinite Impenetrable Cylinder]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2015, no. 10, pp. 153—161. (In Russian)
  2. Mikhaylov I.E., Alisultanov R.S. Stok — okruzhnost’, raspolozhennyy na poverkhnosti ili vnutri beskonechnogo nepronitsaemogo tsilindra [Discharge — Circle Situated on the Surface or Inside an Infinite Impermeable Cylinder]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2015, no. 8, pp. 140—149. (In Russian)
  3. Mikhaylov I.E. Turbinnye kamery gidroelektrostantsiy [Turbine Cases of HPPs]. Moscow, Energiya Publ., 1970, 272 p. (In Russian)
  4. Menter F.R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA J. 1994, vol. 32, no. 8, pp. 1598—1605. DOI: http://dx.doi.org/10.2514/3.12149
  5. Rusanov A.V., Kos’yanov D.Yu., Sukhorebryy P.N., Khorev O.N. Chislennoe issledovanie prostranstvennogo vyazkogo techeniya zhidkosti v spiral’noy kamere osevoy gidroturbiny [Numerical Investigation of Space Viscous Liquid Flow in a Spiral Case of an Axial Flow Turbine]. Vostochno-Evropeyskiy zhurnal peredovykh tekhnologiy [Eastern-European Journal of Enterprise Technologies]. 2010, vol. 5, no. 7, pp. 33—36. (In Russian)
  6. Rusanov A.V., Kos’yanov D.Yu. Chislennoe modelirovanie techeniy vyazkoy neszhimaemoy zhidkosti s ispol’zovaniem neyavnoy kvazimonotonnoy skhemy Godunova povyshennoy tochnosti [Numerical Modelling of the Flows of a Viscous Incompressible Fluid Using Implicit Quasimotor Godunov Scheme of an Extended Precision]. ]. Vostochno-Evropeyskiy zhurnal peredovykh tekhnologiy [Eastern-European Journal of Enterprise Technologies]. 2009, vol. 5, no. 4, pp. 4—7. (In Russian)
  7. Tao Jiang, Kezhen Huang. The Numerical Simulation of Gas Turbine Inlet-Volute Flow Field. World Journal of Mechanics. 2013, vol. 3 (04), pp. 230—235. DOI: http://dx.doi.org/10.4236/wjm.2013.34023.
  8. Shi F. and Tsukamoto H. Numerical Study of Pressure Fluctuations Caused by Impeller-Diffuser Interaction Diffuser Pump Stage. ASME Journal of Fluid Engineering. 2001, vol. 123 (3). DOI: http://dx.doi.org/10.1115/1.1385835.
  9. Wu K.Q. and Huang J. Numerical Analysis of the Fan Volute Internal Vortex Flow. Engineering Thermophysics. 2001, vol. 22, no. 3, pp. 316—319.
  10. Pfau A., Treiber M., Sell M., Gyarmathy G. Flow Interaction from the Exit Cavity of an Axial Turbine Blade Row Labyrinth Seal. Journal of Turbomachinery. 2001, vol. 123 (2), pp. 342—352. DOI: http://dx.doi.org/10.1115/1.1368124
  11. Schlienger J., Pfau A., Kalfas A.I., Abhari R.S. Single Pressure Transducer Probe for 3D Flow Measurements. 16 Symposium on Measurement Technology in Turbomachinery, 24—25.9.2002. Cambridge, 2002, 8 p.
  12. Rusch D., Pfau A., Schlienger J., Kalfas A.I., Abhari R.S. Deterministic Unsteady Vorticity Field in a Driven Axisymmetric Cavity Flow. Accepted at the 12th International Conference on Fluid Flow Technologies, September 3—6, 2003, Budapest, Hungary. 2003.
  13. Bubenchikov A.M., Korobitsyn V.A., Korobitsyn D.V., Kotov P.P., Shokin Yu.I. Chislennoe modelirovanie osesimmetrichnykh razryvnykh potentsial’nykh mnogosvyaznykh techeniy neszhimaemoy zhidkosti [Numerical Modeling of Axisymmetric Noncontinuous Potential Multiple Connected Flows of Incompressible Fluids]. Zhurnal vychislitel’noy matematiki i matematicheskoy fiziki [Computational Mathematics and Mathematical Physics]. 2014, vol. 54, no. 7, pp. 1194—1202. (In Russian)
  14. Vaynshteyn I.I., Litvinov P.S. Model‘ M. A. Lavrent‘eva o skleyke vikhrevykh i potentsial‘nykh techeniy ideal‘noy zhidkosti [The Model of M. A. Lavrentiev on Adhesion of Vortex and Potential Flows]. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva [Vestnik SibSAU. Aerospace Technologies and Control Systems]. 2009, no. 3 (24), pp. 7—9. (In Russian)
  15. Vaynshteyn I.I., Fedotova I.M. Zadacha Gol’dshtika o skleyke vikhrevykh techeniy ideal’noy zhidkosti v osesimmetricheskom sluchae [Goldshtick Problem on Adhesion of Vortex Flows of an Ideal Fluid in Axisymmetric Case]. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta im. akademika M.F. Reshetneva [Vestnik SibSAU. Aerospace Technologies and Control Systems]. 2014, no. 3 (55), pp. 48—54. (In Russian)
  16. Yan H.J., Hu D.M. and Li J. Numerical Simulation of Flow Field for Horizontal-Axis Wind Turbine Rotor. Journal of Shanghai University of Electric Power. 2010, vol. 26, no. 2, pp. 123—126.
  17. Yang C.Z., Liu H.C. and Zhou Y.L. The Design of Horizontal Axis Wind Turbine Blades and the Analysis of Flow Field Based on CFD. Journal of Northeast Dianli University. 2010, vol. 30, no. 1, pp. 21—26.
  18. Zhang D.H., Li W., Lin Y.G., Ying Y. and Yang C.J. Simulation of Generation System of Marine Current Turbine with Pressure-Maintaining Storage Based on Hydraulic Transmission. Automation of Electric Power Systems. 2009, vol. 33, no. 7, pp. 70—74.
  19. Berend G., van der Wall, Richard H. Analysis Methodology for 3C-PIV Data of Rotary Wing Vortices. Experiments in Fluids. 2006, vol. 40, no. 5, pp. 798—812. DOI: http://dx.doi.org/10.1007/s00348-006-0117-x.
  20. Badie R., Jonker J.B., Van Den Braembussche R.A. Finite Element Calculations and Experimental Verification of the Unsteady Potential Flow in a Centrifugal Volute Pump. International Journal for Numerical Methods in Fluids, vol. 19 (12), pp. 1083—1102. DOI: http://dx.doi.org/10.1002/fld.1650191203.

