Geodesic
Multigrid curvilinear elements in the three-dimensional analysis of composite cylindrical panels and shells with cavities and openings
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 4, pp. 47-59
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The paper presents the procedure of construction of curvilinear double-grid finite elements (DgFE) and complex multigrid finite elements (MgFE) for calculating three-dimensional elastic composite cylindrical panels and shells with cavities and openings. The standard discrete models of three-dimensional composite panels and shells, taking into account their inhomogeneous (micro-inhomogeneous) structure and complex form, have very high dimension. DgFE and complex MgFE are built based on the standard discrete models of panels and shells using the interpolating polynomials and equations of the three-dimensional problem of elasticity, written in the local Cartesian coordinate systems of these elements. DgFE and complex MgFE describe the three-dimensional stress state in the composite panels and shells taking into account their structure and thus generating the discrete models of small dimensions. Calculations of panels with fibrous structure demonstrate that the maximum displacement and equivalent stress of the basic and double-grid (multigrid) discrete panel models differ by $1\div12$ %. Implementation of the finite element method for two- and multigrid discrete models of panels requires $10^3\div10^4$ times less computer memory and $10^2\div10^3$ times less time than for the basic model.
Mots-clés : composites
Keywords: elasticity, cylindrical shells and panels, complex multigrid and double-grid curvilinear finite elements. 
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     title = {Multigrid curvilinear elements in the three-dimensional analysis of composite cylindrical panels and shells with cavities and openings},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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A. D. Matveev; A. N. Grishanov. Multigrid curvilinear elements in the three-dimensional analysis of composite cylindrical panels and shells with cavities and openings. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 4, pp. 47-59. http://geodesic.mathdoc.fr/item/UZKU_2014_156_4_a5/

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