基于均匀设计法的有限元网格划分与精度提高

本文首次运用均匀设计法的理论到有限元网格划分与精度提高领域，借助MATLAB程序计算，可以得出网格划分的关键点。运用二次开发的理念，在有限元网格划分时进行二次优化。具体思路是在求解同一个工程问题时，分别用均匀设计的方法计算得出结果（应力最优点），再与有限元方法计算得出结果（应力梯度）比较，应力变化图如果吻合，可以在有限元划分网格时使用MATLAB优化的关键点来加密网格。因为结果相等说明均匀设计得到的优化点等价于变化梯度大的点，加密梯度变化大的点当然精度更高。后面的计算结果证明均匀设计法相对自适应网格划分时的优越性，为全部单元都加密时带来结果失真的问题提供了一种有效的解决方法。

Meshing Grid and Accuracy Improvement of Finite Element Method Based on Uniform Design

This paper provides an idea of meshing grid with the uniform design method first time. We can achieve the emphasis of meshing grid by the calculating of matlab program. The main point of the idea is using the percepts of Secondary development When it is meshing grid and doing second optimal. This paper uses two different methods to solve one problem, using the uniform design method to obtain the result by the matlab program and obtaining the result with the finite element method by the ansys. If the two results of stress gradient variation basically match each other, it will be possible to provide a criterion when it is meshing grid with the finite element method. When the result is equal it is meaned that the optimization points obtained with the uniform design are equivalent to the the serious stress gradient poits. It is knowed that the results will be more precise when it encrypts the serious stress gradient poits. It can be telled from the result that the advantages of uniform design method compared with adapting, finite element method, and it also offers a measure to solve the problem which the answer is wrong when it encrypts all elements.