摘要
等几何分析(IGA)相对有限元分析是一种新型的数值仿真方法.本文针对平面静力问题提出了一种平均值等几何分析方法.该方法首先给定控制点,采用平均值法计算节点向量,求得NURBS基函数,建立控制点模型;其次用等参元思想将物理空间转化到[-1,1]的父空间,再将父空间转化到[0,1]参数空间,建立等几何分析模型;然后施加边界条件后,由单元刚度矩阵组建整体刚度矩阵,建立本构方程;最终通过求解运动控制方程得到位移变化,经后处理构建位移云图.将改进的等几何分析应用于经典悬臂梁静力学问题,所得结果与有限元法对比表明:两者的位移云图分布基本一致,等几何分析的最大位移比有限元分析的精度更高;在控制精度和网格数量的情况下比较两者的运算时间,等几何法的计算效率提高了47.72%,验证了改进等几何分析方法的可行性.
Compared with finite element analysis,isogeometric analysis(IGA)is a new numerical simulation method.In this paper,a set of average value isogeometric analysis method were proposed for plane static problems.The method first gave the control point,and the node vector was calculated by the average method to obtain the NURBS basis function which could establish the control point model.Secondly,the physical space was transformed into the parent space of[-1,1]by the isoparametric element method which was transformed into the parameter space of[0,1]to establish the isogeometric analysis model.The element stiffness matrix was absorbed into the overall stiffness matrix to establish the constitutive equation after the boundary conditions were applied.Finally,by solving the constitutive equation we could obtain the displacement change which was used to construct the displacement nephogram by post-processing.The classical plane rectangular statics problem was taken as an example to carry out the isogeometric analysis.The displacement nephograms of the two methods are basically the same by compared with the finite element analysis,and maximum displacement of isogeometric analysis is more accurate than finite element analysis.At the same time,under the control accuracy and the number of grids,the calculation efficiency of the isogeometric method is improved by 47.72%,which verifies the feasibility of the method.
作者
孙振山
毛虎平
贾冰潮
张稣宁
SUN Zhenshan;MAO Huping;JIA Bingchao;ZHANG Suning(School of Energy and Power Engineering,North University of China,Taiyuan 030051,China)
出处
《中北大学学报（自然科学版）》
CAS
2022年第6期498-505,共8页
Journal of North University of China(Natural Science Edition)
基金
国家自然科学基金资助项目(51275489)
山西省自然科学基金资助项目(201701D121082)。
