在CAD模型的性能模拟分析过程中,经常需要对计算域模型进行细化以提高模拟的精度.针对等几何分析这一新兴的模拟分析方法,提出一种新的细化方法,称之为r-p型细化方法.该细化方法包括2个步骤:首先通过极小化后验误差估计,对初始计算域的内部控制顶点的位置进行优化(即r型细化)；然后对通过r型细化得到的计算域模型进行升阶操作以增加自由度(即p型细化).将r-p型细化方法应用于二维热传导问题的等几何模拟分析,通过实例验证了r-p型细化方法在等几何分析中的有效性,并与经典的h型细化方法进行了比较.%In the simulation and analysis process of CAD models, some refinement operations are often performed to improve the simulation accuracy. In this paper, we propose a new refinement method called r-p-refinement for isogeometric analysis. There are mainly two steps in the proposed method. Firstly, we optimize the replacement of inner control points in initial computational domain by minimizing posteriori error estimation (r-refinement). Secondly, the degree elevation is performed for the computational domain obtained after the first step to increase the degree of freedom (p-refinement). The proposed r-p-refinement method is applied in the isogeometric analysis for two dimensional heat-conduction problems. The experimental results show the efficiency of r-p-refinement in isogeometric analysis. Comparison examples with h-refinement are also provided in this paper.
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