DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

EXAMINATION OF THE STRESS-STRAIN STATE OF HETEROGENEOUS BODIES THROUGH THE EMPLOYMENT OF THE METHOD OF BOUNDARY EQUATIONS

Vestnik MGSU 7/2012
  • Khodzhiboev Abduaziz Abdusattorovich - Tajik Technical University named after academic M.S. Osimi Candidate of Technical Sciences, Associated Professor, Chair, Department of Structural Mechanics and Seismic Resistance of Structures, +7 (992) 918-89-35-14, Tajik Technical University named after academic M.S. Osimi, 10 Akademikov Radzhabovyh St., Dushanbe, 734042, Republic of Tajikistan; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 96 - 100

The subject matter of the article represents a solution to the problem of the stress-strain state of a heterogeneous structure resting on the elastic half-plane. The condition of continuity of deformations and stresses alongside the line of contact between the sections of the structure and between the structure and the half-plane is observed; the system of boundary equations is derived on the basis of the above. Coefficients associated with unknown values of the structure are identified with the help of Kelvin's fundamental solutions, while the coefficients associated with the half-plane are identified on the basis of the Mindlin's solutions. The mathematical model and the analytical algorithm developed by the author are implemented within the framework of the examination of the stress-strained state of an earth dam.
Analysis of application of the algorithm has proven that concentrated shearing stresses emerge in the area of the upper wall alongside the line of contact between the structure and the half-plane, while mechanical properties of sections of the structure and the half-plane influence the distribution of vertical relocations of the half-plane contour line.

DOI: 10.22227/1997-0935.2012.7.96 - 100

References
  1. Andreev V.I. Nekotorye zadachi i metody mekhaniki neodnorodnykh tel [Several Problems and Methods of Mechanics of Heterogeneous Bodies]. Ìoscow, ASV Publ., 2002, 288 p.
  2. Andreev V.I., Zolotov A.B., Prokop’ev V.I., Sidorov V.N. Opredelenie napryazheniy v uprugom poluprostranstve so sfericheskoy polost’yu s uchetom neodnorodnosti sredy [Identification of Stresses in the Elastic Half-space with a Spherical Enclosure with Account for the Heterogeneity of the Medium]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Analysis of Structures]. 1980, no. 6.
  3. Andreev V.I., Gasilov V.A., Smolov A.V. Raschet termouprugikh napryazheniy v neodnorodnom tsilindre [Calculation of Thermo-elastic Stresses inside a Heterogeneous Cylinder]. Vychislitel’nye metody i matematicheskoe modelirovanie [Computational Methods and Mathematical Modeling]. Abstracts of reports, Shushenskoye, 1986.
  4. Andreev V.I. Ob odnom metode resheniya v peremeshcheniyakh ploskoy zadachi teorii uprugosti dlya radial’no-neodnorodnogo tela [About One Solution in Respect of Displacements within the Framework of the 2D Problem of the Theory of Elasticity in Respect of a Radially Heterogeneous Body]. Prikladnaya mekhanika [Applied Mechanics]. 1987, vol. 23, no. 4, pp. 16—23.
  5. Andreev V.I. Priblizhennyy metod resheniya smeshannoy kraevoy zadachi dlya neodnorodnogo tsilindra [Approximate Solution of the Mixed Boundary Value Problem for a Heterogeneous Cylinder]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Analysis of Structures]. 1989, no. 2, pp. 8—11.
  6. Andreev V.I., Kerimov Ê.À., Smolov À.V. Chislenno-analiticheskoe reshenie ploskoy zadachi dlya neodnorodnogo uprugogo kol’tsa [Numerical-analytical Solution of the 2D Problem in Respect of a Heterogeneous Elastic Ring]. Soprotivlenie materialov i teoriya sooruzheniy [Strength of Materials and Structural Theory]. Kyev, 1989, no. 53, pp. 62—67.
  7. Kiselev A.P., Gureeva N.P., Kiseleva R.Z. Ispol’zovanie trekhmernykh konechnykh elementov v raschetakh prochnosti mnogosloynykh paneley [Application of Three-Dimensional Finite Elements in Analysis of Strength of Multi-Layered Panels]. Stroitel’naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Constructions and Structures]. 2009, no. 4, pp. 37—40.
  8. Kiselev A.P., Gureeva N.P., Kiseleva R.Z., Leont’eva V.V. Opredelenie napryazheniy v zone peresecheniya plastin pri ploskom nagruzhenii na osnove MKE [Identification of Stresses in the Zone of Intersecting Plates in the Event of 2D Loading Based on FEM]. Stroitel’naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Constructions and Structures]. 2012, no. 2, pp. 55—62.
  9. Nizomov D.N. Metod granichnykh uravneniy v reshenii staticheskikh i dinamicheskikh zadach stroitel’noy mekhaniki [Method of Boundary Equations Employed to Resolve Static and Dynamic Problems of Structural Mechanics]. Moscow, ASV Publ., 2000, 282 p.
  10. Novatskiy V. Teoriya uprugosti [Theory of Elasticity]. Moscow, Mir Publ., 1975, 872 p.

