Numerical manifold space of Hermitian form and application to Kirchhoff's thin plate problems

Hong Zheng; Zhijun Liu; Xiurun Ge

doi:10.1002/nme.4515

journal article May 28, 2013

Numerical manifold space of Hermitian form and application to Kirchhoff's thin plate problems

Hong Zheng

Zhijun Liu

Xiurun Ge

International Journal for Numerical Methods in Engineering Vol. 95 No. 9 pp. 721-739 · Wiley

View at Publisher Save 10.1002/nme.4515

Abstract

SUMMARYFor 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.

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Metrics

94

Citations

28

References

Details

Published: May 28, 2013
Vol/Issue: 95(9)
Pages: 721-739
License: View

Authors

H

Hong Zheng

Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education Beijing University of Technology Beijing 100124 China

Z

Zhijun Liu

State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics Chinese Academy of Sciences Wuhan 430071 China

X

Xiurun Ge

State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics Chinese Academy of Sciences Wuhan 430071 China

Funding

National Natural Science Foundation of China Award: 50779031

National Basic Research Program of China Award: 2011CB013505

Cite This Article

Hong Zheng, Zhijun Liu, Xiurun Ge (2013). Numerical manifold space of Hermitian form and application to Kirchhoff's thin plate problems. International Journal for Numerical Methods in Engineering, 95(9), 721-739. https://doi.org/10.1002/nme.4515

Numerical manifold space of Hermitian form and application to Kirchhoff's thin plate problems

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