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Foundation calculation for buildings and structures with two elastic characteristics of the foundation using features of Fourier transformsfor finite functions

Vestnik MGSU 1/2014
  • Kurbatskiy Evgeniy Nikolaevich - Moscow State University of Railway Engineering (MIIT) Doctor of Technical Sci- ences, Professor, head, Department of Underground Structures, Moscow State University of Railway Engineering (MIIT), 9-9 Obraztsova st., Moscow, 127994, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Mai Duc Minh. - Moscow State University of Railway Engineering (MIIT) postgraduate student, Department of Underground Structures, Moscow State University of Railway Engineering (MIIT), 9-9 Obraztsova st., Moscow, 127994, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 41-51

The problem of a beam resting on elastic foundation often occurs in the analysis of building, geotechnical, highway, and railroad structures. Its solution demands modeling of the mechanical behavior of the beam, the mechanical behavior of the soil as elastic subgrade and the form of interaction between the beam and the soil. The oldest, most fa- mous and most frequently used mechanical model is the one devised by Winkler (1867), in which the beam-supporting soil is modeled as a series of closely spaced, mutually independent, linear elastic vertical springs, which, evidently, provide resistance in direct proportion to the deflection of the beam.The solution is presented for the problem of an Euler–Bernoulli beam supported by an infinite two-parameter Pasternak foundation. The beam is subjected to arbitrarily distributed or concentrated vertical loading along its length. Static response of a beam on an elastic foundation characterized by two parameters is investigated assuming, that the beam is subjected to external loads and two concentrated edge load. The governing equations of the problem are obtained and solved by pointing out that there is a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact in the foundation reactions of the two-parameter foundation model. The proposed method is based on the properties of Fourier transforms of the finite functions. Particular attention is paid to the problem, taking into account the deformation of soil areas outside the beam. The beam model with two foundation coefficients more realistically describes the behavior of strip footings under loading.

DOI: 10.22227/1997-0935.2014.1.41-51

References
  1. Korenev B.G. Voprosy rascheta balok i plit na uprugom osnovanii [Problems of Calculating Beams and Slabs on Elastic Foundation]. Moscow, Gosstroyizdat Publ., 1954, 231 p.
  2. Gorbunov-Posadov M.I, Malikova T.A. Raschet konstruktsiy na uprugom osnovanii [Calculation of Structures on Elastic Foundation]. 2-nd edition. Moscow, Stroyizdat Publ., 1973, 627 p.
  3. Pasternak P.L. Osnovy novogo metoda rascheta fundamentov na uprugom osnovanii pri pomoshchi dvukh koeffitsientov posteli [Fundamentals of a New Method of Elastic Foundation Analysis by Means of Two-constants]. Moscow, 1954, 55 p.
  4. Celep Z., Demir F. Symmetrically Loaded Beam on a Two-parameter Tensionless Foundation. Structural Engineering and Mechanics. 2007, vol. 27, no. 5, pp. 555—574.
  5. Eisenberger M., Bielak J. Finite Beams on Infinite Two-parameter Elastic Foundations. Computers & Structures. 1992, vol. 42, no. 4, pp. 661—664.
  6. Sapountzakis E.J., Kampitsis A.E. Inelastic Analysis of Beams on Two Parameter Tensionless Elastoplastic Foundation. Engineering Structures. 2013, no. 48, pp. 389—401.
  7. Ma X., Butterworth J.W., Clifton G.C. Static Analysis of an Infinite Beam Resting on a Tensionless Pasternak Foundation. European Journal of Mechanics — A/Solids. 2009, vol. 28, no. 4, ðð. 697—703.
  8. Razaqpur A., Shah K. Exact Analysis of Beams on Two-parameter Elastic Foundations. International Journal of Solids and Structures. 1991, vol. 27, no. 4, pp. 435—454.
  9. Morfidis K., Avramidis I.E. Formulation of a Generalized Beam Element on a Twoparameter Elastic Foundation with Semi-rigid Connections and Rigid Offsets. Computers & Structures. 2002, vol. 80, no. 25, ðð. 1919—1934.
  10. Kurbatskiy E.N. Metod resheniya zadach stroitel'noy mekhaniki i teorii uprugosti, osnovannyy na svoystvakh izobrazheniy Fur'e finitnykh funktsiy [Solution Method for the Tasks of Construction Mechanics and the Elasticity Theory Based on the Properties of Fourier Transform for Finite Functions]. Dissertatsiya na soiskanie uchenoy stepeni doktora tekhnicheskikh nauk [Doctoral Thesis in Engineering Sciences]. Moscow, MIIT Publ., 1995, 205 p.
  11. Mai Duc Minh. Raschet tonneley, raspolozhennykh v uprugoplasticheskikh gruntakh, peresekayushchikh zony razloma, na seysmicheskie vozdeystviya [Seismic Design for the Tunnels Located on Elasto-plastic Soils Across Fault Zones]. Stroitel'stvo i rekonstruktsiya [Construction and Reconstruction]. 2013, no. 1 (45), pp.19—25.
  12. Klepikov S.N. Raschet konstruktsiy na uprugom osnovanii [Calculation of Structures on Elastic Foundation]. Moscow, Kiev Publ., 1967, 185 p.

