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. https://resolver.caltech.edu/CaltechAUTHORS:20171213-090454075
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Abstract
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.
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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. | ||||||||||||||
Group: | GALCIT | ||||||||||||||
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Subject Keywords: | shells; finite elements; subdivision surfaces | ||||||||||||||
Issue or Number: | 12 | ||||||||||||||
DOI: | 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1 | ||||||||||||||
Record Number: | CaltechAUTHORS:20171213-090454075 | ||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20171213-090454075 | ||||||||||||||
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 | ||||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||||
Deposited By: | Lydia Suarez | ||||||||||||||
Deposited On: | 19 Dec 2017 19:42 | ||||||||||||||
Last Modified: | 15 Nov 2021 20:14 |
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