DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Inverse problemfor an inhomogeneous elastic beam at a combined strength

Vestnik MGSU 1/2014
  • 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 .
  • Barmenkova Elena Vyacheslavovna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Science, Associate Professor, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Matveeva Alena Vladimirovna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 25-32

In the article the authors describe a method of optimizing the stress state of an elastic beam, subject to the simultaneous action of the central concentrated force and bending moment. The optimization method is based on solving the inverse problem of the strength of materials, consisting in defining the law of changing in elasticity modulus with beam cross-section altitude. With this changing the stress state will be preset. Most problems of the elasticity theory of inhomogeneous bodies are solved in direct formulation, the essence of which is to determine the stress-strain state of a body at the known dependences of the material elastic characteristics from the coordinates. There are also some solutions of the inverse problems of the elasticity theory, in which the dependences of the mechanical characteristics from the coordinates, at which the stress state of a body is preset, are determined. In the paper the authors solve the problem of finding a dependence modulus of elasticity, where the stresses will be constant over the beam’s cross section. We will solve the problem of combined strength (in the case of the central stretching and bending). We will use an iterative method. As the initial solution, we take the solution for a homogeneous material. As the first approximation, we consider the stress state of a beam, when the modulus of elasticity varies linearly. According to the results, it can be stated that three approximations are sufficient in the considered problem. The obtained results allow us to use them in assessing the strength of a beam and its optimization.

DOI: 10.22227/1997-0935.2014.1.25-32

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Glass transition temperature and elastic modulusof nanocomposites based on polyimides

Vestnik MGSU 6/2015
  • Matseevich Tat’yana Anatol’evna - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Higher Mathematics, 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 .
  • Popova Marina Nikolaevna - Moscow State University of Civil Engineering (MGSU) Doctor of Chemical Sciences, Associate Professor, Department of Composite Materials Technology and Applied Chemistry, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Askadskiy Andrey Aleksandrovich - Moscow State University of Civil Engineering (MGSU) Doctor of Chemical Sciences, Professor, Department of Composite Materials Technology and Applied Chemistry, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 50-63

Today great attention is paid to production and research of the mechanical and termal properties of nanocomposites based on polyimides. These polymers are heatresisting and possess the increased mechanical properties in wide range of temperatures. Various nanoparticles are introduced into polyimides: graphite nanotubes and flatparticles, the particles of SiO , the surface of which is modified, the particles of ZrOandmontmorillonite, etc.The authors analyzed the influence of nanoparticles on the glass transition temper-ature T and elastic modulus E of the polyimides based on 1,3-bis-(3,3’,4,4’-dicarboxy-phenoxy)benzene and 4,4’-bis-(4-aminophenoxy)biphenyl, and pyromellitic dianhydride and oxydianiline. Nanoparticles introduced in small amounts are produced of graphite and ZrO . The suggested ratios take into account the chemical structure of the polymer and nanoparticles, as well as the structure of their surface in case of chemical modification; the concentration of nanoparticles and their form, the number of polar groups on the surface. The number of polar groups and nanoparticles’ concentration have the greatest influence on T . The elastic modulus of nanocomposites depending on nanoparticles’ concentration is connected with van der Waals volume of the repeating unit of polymer and nanoparticle.

DOI: 10.22227/1997-0935.2015.6.50-63

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