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Calculation of plates with variable rigidity on elastic basis by finite difference method

Vestnik MGSU 12/2014
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Barmenkova Elena Vyacheslavovna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Science, Associate Professor, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Matveeva Alena Vladimirovna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 31-39

The article describes the calculation of plates on the elastic basis, both two-layer and single-layer. The calculation is based on the solution of the differential equation of bending plate by finite difference method. The calculation results are compared with the numerical solution in the program complex. The percentage of differences of values depending on the method of division or method of solving is shown. We considered a problem when a foundation plate and a construction are plates, which are deformed together, that, in fact, corresponds to the problem of bending a two-layer plate on elastic basis. In case of a two-layer plate in order to find the solution of the problem we need to solve the equation of bending of plates that are structurally similar to the traditional, but still give different results. In solving finite difference operators derivatives are substituted into differential equation which must be in accordance with each grid point, as well as at the border. If we consider the problem in the conventional formulation, only the lower layer is bended in the plate; the analysis of the plate, which takes into account the weight of its own layers, both layers are deformed together. Also when considering a two-layer plate, the neutral layer is deposed away from the upper layer, consequently, the whole foundation plate may be in the condition of stretching. When comparing the results of analytical and numerical calculations of the values obtained in general there are little discrepancies. Thus, there is the possibility of holding combined calculation of the “structure-foundation-base system” by finite difference method using a two-layer model of a plate on elastic basis.

