Subdivision surfaces: a new paradigm for thin-shell finite-element analysis
Article first published online: 15 MAR 2000
Copyright © 2000 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 47, Issue 12, pages 2039–2072, 30 April 2000
How to Cite
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
- Issue published online: 15 MAR 2000
- Article first published online: 15 MAR 2000
- Manuscript Revised: 30 SEP 1999
- Manuscript Received: 1 JUL 1999
- DARPA/NSF. Grant Number: DMS-9875042
- NSF. Grant Numbers: ACI-9624957, ACI-9721349, ASC-892029
- finite elements;
- subdivision surfaces
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.  obstacle course of benchmark problems, demonstrate the high accuracy and optimal convergence of the method. Copyright © 2000 John Wiley & Sons, Ltd.