A mixed-hybrid model similar to one already presented for the case of beams is developed: for a Reissner-Mindlin-type plate local stresses (rather than stress resultants and moments) are explicitly modelled. By following the ideas previously used for membranes, it is assumed that in plane shear stresses are not a priori symmetric. This choice allows the decoupling of the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling dofs. Out-of plane shear stresses are then chosen such that equilibrium equation are exactly satisfied. Details of the formulation are provided, and the performances of the new element are assessed with reference to well-established benchmark problems.
Mixed finite elements for plate analysis with unsymmetric stresses
CAZZANI, ANTONIO MARIA;
2002-01-01
Abstract
A mixed-hybrid model similar to one already presented for the case of beams is developed: for a Reissner-Mindlin-type plate local stresses (rather than stress resultants and moments) are explicitly modelled. By following the ideas previously used for membranes, it is assumed that in plane shear stresses are not a priori symmetric. This choice allows the decoupling of the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling dofs. Out-of plane shear stresses are then chosen such that equilibrium equation are exactly satisfied. Details of the formulation are provided, and the performances of the new element are assessed with reference to well-established benchmark problems.
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