三维实体结构NURBS等几何分析  

NURBS-BASED ISOGEOMETRIC ANALYSIS OF THREE-DIMENSIONAL SOLID STRUCTURES

作　　者：过斌[1] 葛建立[1] 杨国来[1] 吕加 

机构地区：[1]南京理工大学机械工程学院,南京210094 [2]Iowa大学机械与工业工程系,iowaia522421527

出　　处：《工程力学》2015年第9期42-48,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(11172139);国家重大科学仪器设备开发专项项目(2013YQ47076508)

摘　　要：等几何分析是近年来在有限元法基础上发展起来的一种新的数值方法,它消除了有限元的几何误差,具有高阶连续性。该文研究了三维结构等几何分析中NURBS几何体的表示方式及载荷、约束的施加方法,分别从计算精度和仿真效率两个方面对比了等几何分析的计算结果与有限元法一阶单元和二阶单元的计算结果,展示了等几何分析相对于标准有限元法的优势,并以厚壁圆筒模型算例验证了等几何分析的实用性。将NURBS单元应用于几何形状精度要求高的齿轮和变截面圆筒,数值结果表明三维NURBS等几何分析方法在复杂三维结构的仿真计算中具有较好的灵活性和适用性,可得到连续的应力场,有望在工程中得到广泛应用。Isogeometric analysis （IGA） is a new numerical method developed based on the standard finite element method （FEM） in recent years, which eliminates the geometric error of FEM and has high-order continuity. This paper presents the IGA of three-dimensional structures by using the representation of non-uniform rational B-splines （NURBS） geometry and the applied load and constraints. The simulation results with IGA are compared to those with FEM using linear elements and quadratic elements. Compared to the standard FEM, the advantages of IGA are demonstrated through accuracy and efficiency. A thick-walled cylinder model is chosen as an illustrative example to verify the practicability of IGA. The NURBS elements are applied to the gear and cylinder which have structures with variable sections and need high geometrical accuracy. The results show that the proposed three-dimensional IGA based on NURBS is flexible and applicable for complex three-dimensional structures and the method can generate continuous stress field. The IGA method is expected to be widely used in engineering.

关 键 词：等几何分析 非均匀有理B样条 有限元分析 计算精度 单元间连续性 

分 类 号：O343.2[理学—固体力学]