有限元网格划分中的圣维南原理及其应用

Sain Vaint Principle of Meshing in Finite Elememt Method and its Application

网格划分是有限元分析前处理中的一个关键步骤,如何进行有效的网格划分,既保证计算的精度,又能提高计算效率,是一个重要的研究课题。对此提出了有限元网格划分中的圣维南原理。该原理以为,某局部区域的网格疏密对其稍远处节点的计算精度影响很小。基于该原理提出了网格划分的新思路:首先对全局进行一般的网格划分,然后只对关注地方及其周围的关键区域进行局部细分,就可以达到较高的仿真精度。使用实际算例对该原理进行了验证,结果表明该方法具有较高的精度和计算效率。

Meshing is a key preprocessing step in finite element method（FEM）analysis.How to mesh efficiently and accurately is an important research topic.Saint Venant Principle of meshing in FEM is proposed to focus this problem in this paper,which supposes that the rarefaction of concentration of mesh somewhere affects little on the result of faraway nodes.A new approach of meshing is proposed based on this principle：firstly a general meshing is carried out in the whole region,secondly a local refinement at key areas is done to achieve a high simulation accuracy.An actual example is illustrated to verify this method.And the result shows that this meshing method is high in simulation accuracy and calculation efficiency.