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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

COMPARISON OF FINDINGS OF THE FINITE ELEMENT ANALYSISWITH THE FINDINGS OF THE ASYMPTOTIC HOMOGENIZATIONMETHOD IN RESPECT OF THE PLATE IN ELASTOPLASTIC BENDING

Vestnik MGSU 8/2013
  • Savenkova Margarita Ivanovna - Lomonosov Moscow State University (MGU) postgraduate student, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University (MGU), ; Leninskie Gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sheshenin Sergey Vladimirovich - Lomonosov Moscow State University (MGU) Doctor of Physical and Mathematical Sciences, Professor, Department of Composite Mechanics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University (MGU), ; Leninskie Gory, Moscow, 119991, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zakalyukina Irina Mikhailovna - Moscow State University of Civil Engineering (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Theoretical Mechanics and Aerodynamics, 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 42-50

The authors present numerical results of the asymptotic homogenization method for elastoplastic bending of the plate. The plate is supposed to be laminated and exposed to the transversal load. Stresses and displacements in the cylindrical bending problem are compared with those calculated using the 2D finite element method. The new trend in the mathematical simulation of structures, made of composite materials, contemplates accurate consideration of their nonlinear properties (for instance, plasticity or damage) on the micro-structural level of materials. The homogenization method provides for the coupling between the microstructural level and the level of the entire structure. The authors have developed a numerical implementation of this coupling. It represents a combination of the homogenization method and linearization with account for the loading parameter. The approach was implemented as a parallel algorithm and applied to the plastic bending simulation of the FGM plate. The parallel algorithm is based on the overlapping subdomain decomposition method and the Euler explicit and implicit integration methods. MPI was used for software development purposes.In this paper, the authors provide a concise description of the proposed method applied to the 3D boundary-value problem. The authors compare numerical solutions obtained through the application of the homogenization approach and the finite element method. Two types of laminated plates are taken as an example. Three-layered plate was exposed to uniformly distributed transversal loading. The second five-layered plate, that was a lot thinner than the first one, was exposed to piecewise constant transversal loading. All layers of both plates are homogenous; they are supposed to be elastic or bilinearly plastic. It was discovered that the asymptotic homogenization technique provides a more accurate solution for the five-layered plate than for the three-layered one. Edge effects near the edges of the plates are smaller for the thin five-layered plate if compared with the thick three-layered plate. The edge effect appears due to the large value of the plate height-to-length ratio. Nevertheless, the first order asymptotic homogenized method provides sufficient accuracy in both cases.

DOI: 10.22227/1997-0935.2013.8.42-50

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