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NUMERICAL MODELING OF THE PROBLEM OF DOUBLE-LAYER REINFORCEMENT

Vestnik MGSU 5/2012
  • Nizomov Dzhakhongir Nizomovich - Institute of Geology, Seismic Construction and Seismology Doctor of Technical Sciences, Professor, Associate Member of the Academy of Sciences of the Republic of Tajikistan; Director, Laboratory of Theory of Seismic Stability and Modeling +7 (992) 919-35-57-34, Institute of Geology, Seismic Construction and Seismology, Academy of Sciences of the Republic of Tajikistan, 267 Ayni st., Dushanbe, 734029, Republic of Tajikistan; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Khodzhiboev Abduaziz Abdusattorovich - Tajik Technical University named after academic M.S. Osimi Candidate of Technical Sciences, Associated Professor, Chair, Department of Structural Mechanics and Seismic Resistance of Structures, +7 (992) 918-89-35-14, Tajik Technical University named after academic M.S. Osimi, 10 Akademikov Radzhabovyh St., Dushanbe, 734042, Republic of Tajikistan; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 67 - 71

The article covers the mathematical model and the algorithm of calculation of the double-layer reinforcement based on the method of boundary integral equations developed by the authors. The system of equations, based on discrete representation, is a combination of equations describing each of sub-domains with account for the conditions of compatibility alongside the contact boundaries. The convergence and accuracy of numerical modeling is based on the testing results of the problem under consideration. Results of the numerical solution of the problem of uniaxial tension of the plate that has two layers of reinforcement are provided in the article. The algorithm is implemented by analyzing the stress-strained state of structures of Nurek hydraulic power plant.
The proposed solution is applicable in the lining of tunnels and subterranean structures in rock massifs, as well as galleries arranged in the body of earth dams. It represents two layers of concrete with different values of the modulus of elasticity and Poisson ratio. Tangential stress and reinforcement ring graphs are presented in the article.

DOI: 10.22227/1997-0935.2012.5.67 - 71

References
  1. Brebbiya K., Telles Zh., Vroubel L. Metody granichnykh elementov [Methods of Boundary Elements]. Moscow, Mir Publ., 1987, 524 p.
  2. Nizomov D.N. Metod granichnykh uravneniy v reshenii staticheskikh i dinamicheskikh zadach stroitel’noy mekhaniki [Method of Boundary Elements Applicable for Resolution of Static and Dynamic Problems of Structural Mechanics]. Moscow, ASV Publ., 2000, 282 p.

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RESEARCH OF THE CONCENTRATION OF STRESSES IN A RECESSED PLATE USING THE METHOD OF BOUNDARY EQUATIONS

Vestnik MGSU 8/2012
  • Khodzhiboev Abduaziz Abdusattorovich - Tajik Technical University named after academic M.S. Osimi Candidate of Technical Sciences, Associated Professor, Chair, Department of Structural Mechanics and Seismic Resistance of Structures, +7 (992) 918-89-35-14, Tajik Technical University named after academic M.S. Osimi, 10 Akademikov Radzhabovyh St., Dushanbe, 734042, Republic of Tajikistan; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 121 - 124

The subject of the research is the concentration of stresses in a plate that has two side
recesses, if the plate is exposed to the pre-set surface stress. Boundary integral equations are
derived on the basis of the reciprocity theorem. The fundamental Kelvin solution is used to define
the displacement area in the finite isotropic elastic plane. The mathematical model and the solution
algorithm, both developed by the author, represent a numerical solution designated for the plate
that has two side recesses. Comparison of results with well-known solutions demonstrates their
good convergence. The author has discovered that the smaller the radius of the recess, the higher
the stress concentration

DOI: 10.22227/1997-0935.2012.8.121 - 124

References
  1. Novatskiy V. Teoriya uprugosti [Theory of Elasticity]. Moscow, Mir Publ., 1975, 872 p.
  2. Nizomov D.N. Metod granichnykh uravneniy v reshenii staticheskikh i dinamicheskikh zadach stroitel’noy mekhaniki [Method of Boundary Equations Employed to Solve Static and Dynamic Problems of Structural Mechanics]. Moscow, ASV Publ., 2000, 282 p.
  3. Brebbiya K., Telles Zh., Vroubel L. Metody granichnykh elementov [Methods of Boundary Elements]. Moscow, Mir Publ., 1987, 524 p.
  4. Mavlyutov R.R. Kontsentratsiya napryazheniy v elementakh aviatsionnykh konstruktsiy [Concentration of Stresses in Elements of Aircraft Structures]. Moscow, Nauka Publ., 1981, 141 p.

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