采用前期研究的基于矩形独立覆盖的新型数值流形法,提出结构线弹性静力分析的自动计算方法,包括自动的前处理、自适应分析等。根据独立覆盖的特点提出几个后验误差指标:独立覆盖之间条形连接区域的应变连续性指标;边界应力指标和独立覆盖的高阶误差指标。利用新方法的h型网格加密及p型升阶的方便性,选择一种路径尝试h-p型的混合自适应,其中,对于矩形独立覆盖采用简单的二分法实现覆盖加密。通过几个二维算例验证了新方法实现自动计算的可行性,只需人工输入结构外形、材料参数和边界条件,其它工作完全交由计算机完成,最终得到满足一定精度的计算结果。
Abstract
By means of numerical manifold method (NMM) based on independent rectangular covers proposed in previous study, we present an automatic computation method for static analysis of linear-elastic structures, including automatic pre-processing, self-adaptive analyses and so on. According to the characteristics of independent covers, we give 3 indexes for posterior error such as index of strain continuity in strip area between two covers, stress index on boundary surfaces and high-order error in an independent cover. By using convenient h-version mesh refinement and p-version order increasing in the new method, we implement h-p version self-adaptivity in a selected way to realize h-version refinement of rectangular covers by using simple bisection method. Some 2D numerical examples are given to illustrate the feasibility of automatic computation, in which all the procedures are automatically accomplished by the computer, except for necessary manual input of structural outlines, material parameters, and boundary conditions. Finally, we obtain calculated data with certain precision.
关键词
数值流形方法 /
独立覆盖 /
自动计算 /
误差估计 /
h-p混合自适应 /
静力分析
Key words
numerical manifold method (NMM) /
independent covers /
automatic computation /
error estimation /
h-p hybrid adaptivity /
static analysis of structures
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参考文献
[1] 百度百科.CAE [EB/OL].(2015-06-11)[2015-07-10]. http:∥baike.baidu.com/view/112169.htm.
[2] ZIENKIEWICZ O C, TAYLOR R L. The Finite Element Method (The Fifth Edition) [M]. Oxford, Great Britain: Butterworth-Heinemann, 2000.
[3] DUARTE C A, BABUSKA I, ODEN J T. Generalized Finite Element Methods for Three-dimensional Structural Mechanics Problems [J]. Computer & Structures, 2000,77:215-232.
[4] 李录贤, 刘书静, 张慧华, 等. 广义有限元方法研究进展 [J]. 应用力学学报, 2009, 26(1): 96-108.
[5] MOES N, DOLBOW J, BELYTSCHKO T. A Finite Element Method for Crack Growth without Remeshing [J]. International Journal for Numerical Methods in Engineering, 1999, 46: 131-150.
[6] 李录贤,王铁军. 扩展有限元法(XFEM)及其应用 [J]. 力学进展, 2005, 35(1): 5-20.
[7] 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: 3-47.
[8] 张 雄,刘 岩,马 上.无网格法的理论及应用[J]. 力学进展, 2009, 39(1): 1-36.
[9] 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 18-21,1991:57-76.
[10]BABUSKA I,MELENK J M.The Partition of Unity Method[J]. International Journal for Numerical Methods in Engineering,1997, 40:727-758.
[11]张湘伟, 章争荣, 吕文阁, 等. 数值流形方法研究及应用进展 [J]. 力学进展, 2010, 40(1): 1-12.
[12]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]. raybet体育在线
院报, 2013, 30(1):65-70.
[13]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: 341-347.
[14]苏海东,颉志强,龚亚琦,等. 基于独立覆盖的流形法的收敛性及覆盖网格特性[J]. raybet体育在线
院报,2016,(2):131-136.
[15]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].raybet体育在线
院报,2013,30(12):91-96.
[16]苏海东,祁勇峰. 部分重叠覆盖流形法的覆盖加密方法[J]. raybet体育在线
院报, 2013, 30(7): 95-100.
[17]林绍忠, 苏海东. 数值流形法独立覆盖区域的一种自动选取方法[J].raybet体育在线
院报,2014,31(12):88-91.
[18]苏海东, 祁勇峰, 龚亚琦. 裂纹尖端解析解与周边数值解联合求解应力强度因子[J]. raybet体育在线
院报, 2013, 30 (6): 83-89 .
[19]AKIN J E.Finite Element Analysis with Error Estimators[M]. Oxford, Great Britain: Elseviewer Butterworth-Heinemann,2005.
[20]O C 辛克维奇,K 摩根.有限元与近似法[M]. 陶振宗,张述良,周之德,译.北京:人民交通出版社,1989.
[21]石根华.数值流形方法与非连续变形分析[M]. 裴觉民译.北京: 清华大学出版社, 1997 .
[22]中国航空研究院.应力强度因子手册[M]. 北京:科学出版社,1993.
基金
国家自然科学基金项目(51409012);中央级公益性科研院所基本科研业务费项目(CKSF2013031/CL,CKSF2014054/CL)
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