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Évaluation numérique des éléments finis DKMQ pour les plaques et les coques

Abstract : In the linear case, the Mindlin-Reissner model for thick plates and the Naghdi model for thick shells are commonly used. The finite element discretization of these models leads to numerical locking phenomenon when the thickness approaches zero : shear locking for plates and both shear and membrane locking for shells. There are some finite elements that could reduce or even eliminate this phenomenon. DKMQ element for plates or DKMQ24 element for shells, are low-order elements, based on a mixed formulation, introduced a few years ago to prevent the numerical locking phenomenon. In this thesis, we concentrated on numerical evaluation of the performance of these elements. Besides the classical benchmark tests, we also focused on the analysis of discrete inf-sup condition for DKMQ element. We studied the s-norm test proposed by Bathe for DKMQ24 element. Finally, we performed a posteriori error estimation for DKMQ and DKMQ24 elements, using the error estimator Z2 (proposed by Zienkiewicz and Zhu), associated with the averaging, projection or SPR recovery methods. The results obtained have enabled us to quantify the performance of these two finite elements for locking problems, and to identify their limits. Two important applications of these elements DKMQ and DKMQ24 were then presented ; the first one concerns thin-walled beams with open cross-section and the second one composite plates.
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Imam Jauhari Maknun. Évaluation numérique des éléments finis DKMQ pour les plaques et les coques. Mécanique [physics.med-ph]. Université de La Rochelle, 2015. Français. ⟨NNT : 2015LAROS040⟩. ⟨tel-01661483⟩

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