比例边界等几何方法在断裂力学中的应用  

SCALED BOUNDARY ISOGEOMTRIC ANALYS APPLIED TO FRACTURE MECHANICS PROBLEM

作　　者：庞林[1] 林皋[1] 钟红[1] 

机构地区：[1]大连理工大学建设工程学部水利工程学院,大连116024

出　　处：《工程力学》2016年第7期7-14,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51579033);国家自然科学青年基金项目(51109134);中国博士后基金特别项目(2013T60283);国家自然科学基金委创新研究群体项目(51421064)

摘　　要：该文将比例边界等几何方法(SBIGA)应用在断裂力学中,并就应力强度因子(SIFs)计算精度和收敛速度与传统比例边界有限元(SBFEM)进行了比较。与SBFEM不同,SBIGA采用非均匀有理B样条(NURBS)作为造型和离散的工具。主要包括了以下两个特点:一方面,有限元模型可直接继承于CAD系统,即节约划分网格的时间也避免了几何近似。另一方面,因为不需要进一步与CAD系统数据交换就可以保型细分,二维问题中自适应分析策略的实施十分方便。算例表明,SBIGA方法可以给出较SBFEM更为精确的结果和更快的收敛速度。其原因不仅得益于对曲边几何形状的精确描述,还来源于NURBS高阶的连续性。A novel numerical boundary method, scaled boundary isogeomtric analys （SBIGA）, is applied to fracture mechanics problem. Comparisons on accuracy and convergence rate in calculating stress intensity factor （SIFs） have been carried out for SBIGA and the scaled boundary finite element method （SBFEM）. In contrast to SBFEM, NURBS is used to geometric modeling and boundary discretization in SBIGA. It is characterized by the following two aspects. Firstly, the model of boundary isogeometric representation can be imported from CAD directly. Thus, the time costs of mesh generation are saved and it avoids geometric approximation. On the other hand, it can be automatically refined without further communication with the CAD system and keeps geometry invariability. Adaptive analysis strategy can be employed conveniently for 2D problems. The numerical results show that, in comparison with SBFEM, more accurate result and higher convergence rate could be achieved through SBIGA. This is due to geometric accurate description, as well as higher order continuity of NURBS.

关 键 词：比例边界有限元 非均匀有理B样条 应力强度因子 断裂力学 自适应分析 

分 类 号：O346.1[理学—固体力学]