Submodel Method for Error Analysis in Numerical Manifold MethodBased on Independent Covers

SU Hai-dong; YUAN Xiao-chen; GONG Ya-qi

doi:10.11988/ckyyb.20170128

PDF(2941 KB)

Journal of Changjiang River Scientific Research Institute ›› 2017, Vol. 34 ›› Issue (12) : 147-154. DOI: 10.11988/ckyyb.20170128

NUMERICAL MANIFOLG METHOD BASED ON INDEPENDENT COVERS

Submodel Method for Error Analysis in Numerical Manifold MethodBased on Independent Covers

SU Hai-dong^{1, 2}, YUAN Xiao-chen¹, GONG Ya-qi^{1, 2}

Author information +

History +

Abstract

In previous research of adaptive analysis using Numerical Manifold Method based on independent covers, the internal error in an independent cover cannot be effectively controlled. In view of this, a submodel method for error analysis of independent covers is presented, in which, by means of increasing the cover function order in an individual independent cover, a new error estimator for point-by-point error is obtained by calculating the differences of the results between high-order and low-order cover functions. The procedures of the submodel method are introduced in detail, and a case study of a gravity dam shows that the method could effectively control the internal error of independent covers, laying foundation for point-by-point error control in the future. Finally some preliminary theoretical analysis and discussions are given for the convergence principle and the error-control method of Numerical Manifold Method based on independent covers.

Key words

Numerical Manifold Method(NMM) / independent covers / error analysis / submodel method / adaptive analysis

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

SU Hai-dong, YUAN Xiao-chen, GONG Ya-qi. Submodel Method for Error Analysis in Numerical Manifold MethodBased on Independent Covers[J]. Journal of Changjiang River Scientific Research Institute. 2017, 34(12): 147-154 https://doi.org/10.11988/ckyyb.20170128

References

[1] 王勖成.有限单元法[M].北京:清华大学出版社,2003.[2] STROUBOULIS T, COPPS K, BABUSKA I. The Generalized Finite Element Method[J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(32):4081-4192.[3]BELYTSCHKO T, KRONGAUZ Y, ORGAN D, et al. Meshless Methods: An Overview and Recent Developments[J]. Computer Methods in Applied Mechanics and Engineering , 1996, 139(1/2/3/4): 3-47[4] 苏海东,颉志强,龚亚琦, 等.基于独立覆盖的流形法收敛性及覆盖网格特性[J]. 长江科学院院报,2016,32(2):131-136.[5] 苏海东,龚亚琦,颉志强, 等. 基于矩形独立覆盖初步实现结构静力分析的自动计算[J]. 长江科学院院报,2016,33(2):144-150.[6] 苏海东,陈积瞻,颉志强, 等. 基于独立覆盖流形法的CAD与CAE融合研究[J]. 长江科学院院报,2017,34(12):133-139.[7] SHI G H.Manifold Method of Material Analysis[C]∥U.S. Army Research Office. Transactions of the Ninth Army Conference on Applied Mathematics and Computing. Minneapolis, Minnesota, U. S. A, June 18-21,1991:51-76.[8] 祁勇峰, 苏海东, 崔建华.部分重叠覆盖的数值流形方法初步研究[J].长江科学院院报, 2013,30(1):65-70.[9] SU Hai-dong, QI Yong-feng, GONG Ya-qi, et al. Preliminary Research of Numerical Manifold Method Based on Partly Overlapping Rectangular Covers[C]∥DDA Commission of International Society for Rock Mechanics. Proceedings of the 11th International Conference on Analysis of Discontinuous Deformation (ICADD11). Fukuoka, Japan, August 27-29, 2013, London :Taylor & Francis Group, 2013: 341-347.[10]苏海东,祁勇峰. 部分重叠覆盖流形法的覆盖加密方法[J]. 长江科学院院报, 2013,30(7):95-100.[11]苏海东, 祁勇峰, 龚亚琦, 等任意形状覆盖的数值流形方法初步研究[J]. 长江科学院院报, 2013, 30(12): 91-96.[12]中国航空研究院.应力强度因子手册[M]. 北京:科学出版社,1993.[13]苏海东,颉志强.独立覆盖流形法的本质边界条件施加方法[J]. 长江科学院院报,2017,34(12):140-146. [14]ZIENKIEWICZ O C, ZHU J Z. A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis[J]. International Journal of Numerical Methods in Engineering,1987, 24(2): 337-357.[15]CHUNG H J, BELYTSCHKO T. An Error Estimate in the EFG Method[J]. Computational Mechanics,1998,21(2):91-100.[16]BABUSKA I,STROUBOULIS T,GANGARAJ S K,et al. Practical Aspects of A-posteriori Estimation for Reliable Finite Element Analysis[J]. Computer & Structures, 1998, 66(5):627-664.