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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

OPERATOR-RELATED FORMULATION OF THE EIGENVALUE PROBLEM FOR THE BOUNDARY PROBLEM OF ANALYSIS OF A THREE-DIMENSIONAL STRUCTURE WITH PIECEWISE-CONSTANT PHYSICAL AND GEOMETRICAL PARAMETERS ALONGSIDE THE BASIC DIRECTION WITHIN THE FRAMEWORK OF THE DISCRETE-CONTINUAL APPROACH

Vestnik MGSU 6/2012
  • Akimov Pavel Alekseevich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Corresponding Member of the Russian Academy of Architecture and Construction Science, Professor, Department of Computer Science 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 .
  • Mozgaleva Marina Leonidovna - Moscow State University of Civil Engineering (MSUCE) Candidate of Technical Sciences, Associated Professor, Department of Computer Science 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 .
  • Sidorov Vladimir Nikolaevich - Moscow State University of Civil Engineering (MSUCE) Doctor of Technical Sciences, Professor, Advisor of Russian Academy of Architecture and Construction Science; Chair, Department of Computer Science 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 29 - 36

The proposed paper covers the operator-related formulation of the eigenvalue problem of analysis of a three-dimensional structure that has piecewise-constant physical and geometrical parameters alongside the so-called basic direction within the framework of a discrete-continual approach (a discrete-continual finite element method, a discrete-continual variation method).
Generally, discrete-continual formulations represent contemporary mathematical models that become available for computer implementation. They make it possible for a researcher to consider the boundary effects whenever particular components of the solution represent rapidly varying functions. Another feature of discrete-continual methods is the absence of any limitations imposed on lengths of structures. The three-dimensional problem of elasticity is used as the design model of a structure. In accordance with the so-called method of extended domain, the domain in question is embordered by an extended one of an arbitrary shape. At the stage of numerical implementation, relative key features of discrete-continual methods include convenient mathematical formulas, effective computational patterns and algorithms, simple data processing, etc. The authors present their formulation of the problem in question for an isotropic medium with allowance for supports restrained by elastic elements while standard boundary conditions are also taken into consideration.

DOI: 10.22227/1997-0935.2012.6.29 - 36

References
  1. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Diskretnye i diskretno-kontinual’nye realizatsii metoda granichnykh integral’nykh uravneniy [Discrete and Discrete-Continual Versions of Boundary Integral Equation Method]. Moscow, MSUCE, 2011, 368 p.
  2. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Diskretno-kontinual’nye metody rascheta sooruzheniy [Discrete-Continual Methods of Structural Analysis]. Moscow, Arhitektura-S Publ., 2010, 336 p.
  3. Zolotov A.B., Akimov P.A., Sidorov V.N., Mozgaleva M.L. Chislennye i analiticheskie metody rascheta stroitel’nykh konstruktsiy [Numerical and Analytical Methods of Structural Analysis]. Moscow, ASV Publ., 2009, 336 p.
  4. Shilov G.E. Matematicheskiy analiz. Vtoroy spetsial’nyy kurs. [Mathematical Analysis. Second Special Course]. Moscow, Nauka Publ., 1965, 327 p.
  5. Slivker V.I. Stroitel’naya mekhanika. Variatsionnye osnovy [Structural Mechanics. Variation Fundamentals]. Moscow, ASV Publ., 2005, 736 p.

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