摘要
在传统的有限元分析中,对于曲边区域或者曲边的分界面并没有很好的近似方法,通常使用大量的线性单元近似的描述曲边计算区域.这些新增加的单元不仅浪费了计算时间,而且往往并不是需要求解的部分.采用曲线单元可以避免对单元的强制细化,有效的提高计算的精度.曲边单元使用非均匀有理B样条(NURBS)曲线实现,可以有效的消除几何离散误差,保证整体的高阶连续性.详细讨论了基于NURBS曲线的自适应三角形网格剖分和四边形网格剖分,并结合自适应hp有限元算法解决实际问题.从计算自由度和计算时间的角度比较典型的工程算例结果,采用NURBS曲边单元的hp有限元算法能够很好的消除几何近似导致的误差,提高计算的效率.
In the traditional finite element analysis,there is not a good approximation method for curved boundaries or the interface of curved edge,and a large number of linear elements are used to describe the computational domain of curved edges.These additional elements not only waste computing time,and often are not the necessary part to solve.To use curved element can avoid the force refinement of the elements and effectively improve the calculation accuracy.By using the non-uniform rational B-spline（NURBS） curve algorithm can effectively eliminate the geometric discretization error,and ensured the overall high continuity.This paper discusses adaptive triangular mesh generation and quadrilateral mesh generation based on the NURBS curves in detail and solves practical problems with hp-adaptive finite element algorithm.The results were compared from the degree of freedom and the computing time,the NURBS based hp finite element method can eliminate the errors caused by geometric approximation and improve the computational efficiency.
出处
《微电子学与计算机》
CSCD
北大核心
2011年第8期216-218,221,共4页
Microelectronics & Computer
基金
国家自然科学基金项目(41074099)
