DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

INTERACTION BETWEEN THE IMMEDIATE SUPPORT AND THE ROCK MASSIF CLOSE TO RECTILINEAR BOUNDARIES OF THE HALF-PLANE

Vestnik MGSU 6/2012
  • Nizomov Dzhakhongir Nizomovich - Institute of Geology, Antiseismic Construction and Seismology Professor, Doctor of Technical Sciences, Associate Member, Academy of Sciences of the Republic of Tajikistan; Director, Laboratory of Theoretical Seismic Resistance and Modeling, +7 (992) 919-35-57-34, Institute of Geology, Antiseismic Construction and Seismology, Dushanbe, Republic of Tajikistan; 267 Ayni St., Dushanbe, 734029, 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 68 - 72

In the article, the authors analyze the stress-strain state of structural contours of subterranean structures located at different distances from the boundary of the half-plane. The authors provide a numerical solution through the employment of the method of boundary equations. The problem represents reinforced holes exposed to uniform internal pressure and tensile stress in the direction that is parallel to the boundary of the half-plane. If the pre-set load applied to a particular section of the half-space is taken into account, the reciprocal theorem is used to derive Somigliana's identity for a reinforced hole located in the semi-infinite domain. This equation identifies the component of displacement in a point within the ring, within the elastic half-space or the ground line. Contours of simulation models, conditions of compatibility and equilibrium alongside the contact boundary are discrete, and the system of algebraic equations is derived on their basis. Results of numerical experiments substantiate the accuracy and convergence of the proposed algorithm.

DOI: 10.22227/1997-0935.2012.6.68 - 72

References
  1. Mavlyutov R.R. Kontsentratsiya napryazheniy v elementakh aviatsionnykh konstruktsiy [Concentration of Stresses in Elements of Aircraft Structures]. Moscow, Nauka Publ., 1981, 141 p.
  2. Bulychev N.S. Mekhanika podzemnykh sooruzheniy [Mechanics of Subterranean Structures]. Moscow, Nedra Publ., 1982, 272 p.
  3. Barbakadze V.S., Murakami S. Raschet i proektirovanie stroitel’nykh konstruktsiy i sooruzheniy v deformiruemykh sredakh [Calculation and Design of Building Structures and Constructions in Deformable Media]. Moscow, Stroyizdat Publ., 1989, 472 p.
  4. Novatskiy V. Teoriya uprugosti [Theory of Elasticity]. Moscow, Mir Publ., 1975, 872 p.
  5. Brebbiya K., Telles Zh., Vroubel L. Metody granichnykh elementov [Methods of Boundary Elements]. Moscow, Mir Publ., 1987, 524 p.
  6. 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.
  7. Jeffery G.B. Plane Stress and Plane Strain in Bipolar Coordinates. Trans. Roy. Soc. (London), Ser. A 221, 265—293 (1920).
  8. Mindlin R.D. Stress Distribution around a Hole near the Edge of a Plate under Tension. Proc. Soc. Exptl. Stress. Anal. 5, 56—68 (1948).
  9. Timoshenko S.P., Goodyear J. Teoriya uprugosti [Theory of Elasticity]. Moscow, Nauka Publ., 1975, 575 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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Phenomenological model of local plasticity

Vestnik MGSU 9/2012
  • Dolgorukov Vadim Aleksandrovich - Ryazan Institute (Branch) of Mosсow State Open University (MGOU) Candidate of Technical Sciences, Associated Professor, Chair, Department of Architecture and Urban Planning, Ryazan Institute (Branch) of Mosсow State Open University (MGOU), 26/53 Pravo-Libetskaya st., Ryazan, 390000, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 101 - 108

Two points of an elastic and perfectly plastic material exposed to the plane stress are examined by the author. One point is located on the stress concentrator surface. The other one is located at a certain distance from the first one (it is considered as a secondary point within the framework of the kinetic theory of a plastic flow).
As a result of the finite element analysis of the stress-strain state it has been discovered that the material in the point located in the front area of the kinetic plastic flow remains linearly elastic in terms of its physical condition, and the load is applied to it in accordance with a curved trajectory. This trajectory is represented by





U
0




-


U











coordinates, where Uф and U0 are the density-related components of dilatation and distortion strain. For the purposes of modeling, the trajectory is represented as a two-component broken line.
As a result, the kinetic plastic flow prolongation is limited. This effect intensifies while the value of the elastic Poisson ratio (µ) goes down. For example, for ? < 0.5, dimensions of the plastic zone outstretched along the crack curve are smaller than those identified using the Irwin plastic zone solution. Furthermore, in case of ? = 0.25, the effective crack length is



l

eff


=l-
1

18π




(


K


σ
Y






)



2







, and the modified stress distribution is below the singular stress distribution according to the laws of linear elastic fracture mechanics.

