GENERATION OF IRREGULAR HEXAGONAL MESHES

Vestnik MGSU 4/2012
  • Vlasov Aleksandr Nikolaevich - Sergeev Institute of Environmental Geoscience of the Russian Academy of Sciences (IEG RAS), Institute of Applied Mechanics of the Russian Academy of Sciences (IAM RAS) Doctor of Technical Sciences, Principal Researcher, +7 (495) 523-81-92, Sergeev Institute of Environmental Geoscience of the Russian Academy of Sciences (IEG RAS), Institute of Applied Mechanics of the Russian Academy of Sciences (IAM RAS), 32а Leninskiy prospekt, Moscow, 119334, Russian Federation Building 2, 13 Ulanskiy pereulok, 101000, Moscow, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Volkov-Bogorodskiy Dmitriy Borisovich - Institute of Applied Mechanics of the Russian Academy of Sciences (IAM RAS) Candidate of Physics and Mathematics, Senior Researcher, +7 (499) 160-42-82, Institute of Applied Mechanics of the Russian Academy of Sciences (IAM RAS), 32а Leninskiy prospekt, Moscow, 119334, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Znamenskiy Vladimir Valerianovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Professor, Department of Soil Mechanics, Beddings and Foundations, 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 .
  • Mnushkin Mikhail Grigor'evich - Sergeev Institute of Environmental Geoscience Russian Academy of Sciences (IEG RAS) Candidate of Technical Sciences, Principal Researcher, Sergeev Institute of Environmental Geoscience Russian Academy of Sciences (IEG RAS), Building 2, 13 Ulanskiy pereulok, 101000, Moscow, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 78 - 87

In the paper, the authors propose original mesh generation solutions based on the finite element method applicable within the computational domain. The mesh generation procedure contemplates homeomorphic mapping of the initial domain onto the canonical domain. The authors consider mappings generated through the application of differential operators, including the Laplace operator (harmonic mappings) or the Lamé operator. In the latter case, additional control parameter ν is required The following domains are regarded as canonical: a parametric cube (or a square), a cylindrical layer, and a spherical layer. They represent simply connected or biconnected domains.
The above mappings are based on the parametric mesh generated alongside the domain boundary or boundaries dividing heterogeneous elements (inclusions). Therefore, generation of the above mappings is reduced to the resolution of the boundary problems by means of the Laplace or Lamé differential operators. Basically, the proposed approach represents the problem of the theory of elasticity with regard to the prescribed displacement. This problem may have two solutions. The first one is the analytical (meshless) least square solution, and the second one represents consequent mesh refining on the basis of the finite-element discretization of elasticity equations. The least square method assumes decomposition of the initial domain into the system of simply connected sub-domains. In every sub-domain, or a block, numerical/analytical approximation of homeomorphic mapping of the initial domain onto the canonical domain is performed with the help of local representations generated by means of systems of special functions.
Decomposition is performed in a constructive way and, as option, it involves meshless representation. Further, this mapping method is used to generate the calculation mesh. In this paper, the authors analyze different cases of mapping onto simply connected and bi-connected canonical domains. They represent forward and backward mapping techniques. Their potential application for generation of nonuniform meshes within the framework of the asymptotic homogenization theory is also performed to assess and project effective characteristics of heterogeneous materials (composites).

DOI: 10.22227/1997-0935.2012.4.78 - 87

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