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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

STABILITY OF TRUNCATED CIRCULAR CONICAL SHELL EXPOSED TO AXIAL COMPRESSION

Vestnik MGSU 10/2012
  • Litvinov Vladimir Vital'evich - Rostov State University of Civil Engineering (RGSU) Director, Laboratory of Department of Strength of Materials, 8 (863) 201-91-36, Rostov State University of Civil Engineering (RGSU), 162 Sotsialisticheskaya St., Rostov-Don, 344022, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Chepurnenko Anton Sergeevich - Don State Technical University (DGTU) Candidate of Engineering Science, teaching assistant of the strength of materials department, Don State Technical University (DGTU), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 95 - 101

The problem of stability of a freely supported truncated circular conical shell, compressed by the upper base of a uniformly distributed load per unit length , referred to the median shell surface and directed along the generatrix of the cone, was solved by the Ritz-Timoshenko energy method. The orthogonal system of curvilinear coordinates of the points of the middle surface of the shell was adopted to solve the problem. Possible displacements were selected in the form of double series approximation functions. The physical principle of inextensible generatrix of the cone exposed to buckling at the moment of instability was employed. In addition, the fundamental principle of continuum mechanics, or the principle of minimal total potential energy of the system, was taken as the basis. According to the linear elasticity theory, energy methods make it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. As a result, the problem is reduced to the problem of identifying the eigenvalues in the algebraic theory of matrices. The numerical value of the critical load was derived through the employment of the software.

DOI: 10.22227/1997-0935.2012.10.95 - 101

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