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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

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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