We study a reformulated version of Reissner-Mindlin plate theory in which rotation variables are eliminated in favor of transverse shear strains. Upon discretization, this theory has the advantage that the "shear locking" phenomenon is completely precluded, independent of the basis functions used for displacement and shear strains. Any combination works, but due to the appearance of second derivatives in the strain energy expression, smooth basis functions are required. These are provided by Isogeometric Analysis, in particular, NURBS of various degrees and quadratic triangular NURPS. We present a mathematical analysis of the formulation proving convergence and error estimates for all physically interesting quantities, and provide numerical results that corroborate the theory.

BEIRAO DA VEIGA, L., Hughes, T., Kiendl, J., Lovadina, C., Niiranen, J., Reali, A., et al. (2015). A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 25(8), 1519-1551 [10.1142/S0218202515500402].

### A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS

#### Abstract

We study a reformulated version of Reissner-Mindlin plate theory in which rotation variables are eliminated in favor of transverse shear strains. Upon discretization, this theory has the advantage that the "shear locking" phenomenon is completely precluded, independent of the basis functions used for displacement and shear strains. Any combination works, but due to the appearance of second derivatives in the strain energy expression, smooth basis functions are required. These are provided by Isogeometric Analysis, in particular, NURBS of various degrees and quadratic triangular NURPS. We present a mathematical analysis of the formulation proving convergence and error estimates for all physically interesting quantities, and provide numerical results that corroborate the theory.
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Articolo in rivista - Articolo scientifico
convergence analysis; Isogeometric Analysis; plate models;
convergence analysis; Isogeometric Analysis; plate models;
English
2015
25
8
1519
1551
reserved
BEIRAO DA VEIGA, L., Hughes, T., Kiendl, J., Lovadina, C., Niiranen, J., Reali, A., et al. (2015). A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 25(8), 1519-1551 [10.1142/S0218202515500402].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/98178`