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Numerical manifold space of Hermitian form and application to Kirchhoff's thin plate problems
Author(s) -
Zheng Hong,
Liu Zhijun,
Ge Xiurun
Publication year - 2013
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.4515
Subject(s) - finite element method , mathematics , hermitian matrix , partition of unity , space (punctuation) , manifold (fluid mechanics) , mathematical analysis , order (exchange) , element (criminal law) , numerical analysis , lagrangian , pure mathematics , computer science , engineering , structural engineering , law , mechanical engineering , finance , political science , economics , operating system
SUMMARY For second‐order problems, where the behavior is described by second‐order partial differential equations, the numerical manifold method (NMM) has gained great success. Because of difficulties in the construction of the H 2 ‐regular Lagrangian partition of unity subordinate to the finite element cover; however, few applications of the NMM have been found to fourth‐order problems such as Kirchhoff's thin plate problems. Parallel to the finite element methods, this study constructs the numerical manifold space of the Hermitian form to solve fourth‐order problems. From the minimum potential principle, meanwhile, the mixed primal formulation and the penalized formulation fitted to the NMM for Kirchhoff's thin plate problems are derived. The typical examples indicate that by the proposed procedures, even those earliest developed elements in the finite element history, such as Zienkiewicz's plate element, regain their vigor. Copyright © 2013 John Wiley & Sons, Ltd.