结构自适应有限元分析中的高质量网格生成方案  

High Quality Triangle Mesh Refinement Scheme in Adaptive Finite Element Method

作　　者：杨晓东[1] 申长雨[1] 李倩[1] 陈静波[1] 

机构地区：[1]郑州大学橡塑模具国家工程研究中心,郑州450002

出　　处：《机械工程学报》2009年第8期292-297,共6页Journal of Mechanical Engineering

基　　金：国家自然科学基金(10590352);河南省教育厅自然科学研究(2008A430019)资助项目

摘　　要：许多大型复杂工程结构中物理场分析都采用有限元法。为了估计并控制误差,结构分析中常用的是基于后验误差估计的自适应有限元法。基于后处理法计算误差,与传统算法不同,将网格自适应过程分成均匀化和变密度化两个迭代过程。在均匀化迭代过程中,采用均匀网格尺寸对整体区域进行网格划分,以便得到一个合适的起始均匀网格;在变密度细分迭代过程中只进行网格的细化操作,并充分利用上一次迭代的结果,在单元所在的曲边三角形区域内部进行局部网格细化,保证了全局网格尺寸分布的合理性,使得不同尺寸的网格能光滑衔接,从而提高网格质量。整个方案简单易行,稳定可靠,数次迭代即可快速收敛,生成的网格布局合理,质量高。Finite element method is adopted for many complex engineering structures. In order to estimate and control error, adaptive finite element method is applied very popularly in structure analysis. Based on a posteriori error estimate, the adaptive process is divided into two iterations, i.e. uniform iteration and gradation refinement iteration, and which is different from traditional schemes. In the uniform process, a constant mesh size is applied in the whole domain so that a proper initial uniform mesh can be achieved. In the gradation mesh iteration process, an element required refinement is triangulated locally within the curved triangle region to which it belongs. This step can make use of previous mesh to higher degree and get a satisfactory mesh size distribution so that different size triangles can be jointed smoothly. The whole scheme is simple and can be carded out easily. The iteration process can converged in several steps. The resultant mesh has a better size distribution and higher quality.

关 键 词：自适应有限元 误差估计 网格细化 三角形 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]