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Subdivision surfaces: a new paradigm for thin-shell finite-element analysis

Cirak, Fehmi and Ortiz, Michael and Schröder, Peter (2000) Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. International Journal for Numerical Methods in Engineering, 47 (12). pp. 2039-2072. ISSN 0029-5981. doi:10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1.

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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 H2 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.

Item Type:Article
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URLURL TypeDescription<2039::AID-NME872>3.0.CO;2-1DOIArticle;2-1/abstractPublisherArticle
Ortiz, Michael0000-0001-5877-4824
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2000 John Wiley & Sons. Received 1 July 1999. Revised 30 September 1999.The support of DARPA and NSF through Caltech’s OPAAL Project (DMS-9875042) is gratefully acknowledged. Additional support was provided by NSF (ACI-9624957, ACI-9721349, ASC-8920219) and through a Packard fellowship to PS.
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Subject Keywords:shells; finite elements; subdivision surfaces
Issue or Number:12
Record Number:CaltechAUTHORS:20171213-090454075
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Official Citation:Cirak, F., Ortiz, M. and Schröder, P. (2000), Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Int. J. Numer. Meth. Engng., 47: 2039–2072. doi:10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83857
Deposited By: Lydia Suarez
Deposited On:19 Dec 2017 19:42
Last Modified:15 Nov 2021 20:14

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