A hierarchic family of isogeometric shell finite elements

By R. Echter, Bastian Oesterle, Manfred Bischoff. 2013

301 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5a4036a377efc3a1dcd963d9c4c716f3e9a34cac

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

3D capability of refined GDQ models for the bending analysis of composite and sandwich plates, spherical and doubly-curved shells (2018, methodology): “In particular, different approches were considered such as Discrete Sigular Convolution Methodology [61-63], Meshless Local Petrov-Galerkin Method [64], Semi-Analytical Procedures [65-66], Finite Element Method [67-68] and Isogeometric Analysis [69-71].”
Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis (2014, methodology): “We include examples of shell theory, in particular, a pressurized cylindrical shell and the Scordelis-Lo roof [31, 34, 35] with the Kirchhoff-Love formulation of thin shells [36, 37].”
Isogeometric collocation methods for the Reissner–Mindlin plate problem (2015, unknown): “An alternative approach could be to consider the displacement and the shear strains as primal variables, as shown in the context of Galerkin formulations for shells in [24,25].”
Efficient isogeometric NURBS-based solid-shell elements: Mixed formulation and B-method (2013, methodology): “[32], who developed a hierarchical family of NURBS shell elements whose attractive property is to be intrinsically free for transverse shear locking.”
An isogeometric Reissner–Mindlin shell element based on Bézier dual basis functions: Overcoming locking and improved coarse mesh accuracy (2020, background): “By leveraging C(1)-smoothness, several new shear-deformable shell formulations have been proposed which are based on a hierarchical decomposition of the director in the deformed configuration [41, 42, 43, 44].”
A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS (2015, methodology): “Another innovation that occurred, due to Long, Bornemann & Cirak [21] and Echter, Oesterle & Bischoff [15] in the context of shells, was again motivated by the existence of smooth basis functions.”
Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials (2015, background): “Over the last years, IGA has attracted enormous interest in nearly all fields of computational mechanics and it also gave new life to the development of shell formulations, including rotation-free shells [27–29], Reissner– Mindlin shells [30–33], blended shells [34], hierarchic shells [35], and soli”
Treatment of Reissner–Mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework (2014, methodology): “[13] uses a difference vector formulation with transverse shear deformations instead of rotations as degrees of freedom.”
A parameter-free variational coupling approach for trimmed isogeometric thin shells (2017, methodology): “, based on solid shell theories [14,15], Kirchhoff-Love [16] and ReissnerMindlin theories [17–19], and hierarchic combinations thereof [20].”
Isogeometric analysis: An overview and computer implementation aspects (2012, background): “Shell and plate problems are another field where IGA has demonstrated compelling benefits over conventional approaches [11, 13, 14, 16, 41, 67, 140].”