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Second‐order accurate constraint formulation for subdivision finite element simulation of thin shells
Author(s) -
Green Seth,
Turkiyyah George
Publication year - 2004
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/nme.1070
Subject(s) - subdivision , quadrilateral , subdivision surface , finite element method , boundary (topology) , convergence (economics) , norm (philosophy) , boundary value problem , computer science , mathematical optimization , constraint (computer aided design) , mathematics , topology (electrical circuits) , geometry , mathematical analysis , structural engineering , engineering , combinatorics , civil engineering , political science , law , economics , economic growth
We present a new method for enforcing boundary conditions within subdivision finite element simulations of thin shells. The proposed framework is demonstrated to be second‐order accurate with respect to increasing refinement in the displacement and energy norm for simply supported, clamped, free and symmetric boundary conditions. Second‐order accuracy on the boundary is consistent with the accuracy of subdivision‐based approaches for the interior of a body. Our proposed framework is applicable to both triangular and quadrilateral refinement schemes, and does not impose any topological requirements upon the underlying subdivision control mesh. Several examples from an obstacle course of benchmark problems are used to demonstrate the convergence of the scheme. Copyright © 2004 John Wiley & Sons, Ltd.