DOI: 10.22227/1997-0935.2012.9.101 - 108

References
  1. O’Dowd N.P. and Shih C.F. Family of Crack-tip Fields Characterized by a Triaxiality Parameter-I. Structure of Fields. Journal of the Mechanics and Physics of Solids. 1991, no. 39, pp. 989—1015.
  2. Matvienko Yu.G. Modeli i kriterii mekhaniki razrusheniya [Models and Criteria of Fracture Mechanics]. Moscow, FIZMATLIT Publ., 2006, 328 p.
  3. Molsk K., Glinka G. A Method of Elastic-Plastic Stress and Strain Calculation at a Notch Root. Mater. Sci. Engng, vol. 50, 1981, pp. 93—100.
  4. Makhutov N.A. Konstruktsionnaya prochnost’, resurs i tekhnogennaya bezopasnost’ [Structural Strength, Durability and Anthropogenic Safety]. Novosibirsk, Nauka Publ., 2005. Part 1. Kriterii prochnosti i resursa [Criteria of Strength and Durability]. 494 p.
  5. Neuber H. Theory of Stress Concentration for Shear-Strained Prismatical Bodies with Arbitrary Nonlinear Stress-Strain Law. ASME Journal of Applied Mechanics, no. 28, 1961.
  6. Morozov E.M. Kontseptsiya predela treshchinostoykosti [Concept of Crack Resistance Limit]. Zavodskaya laboratoriya [Industrial Laboratory]. 1997, no. 12, pp. 42—46.
  7. Irwin, G.R. Plastic Zone Near a Crack and Fracture Toughness, Mechanical and Metallurgical Behavior of Sheet Materials. Proceedings of Seventh Sagamore Ordnance Materials Conference. Syracuse University Research Institute, 1960, pp. IV-63 — IV-78.
  8. Jaku?ovas A., Daunys M. Investigation of Low Cycle Fatigue Crack Opening by Finite Element Method MECHANIKA. Tekhnologiya [Technology]. Kaunas, 2009, no. 3(77), pp. 13—17.
  9. Khezrzadeh H., Wnuk M., Yavari A. Infl uence of Material Ductility and Crack Surface Roughness on Fracture Instability. J. Phys. D. Appl. Phys., 2011, no. 44, 22 p.
  10. Malinin N.N. Prikladnaya teoriya plastichnosti i polzuchesti [Applied Theory of Strength and Creep]. Moscow, Mashinostroenie Publ., 1975, 400 p.
  11. Hutchinson, J.W. Singular Behavior at the End of a Tensile Crack in a Hardening Material. Journal of Mech. Phys. Solids, Vol. 16, 1968, pp. 13—31.
  12. Skudnov V.A. Predel’nye plasticheskie deformatsii metallov [Ultimate Plastic Strain of Metals]. Moscow, Metallurgiya Publ., 1989, 176 p.
  13. Dolgorukov V.A. Inzhenernaya model’ kinetiki plasticheskogo techeniya vblizi kontsentratora napryazheniy [Engineering Model of the Kinetics of the Plastic Flow Close to the Stress Concentrator]. Collected works of the 3d International Conference “Deformation and Destruction of Materials and Nanomaterials]. Moscow, Interkontakt Nauka Publ., 2009, vol. 2, 407 p., pp. 313—314.
  14. Novopashin M.D., Suknev S.V. Gradientnye kriterii predel’nogo sostoyaniya Gradient Criteria of the Limit State]. Vestnik SamGU. Estestvennonauchnaya seriya. [Proceedings of Samara State University. Natural Science Series]. 2007, no. 4(54), pp. 316—335.
  15. Mosolov A. B. Cracks with a Fractal Surface. Reports of the Academy of Sciences of the USSR, 1991, 319 840–4.
  16. Bogatov A.A. Mekhanicheskie svoystva i modeli razrusheniya metallov [Mechanical Properties and Fracture Models of Metals]. Ekaterinburg, UGTU-UPI Publ., 2002, 329 p.
  17. McClintock F.A. Irwin G.R., Plasticity Aspects of Fracture Mechanics. ASTM STP 381, 1965, pp. 84—113.
  18. Rice J.R., Liebowitz H, ed. Mathematical Analysis in the Mechanics of Fracture. Fracture An Advanced Treatise. Academic Press, New York, 1968, vol. 2, chap. 3, pp. 191—311.

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