自然单元法的自适应研究  

Study on adaptive method for natural element method

作　　者：仲健 江涛[2,3] 章青[3] 

机构地区：[1]安徽汇华建筑设计有限公司,马鞍山243000 [2]安徽工业大学土木工程系,马鞍山243000 [3]河海大学水文水资源与水利工程科学国家重点实验室,南京210098

出　　处：《计算力学学报》2011年第B04期10-14,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10972072);国家重点基础研究发展计划资助(2007CB714104);河海大学水文水资源与水利工程科学国家重点实验室专项基金(2009585912)

摘　　要：自然单元法(NEM)是一种新兴的无网格数值计算方法,具有前处理简单和易于准确施加本质边界条件等优点。本文基于Z-Z后验误差估计方法,给出了一种自然单元法的误差估计因子和自适应分析细化方案。采用结点处的光滑应变计算相应的恢复应力,并用于构造全域上的恢复应力场。通过结点Voronoi单胞内的能量范数相对误差指示需要进行结点加密的区域。提出了一种改进的结点加密方案,在结点加密过程中考虑了局部区域结点布置的不均匀因素,使得加密后的结点布置在局部区域趋于均匀。算例结果验证了误差估计因子的有效性,自适应分析时加密结点主要分布于应力梯度较大的区域。The natural element method（NEM） is a recently developed meshless numerical method. NEM has the advantages such as simple preprocessing and easy for imposition of essential boundary conditions exactly. Based on Z-Z posterior error estimation, the error estimator and adaptive refinement procedure for NEM is presented. By using smoothed strain at the nodal points, the recovery stresses on all nodes can be calculated. Then the whole domain recovery stress field can be obtained by natural neighbour interpolation. Error estimator is the global or local error in energy norm, which is calculated by replacing the exact strss field with a recovery one. The estimated relative error in energy norm can be used to indicate if further refinement is needed and the sub-demains to be refined. An adaptive refinement strategy for the determination of optimal node spacing is proposed, which can lead to that nodal distribution tends to be homogeneous in local domain when a sequence of adaptive refinement is implemented. Numerical example is presented to demonstrate the effectivity of the error estimator. results also illustrate that the refined nodes are mainly distrbuted in the area with high stress gradient.

关 键 词：固体力学 无网格法 自然单元法 误差估计 自适应分析 

分 类 号：O242[理学—计算数学]