数值流形法局部网格加密算法

数值流形方法中网格加密是提高精度的方法之一,全局加密会严重导致计算效率低下,因此需要研究在数值流形法中覆盖系统网格局部加密.提出了数值流形法一到四级局部网格加密,可以根据实际情况需求自主选择网格加密等级进行计算分析.在数值流形法覆盖系统生成的算法基础上,采用C++面向对象编程技术开发程序.最后绘制裂纹分析数值算例计算后的位移图.结果表明:按照一到四级加密顺序对需加密区进行网格加密后,应力强度因子(stress intensity factor,SIF)与解析解误差均在5％以内,且符合加密越精细、计算结果精度越高的规律.可见此局部加密算法有效.

Local Mesh Refinement Algorithm of Numerical Manifold Method

In the numerical manifold method, mesh refinement is one of the methods to improve the accuracy, and the global refinement will lead to low computational efficiency. Therefore, it is necessary to study the local mesh refinement of the covering system in the numerical manifold method. The numerical manifold method with one-to-four level of local mesh refinement is proposed in this paper, which can be used to select the mesh refinement level according to the actual situation. On the basis of numerical manifold method covering system generation algorithm, C + + object-oriented programming technology is used to develop the program. Finally, the displacement plot of numerical examples of crack analysis is drawn. According to the refined order of one-to-four level, the error rate between SIF and analytical solution of SIF is less than 5% after the region that needs refining is refined local mesh. The result is in line with rule that the denser the refined mesh is, the more accurate the result is. It can be concluded that the local refinement algorithm is effective.