DOI: 10.22227/1997-0935.2014.12.31-39

References
  1. Yur’ev A.G., Rubanov V.G., Gorshkov A.S. Raschet mnogosloynykh plit na uprugom osnovanii [Calculation of Multilayered Plates on Elastic Basis]. Vestnik Belgorodskogo gosudarstvennogo tekhnicheskogo universiteta im. V.G. Shukhova [Proceedings of Belgorod State Technological University named after V.G Shukhov]. 2007, no. 1, pp. 51—59. (In Russian)
  2. Matveev S.A. Modelirovanie i raschet mnogosloynoy armirovannoy plity na uprugom osnovanii [Modeling and Calculation of a Multilayer Reinforced Plate on Elastic Foundation]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 2012, no. 3, pp. 29—34. (In Russian)
  3. Gusev G.N., Tashkinov A.A. Matematicheskoe modelirovanie sistem «zdanie — fundament — gruntovoe osnovanie» [Mathematical Modeling of the Systems “Structure — Foundation — Soil Base”]. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Seriya: Fiziko-matematicheskie nauki [Proceedings of Samara State Technical University. Series: Physical and Mathematical Sciences]. 2012, no. 4 (29), pp. 222—226. (In Russian)
  4. Ivanov M.L. Matematicheskaya model’ dlya prochnostnogo analiza prostranstvennoy sistemy «zdanie — fundament — osnovanie» [Mathematical Model For The Structural Analysis Of The Spatial System "Building — Foundation — Base"]. Nauka i sovremennost’ [Science and Modernity]. 2010, no. 5-2, pp. 225—229. (In Russian)
  5. Kashevarova G.G., Trufanov N.A. Chislennoe modelirovanie protsessov deformirovaniya i razrusheniya zdaniy v sisteme «zdanie — fundament — osnovanie» [Numerical Modeling of Deformation and Destruction Processes of the Buildings in the System "Building — Foundation — Base"]. Izvestiya vuzov. Stroitel’stvo [News of Institutions of Higher Education. Construction]. 2005, no. 10, pp. 4—10. (In Russian)
  6. Luchkin M.A. Uchet razvitiya deformatsiy osnovaniya vo vremeni pri sovmestnom raschete sistemy osnovanie — fundament — zdanie [Accounting for the Development of Deformations in the Basis in Time at Joint Calculation of the System Base — Foundation — Building]. Izvestiya Peterburgskogo universiteta putey soobshcheniya [News of the Petersburg State Transport University]. 2006, no. 2 (7), pp. 39—47. (In Russian)
  7. Barvashov V.A., Boltyanskiy E.Z., Chinilin Yu.Yu. Issledovanie povedeniya sistemy osnovanie — fundament — verkhnee stroenie metodami matematicheskogo modelirovaniya na EVM [Research of the Behavior of the System Base — Foundation — the Top Structure by the Methods of Mathematical Modeling on the Computer]. Osnovaniya, fundamenty i mekhanika gruntov [Bases, Foundations and Soil Mechanics]. 1990, no. 6, pp. 21—22. (In Russian)
  8. Mangushev R.A., Sakharov I.I., Konyushkov V.V., Lan’ko S.V. Sravnitel’nyy analiz chislennogo modelirovaniya sistemy «zdanie — fundament — osnovanie» v programmnykh kompleksakh Scad i Plaxis [Comparative Analysis of Numerical Simulation of the System "Building — Foundation — Base" in the Program Complexes Scad and Plaxis]. Vestnik grazhdanskikh inzhenerov [Proceedings of the Civil Engineers]. 2010, no. 3, pp. 96—101. (In Russian)
  9. Andreev V.I., Barmenkova E.V. Ob izgibe sostavnoy balki na uprugom osnovanii [On Bending of a Composite Beam on Elastic Foundation]. Fundamental’nye issledovaniya RAASN v 2009 godu [Fundamental Research the RAACS in 2009]. 2010, vol. 2, pp. 74—79. (In Russian)