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Geometry graphical variationsof the circular conjugate problems

Vestnik MGSU 7/2015
  • Polezhaev Yuriy Olegovich - Moscow State University of Civil Engineering (MGSU) Associate Professor, Department of Descriptive Geometry and Graphics, member, International Union of Russian Artists, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Borisova Anzhelika Yur’evna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Sciences, Associate Professor, Department of Descriptive Geometry and Graphics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.
  • Borisova Viktoriya Aleksandrovna - Moscow State University of Civil Engineering (MGSU) student, Institute of Environmental Engineering and Mechanization, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 137-146

In civil engineering and architectural design the coupling of circular curves are of great importance. There are different requirements for their practical application, including the possibility of approximation of the curves of higher order. The present article contains a brief excursion into the axiomatic description of the properties and concepts uniting the geometric graphics of a circular, a direct and a point into various compositions. One of the main conjunction theorems is presented, which defines the position and properties of orthoelements of pairing and the sequence of mating arcs using symmetry. The content of the theorem is commented in the form of proof by contradiction, in the form of geometric graphical operations that are naturally consistent with the analytical results. The examples are given of the circular conjunctions closed into oval shapes with a slight difference in the algorithms of composition construction. A particular case of the present configuration is a linear model of squaring the circle, the circle when the medial conjunction coincides with the base circle squaring. Here, the rhomb figure is presented as a basic square and the four successively conjugated circles have their centers at the vertices of squaring, their area are equiareals. Then, the straight “tapered” circular number and variations of its geometry graphical construction are analyzed. The summary results of the considered material are as follows. The main qualitative, quantitative, and typical examples of the circular conjunctions allow competently and variably solving certain problems of geometry graphics in the design process of civil engineering, architecture and applied domestic objects, items and personal things.

DOI: 10.22227/1997-0935.2015.7.137-146

References
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  2. Krylova O.V., Polezhaev Yu.O., Tel'noy V.I. Deduktivnyy aspekt postroeniya izometricheskikh monoproektsiy [Deductive Aspect of Isometric Monoprojections Creation]. Fundamental'nye nauki v sovremennom stroitel'stve: Sbornik dokladov Shestoy nauchno-prakticheskoy i uchebno-metodicheskoy konferentsii [Fundamental Sciences in the Modern Construction]. Moscow, MGSU Publ., 2008, pp. 163—165. (In Russian)
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  5. Polezhaev Yu.O., Borisova A.Yu., Kondrat’eva T.M. Lineynye puchki v tsirkul’no-ellipticheskikh sootvetstviyakh [Linear Bundles within the Framework of Coincidence of Circle and Ellipse]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 6, pp. 62—67. (In Russian)
  6. Stepura E.A., Zontov R.A. Provedenie pryamoy cherez nedostupnuyu tochku [Drawing a straight through a Remote Point]. Sbornik trudov 2-y Vserossiyskoy nauchno-metodicheskoy konferentsii po inzhenernoy geometrii i komp'yuternoy grafike [Collection of Works of the 2nd All-Russian Scientific Conference on Engineering Geometry and Computer Graphics]. Moscow, MITKhT Publ., 2009, pp. 103—110. (In Russian)
  7. Polezhaev Yu.O., Borisova A.Yu. Lineynye variatsii modelirovaniya svoystv elliptichnosti [Modeling the Properties of Ellipticity: Linear Variations]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 8, pp. 34—38. (In Russian)
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  14. Polezhaev Yu.O., Mitina T.V. K voprosu o metodike resheniya zadach intsidentsii [On the Methodology of Solving Incidence Problems]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2007, no. 1, p. 81. (In Russian)
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  19. Polezhaev Yu.O., Fatkullina A.A., Borisova A.Yu. Geometricheskie modeli sopryazheniy kvadrik na fragmentakh arkhitekturnykh ob”ektov [Geometric Models of Junctions of Quadrics in Fragments of Architectural Pieces]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 9, pp. 18—23. (In Russian)
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