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Recovery of strong equilibrium from displacement‐based finite element models of Reissner‐Mindlin plates
Author(s) -
Maunder E. A. W.,
Moitinho de Almeida J. P.
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5747
Subject(s) - stress resultants , finite element method , partition of unity , deflection (physics) , mathematics , mathematical analysis , context (archaeology) , displacement (psychology) , displacement field , stress (linguistics) , structural engineering , classical mechanics , engineering , physics , linguistics , philosophy , psychology , psychotherapist , paleontology , biology
Summary In this paper, we extend to Reissner‐Mindlin plate bending problems a technique, originally proposed in the context of two‐dimensional and three‐dimensional continua, for recovering fully equilibrated stresses from the solution of a compatible finite element model. The technique involves partition of unity functions and the analyses of overlapping star patches modelled with hybrid equilibrium plate elements. The patches are subjected to balanced systems of loads composed of partitioned and fictitious loads, where the latter are derived from the stresses of the compatible solution. The special case of assumed linear displacement fields of both deflection and rotation for the compatible model is included. This case requires additional fields of stress resultants to correct possible rotational imbalances of star patches, and these are derived elementwise. Other cases of nonconforming elements are briefly considered. Numerical examples are presented to illustrate the effectiveness of these techniques in terms of the deviation of the recovery, which compares the complementary strain energy of a recovered solution with that obtained by a global equilibrated analysis based on the same stress approximations.