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Subdivision surfaces: a new paradigm for thin‐shell finite‐element analysis
Author(s) -
Cirak Fehmi,
Ortiz Michael,
Schröder Peter
Publication year - 2000
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/(sici)1097-0207(20000430)47:12<2039::aid-nme872>3.0.co;2-1
Subject(s) - subdivision , finite element method , interpolation (computer graphics) , subdivision surface , shell (structure) , mathematics , displacement (psychology) , geometry , displacement field , mathematical analysis , physics , structural engineering , classical mechanics , engineering , civil engineering , motion (physics) , psychology , polygon mesh , psychotherapist
We develop a new paradigm for thin‐shell finite‐element analysis based on the use of subdivision surfaces for (i) describing the geometry of the shell in its undeformed configuration, and (ii) generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the Kirchhoff–Love theory of thin shells. The particular subdivision strategy adopted here is Loop's scheme, with extensions such as required to account for creases and displacement boundary conditions. The displacement fields obtained by subdivision are H 2 and, consequently, have a finite Kirchhoff–Love energy. The resulting finite elements contain three nodes and element integrals are computed by a one‐point quadrature. The displacement field of the shell is interpolated from nodal displacements only. In particular, no nodal rotations are used in the interpolation. The interpolation scheme induced by subdivision is non‐local, i.e. the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements. However, the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface. Numerical tests, including the Belytschko et al. [10] obstacle course of benchmark problems, demonstrate the high accuracy and optimal convergence of the method. Copyright © 2000 John Wiley & Sons, Ltd.