Implement of Ameliorated ACM Element in Numerical Manifold Space for Tackling Kirchhoff Plate Bending Problems

Abstract:

Abridging the chasm between the prevalently employed continuum methods (e.g. FEM) and discontinuum methods (e.g. DDA),the numerical manifold (NNM),which utilizes two covers, namely the mathematical cover and physical cover, has evinced various advantages in solving solid mechanical issues. The forth-order partial elliptic differential equation governing Kirchhoff plate bending makes it arduous to establish the -regular Lagrangian partition of unity ,nevertheless, this study renders a modified conforming ACM manifold element, irrespective of accreting its cover degrees, to resolve the fourth-order problems. In tandem with the forming of the finite element cover system that erected on rectangular meshes, a succession of numerical manifold formulas are derived on grounds of the minimum potential energy principle and the displacement boundary conditions are executed by penalty function methods. The numerical example elucidates that, compared with the orthodox ACM element, the proposed methods bespeak the accuracy and precipitating convergence of the NMM.

• Periodical: Applied Mechanics and Materials (Volumes 638-640)
• Pages: 1710-1715
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.638-640.1710
• Online since: September 2014
• Authors: Hong Wei Guo*, Hong Zheng, Wei Li
• Keywords: ACM Element, Compatible Element, Convergence, Mathematical Cover, Modified, Numerical Manifold Method, Physical Cover

References

[1] Shi Genhua. Discontinous deformation analysis and numerical models of static and daymic block system. [PhD Dissertation][D] Berkeley, USA: Dept. of Civil Engrg. , UC, (1989).

[2] O. C. Zienkiewicz. The Finite Element Method [M]. 3rd ed. Mc Graw Hill Book Company, New York, (1977).

[3] Xiaoyi Zhou and Anfu DENG, Numerical Manifold Method of Analysis for beam and plate based on Generalized Variational Principle [J]. Chinese Journal Of Solid Mechanics, 2008, 03: 313-318.

[4] Wei-bin WEN and Kai-lin JIAN. 2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending [J]. Applied Mathematics and Mechanics(English Edition), 2013, 08: 1017-1030.

DOI: 10.1007/s10483-013-1724-x

[5] WEN Wei-bin, LUO Shao-ming, Polygonal Manifold Element for thin plate-bending analysis [J]. Engineering Mechanics, 2012, 10: 249-256.

[6] Hong Zheng, Zhijun Liu and Xiurun Ge, Numerical manifold space of Hermitian form and application to Kirchhoff's thin plate problems [J]. International Journal for Numerical Methods in Engineering, Volume 95, Issue 9, pages 721–739, 31 August (2013).

DOI: 10.1002/nme.4515

[7] Wang, D. ; Chen, T., A Generalized Point Conforming Rectangular Plate Element [J]. CHINA OCEAN ENGINEERING; 9, 3; 297-302.

[8] Zhang Guoxiang, Zeng Qiaoling and Liu Baochen, Theoretical Identification and Application of Harmonized Rectangular Thin Plate Element [J]. China Railway Science, 1999, 01: 92-97.

[9] Xu Zhilun, Elasticity [M], Beijing: Higher Education Press, (2006).