  10. Andreev V.I., Barmenkova E.V. Raschet dvukhsloynoy plity na uprugom osnovanii s uchetom sobstvennogo vesa [Calculation of a Two-layer Plate on Elastic Foundation Considering its Own Weight]. Teoreticheskie osnovy stroitel’stva : trudy 19 Rossiysko-pol’skoslovatskogo seminara [Proceedings of the 19th Russian-Polish-Slovak seminar “Theoretical Foundations of Construction]. Zhilina, 2010, pp. 39—44. (In Russian)
  11. Gabbasov R.F., Uvarova N.B. Primenenie obobshchennykh uravneniy metoda konechnykh raznostey k raschetu plit na uprugom osnovanii [Application of Generalized Equations of the Finite Difference Method as part of the Analysis of Slabs Resting on Elastic Foundations]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 4, pp. 102—107. (In Russian)
  12. Cheng C.N. Solution of Anisotropic Nonuniform Plate Problems by the Differential Quadrature Finite Difference Method. Computational mechanics. 2000, vol. 26, no. 3, pp. 273—280. DOI: http://dx.doi.org/10.1007/s004660000152.
  13. Kim C.K., Hwang M.H. Non-Linear Analysis of Skew Thin Plate by Finite Difference Method. Journal of Mechanical Science and Technology. 2012, vol. 26, no. 4, pp. 1127—1132. DOI: http://dx.doi.org/10.1007/s12206-012-0226-9.
  14. Krys’ko V.A., Krys’ko A.V., Babenkova T.V. The Stress of Multilayered Physically Nonlinear Plates. International Applied Mechanics. 2001, vol. 37, no. 9, pp. 1204—1209. DOI: http://dx.doi.org/10.1023/A:1013242717789.
  15. Wen P.H. The Fundamental Solution of Mindlin Plates Resting on an Elastic Foundation in the Laplace Domain and its Application. International Journal of Solids and Structures. 2008, vol. 45, no. 3, pp. 1032—1050. DOI: http://dx.doi.org/10.1016/j.ijsolstr.2007.09.020.
  16. Chen W.L., Striz A.G., Bert C.W. High-accuracy Plane Stress and Plate Elements in the Quadrature Element Method. International Journal of Solids and Structures. 2000, vol. 37, no. 4, pp. 627—647. DOI: http://dx.doi.org/10.1016/S0020-7683(99)00028-1.
  17. Aizikovich S., Vasiliev A., Trubchik I., Evich L., Ambalova E., Sevostianov I. Analytical Solution for the Bending of a Plate on a Functionally Graded Layer of Complex Structure. Advanced Structured Materials. 2011, vol. 15, pp. 15—28. DOI: http://dx.doi.org/10.1007/978-3-642-21855-2_2.
  18. Golushko S.K., Idimeshev S.V., Shapeev V.P. Metod kollokatsiy i naimen’shikh nevyazok v prilozhenii k zadacham mekhaniki izotropnykh plastin [Collocation and Least Residuals Method as Applied to the Mechanics of Isotropic Plates]. Vychislitel’nye tekhnologii [Computational Technologies]. 2013, vol. 18, no. 6, pp. 31—43. (In Russian)
  19. Idimeshev S.V. Raschet napryazhenno-deformirovannogo sostoyaniya izotropnykh pryamougol’nykh plastin na uprugom osnovanii [Calculation of Stress-Strain State of Isotropic Rectangular Plates on Elastic Foundation]. Izvestiya Altayskogo gosudarstvennogo universiteta [The News of Altai State University]. 2014, vol. 1, no. 1 (81), pp. 53—56. (In Russian)
  20. Isaev V.I., Shapeev V.P. Razvitie metoda kollokatsiy i naimen’shikh kvadratov [Development of Collocations and Least Squares Method]. Trudy Instituta matematiki i mekhaniki [Proceedings of the Institute of Mathematics and Mechanics]. 2008, vol. 14, no. 1, pp. 41—60. (In Russian)

