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Gureeva N.A.,Volgograd State Agricultural Academy | Klochkov Y.V.,Volgograd State Agricultural Academy | Nikolaev A.P.,Volgograd State Agricultural Academy
Russian Aeronautics | Year: 2010

The volume finite element in the form of hexahedron with nodal unknowns as components of the displacement vector and stress tensor has been developed to analyze the shells of revolution. The displacement vector components for the inner point of the finite element and the components of its stress tensor are expressed through the nodal unknowns using the method of vector and tensor fields interpolation by the trilinear shape functions; that provides taking into account the finite element displacement as a whole solid. The variational principle in a mixed formulation is applied to form the matrix of hexahedron deformation. The efficiency of the proposed method for approximating the values being sought as vector and tensor fields in comparison with the traditional method for approximating the values being sought as scalar fields is confirmed by a numerical example. © 2010 Allerton Press, Inc.


Klochkov Yu.V.,Volgograd State Agricultural Academy | Nikolaev A.P.,Volgograd State Agricultural Academy | Vakhnina O.V.,Volgograd State Agricultural Academy | Malovichko R.I.,Volgograd State Agricultural Academy
Russian Aeronautics | Year: 2012

The present paper sets forth an algorithm of analyzing thin shells with significant gradients of meridian curvature based on the Kirchhoff-Love hypothesis and finite element method. As a discretization element use is made of a triangular fragment of the middle surface with the Lagrange multipliers in additional nodes arranged in the triangle side middles. We apply the vector method of displacement interpolation that has a number of advantages over the conventional interpolation procedure. The high efficiency of the algorithm developed is confirmed by the numerical examples. © 2012 Allerton Press, Inc.

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