等几何分析细化收敛性研究

Research on Convergence of Refinement of Isogeometric Analysis

传统有限元分析软件中,CAE模型和CAD模型的数据不一致会造成计算结果的误差,为避免模型转换造成的分析误差提出等几何分析算法。等几何分析算法基于设计和分析统一模型,实现模型从几何设计到力学仿真的无缝集成。采用NURBS曲线分片方法建立几何模型并实现体参数化表达,使用二分K细化方法对CAD模型处理后,用等几何分析算法进行力学分析。等几何分析算法的计算结果与有限元分析软件结果对比,模型不需要转换和离散且保证了模型边界的光滑,更少的模型数据可以得到精确的结果,同时通过相同节点数和单元数的模型分析,等几何分析计算结果收敛更快。

Data inconsistency between CAE and CAD models in traditional finite element analysis software leads to errors in calculation results.In order to avoid analysis errors caused by model conversion,this paper proposes an isogeometric analysis(IGA)algorithm,which is based on a unified model for design and analysis,and realizes seamless integration of models from geometric design into mechanical simulation.NURBS curve slicing method is used to establish the geometric model and realize the volume parameter expression.After the CAD model is processed by the bipartite K refinement method,the mechanical analysis is carried out by the isogeometric analysis algorithm.Compared with the results of the finite element analysis software,the proposed model does not need to be converted and dispersed,and the model boundary is smooth.Less model data can obtain accurate results.At the same time,Isogeometric analysis results converge faster for the model analysis with the same number of nodes and elements.