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DEVELOPMENT OF ANALYTICAL MODELS FOR THE ANALYSIS OF FOUNDATIONS OF BUILDINGS AND STRUCTURES IN THE DENSE URBAN ENVIRONMENT

Vestnik MGSU 6/2012
  • Koreneva Elena Borisovna - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor, +7(499) 183-59-94, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 42 - 47

The author proposes analytical methods of analysis of foundation slabs in the dense environment of present-day cities and towns. The two analytical models, including the model of semi-infinite and finite beams are considered. The influence produced by adjacent tunnels, deep excavations and foundation pits is examined. Bedding properties are described through the employment of the Winkler model. Account of additional deflections and angles of deflections must be taken in the above-mentioned cases.

DOI: 10.22227/1997-0935.2012.6.42 - 47

References
  1. Sheynin V.I., Pushilin A.N. Razrabotka inzhenernoy skhemy rascheta konstruktsiy zdaniy s uchetom smeshcheniy zemnoy poverkhnosti [Development of an Engineering Model for Computation of Structures of Buildings with Account for Displacements of the Earth Surface]. Proceedings of the International Scientific and Practical Conference TAR-Russia. Moscow, 2002, pp. 463—467.
  2. Il’ichev V.A., Nikiforova N.S., Koreneva E.B. Metod rascheta deformatsiy zdaniy vblizi glubokikh kotlovanov [Method of Computation of Deformations of Buildings in Proximity to Deep Pits]. Osnovaniya, fundamenty i mekhanika gruntov [Beddings, Foundations and Soil Mechanics]. 2006, no. 6, pp. 2—6.
  3. Koreneva E.B., Grosman V.R. Raschet lentochnogo fundamenta vblizi glubokoy vyemki [Computation of Strip Foundation in Proximity to Deep Pits]. Proceedings of International Conference on Geomechanics «Development of Cities and Geotechnical Engineering». St.Petersburg, 2008, vol. 3, pp. 146—152.
  4. Koreneva E.B. Voprosy analiticheskogo modelirovaniya raboty polubeskonechnykh fundamentov, raspolozhennykh vblizi glubokikh vyemok ili kotlovanov [Problems of Analytical Simulation of Behaviour of Semi-infinite Foundations in Proximity to Deep Excavations and Pits]. Journal for Computational Civil and Structural Engineering. 2012, no. 1, pp. 12—18.
  5. Korenev B.G. Voprosy rascheta balok i plit na uprugom osnovanii [Problems of Analysis of Beams and Plates resting on Elastic Foundation]. Moscow, Gosstroyizdat Publ., 1954, 231 p.

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CERTAIN STATICS-RELATED PROBLEMS OF CIRCULAR ORTHOTROPIC AND ISOTROPIC PLATES

Vestnik MGSU 7/2012
  • Grosman Valeriy Romanovich - Moscow State University of Civil Engineering (MSUCE) Senior Lecturer, Department of Informatics and Applied Mathematics, +7(499) 183-59-94, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 65 - 68

In the paper, the author considers a relevant problem of structural mechanics. The antisymmetric bending of constant thickness orthotropic and isotropic circular plates, resting on the elastic Winkler foundation, is the subject of the research. Supplemental analytical solutions are obtained. Solutions are represented as Bessel functions.
Problems of symmetric and asymmetric flexure of isotropic circular plates, resting on the Winkler foundation, enjoy extensive coverage in the literature
The paper represents an essential generalization of the research of professor Conway obtained for the case of the axially symmetric flexure of an isotropic circular plate, resting on the Winkler foundation.
Currently, numerous software programmes designated for the analysis of buildings and structures are available. In these programs, numerical methods, namely, the finite element method, are used. The exact results presented in this paper can be used to assess the accuracy of numerical results.

DOI: 10.22227/1997-0935.2012.7.65 - 68

References
  1. Korenev B.G. Vvedenie v teoriyu besselevykh funktsiy [Introduction into the Theory of Bessel Functions]. Moscow, Nauka Publ., 1971, 288 p.
  2. Koreneva E.B. Analiticheskie metody rascheta plastin peremennoy tolshchiny i ikh prakticheskie prilozheniya [Analytical Methods of Analysis of Plates of Variable Thickness and Their Practical Applications]. Moscow, ASV Publ., 2009, 238 p.
  3. Kamke E. Spravochnik po obyknovennym differentsial’nym uravneniyam [Reference Book of Ordinary Differential Equations]. Moscow, Nauka Publ., 1965, 703 p.
  4. Koreneva E.B., Grosman V.R. Nekotorye voprosy rascheta ortotropnykh plastin, lezhashchikh na uprugom osnovanii, i issledovaniya osesimmetrichnykh kolebaniy kruglykh ortotropnykh plastin [Certain Problems of Analysis of Orthotropic Plates, Resting on the Elastic Foundation, Research of Axis-Symmetric Vibrations of Circular Orthotropic Plates]. Collection of works no. 14, part 1 «Problems of Applied Mathematics and Computing Mechanics». Moscow, MSUCE, 2011, pp. 176—178.
  5. Koreneva E.B. Grosman V.R. Analiticheskoe reshenie zadachi ob izgibe krugloy ortotropnoy plastiny peremennoy tolshchiny, lezhashchey na uprugom osnovanii [Analytical Solution of the Problem of Bending of Variable Thickness Circular Orthotropic Plates, Resting on the Elastic Foundation]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2011, no. 8, pp. 156—159.

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