Fully C1‐conforming subdivision elements for finite deformation thin‐shell analysis

By Fehmi Cirak, Magdalena Ortiz. International Journal for Numerical Methods in Engineering, 2001

283 citations recorded by the source corpus.

We have extended the subdivision shell elements of Cirak et al. [18] to the finite‐deformation range. The assumed finite‐deformation kinematics allows for finite membrane and thickness stretching, as well as for large deflections and bending strains. The interpolation of the undeformed and deformed surfaces of the shell is accomplished through the use of subdivision surfaces. The resulting ‘subdivision elements’ are strictly C1‐conforming, contain three nodes and one single quadrature point per element, and carry displacements at the nodes only. The versatility and good performance of the subdivision elements is demonstrated with the aid of a number of test cases, including the stretching of a tension strip; the inflation of a spherical shell under internal pressure; the bending and inflation of a circular plate under the action of uniform pressure; and the inflation of square and circular airbags. In particular, the airbag solutions, while exhibiting intricate folding patterns, appear to converge in certain salient features of the solution, which attests to the robustness of the method. Copyright © 2001 John Wiley & Sons, Ltd.

Subfields: Biomedical Engineering, Computational Mechanics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/cef0e66204abe01a839ebc091e4de172d442ba61

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Citations in the corpus

Isogeometric analysis using T-splines (2010, methodology): “They have been used for shell analysis by Cir-ak et al. [15–17].”
Isogeometric boundary element analysis using unstructured T-splines (2013, methodology): “We mention in passing that certain subdivision schemes have been used as a basis for finite element analysis [82, 83, 84, 85, 86].”
A new discontinuous Galerkin method for Kirchhoff–Love shells (2008, methodology): “In this case, the shape functions do not have to fulfill the high-order continuity requirements, which are hard to enforce in three-dimensional problems, with a few exceptions such as the subdivision method based on NURBS approximation of the surface [10,11].”
Modelling fluid deformable surfaces with an emphasis on biological interfaces (2018, methodology): “Here we focus on Loop subdivision surfaces based on triangular meshes (Loop 1987; Stam 1999; Biermann et al. 2000; Cirak et al. 2000; Cirak & Ortiz 2001; Cirak & Long 2011; Torres-Sánchez 2017).”
A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM (2010, unknown): “Isogeometric analysis [1] uses basis functions from computer aided design (CAD), including NURBS [1, 2], T-Splines [3, 4], and subdivision surfaces [5, 6, 7].”
The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches (2010, background): “[35] F.”
Isogeometric shell analysis: The Reissner-Mindlin shell (2010, methodology): “Subdivision surfaces [15–17] and, more recently, T-Splines [3, 20], were also successfully employed in the analysis context.”
Phase-field modeling of fracture in linear thin shells (2014, unknown): “3 Thin shell model In this section, we review the mechanics of thin shells [42, 43], based on a geometrically exact formulation presented in [30, 44].”
T‐spline finite element method for the analysis of shell structures (2009, background): “[29, 30] and Cirak and Ortiz [31] proposed the use of subdivision surfaces as a common foundation for modeling, simulation, and design in a unified framework.”