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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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Elastic surface simulation as part of the computational solution to dynamic problems of the theory of elasticity with account for the conditions that cause non-reflection from the boundaries of the computational domain

Vestnik MGSU 9/2012
  • 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 144 - 147

The author describes the application of certain conditions that deprive the boundaries of certain
areas from reflecting properties. A numerical simulation of the elastic wave propagation pattern
in the infinite media is to be incorporated into the study of the impact of seismic loads produced on
buildings and structures.
The problem of elimination of reflected waves from the set of boundaries in the course of
calculation of dynamic problems of the theory of elasticity is quite important at this time. The study
of interaction between elastic waves and various engineering facilities has been unfeasible for quite
a long time.
A well-known method of generating counter-propagating waves at the boundary is applied
to compensate for the accumulation of longitudinal and transverse waves. The boundary ratio is
derived for longitudinal, transverse and other types of waves, including conical surface Rayleigh
waves, to check the performance of the proposed methodology.
Longitudinal, transverse, and conical surface Rayleigh waves as the main carriers of the elastic
energy fail to represent the relation. The problem is solved numerically through the application
of the dynamic finite element method. The numerical solution is capable of taking account of the
internal points of the area.

DOI: 10.22227/1997-0935.2012.9.144 - 147

References
  1. Il’gamov M.A., Gil’manov A.N. Neotrazhayushchie usloviya na granitsakh raschetnoy oblasti [Non-reflecting Conditions at the Boundaries of the Computational Domain]. Moscow, Fizmatlit Publ., 2003, 238 p.
  2. Nemchinov V.V. Difraktsiya ploskoy prodol’noy i poperechnoy volny na kruglom otverstii [Diffraction of Plane Longitudinal and Transverse Waves at the Circular Aperture]. Vestnik TsNIISK [Proceedings of Central Research Institute of Structural Units]. 2010, no. 10.
  3. Musaev V.K. Difraktsiya prodol’noy volny na kruglom i kvadratnom otverstiyakh v uprugoy srede [Diffraction of a Longitudinal Wave in Circular and Square Holes of the Elastic Medium]. Abstracts of the “Dissemination of Elastic Waves” Conference. Frunze, Frunze Institute of Technology, 1983, Part 1, pp. 72—74.
  4. Musaev V.K. Metod konechnykh elementov v dinamicheskoy teorii uprugosti [The Finite Element Method in the Dynamic Theory of Elasticity]. Prikladnye problemy prochnosti i plastichnosti [Engineering Problems of Strength and Ductility]. 1983, no. 24, pp. 161—162.
  5. Musaev V.K. Reshenie zadach o rasprostranenii voln metodom konechnykh elementov [Using the Finite Element Method to Resolve the Problems of Wave Propagation]. Mekhanika deformiruemogo tverdogo tela. Referativnyy zhurnal. [Mechanics of Deformable Solid Bodies. A Journal of Abstracts]. 1986, no. 10, p. 15.

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