V型切口平面应力强度因子的等几何分析  

ISOGEOMETRIC ANALYSIS OF STRESS INTENSITY FACTOR IN V-NOTCHED PLANE

作　　者：徐旺 钟冬望[1] 蔡路军[1] XU Wang;ZHONG DongWang;CAI LuJun(Hubei Province Key Laboratory of Systems Science in Metallurgical Process,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学冶金工业过程系统科学湖北省重点实验室,武汉430065

出　　处：《机械强度》2022年第5期1221-1225,共5页Journal of Mechanical Strength

基　　金：武汉科技大学博士后科研启动费(108-1080027)资助。

摘　　要：针对含V型切口的平面断裂问题,提出一种求解切口尖端应力强度因子的等几何分析方法。基于等几何分析,将整体结构离散并构造结构的刚度矩阵,同时获得等几何分析的平衡方程及各节点的坐标信息。结合极坐标系下含V型切口平面问题的位移表达式,将全场的节点坐标信息代入经过坐标转换后的解析表达式获得转换矩阵,进而将等几何分析的平衡方程转换为维度更小的方程,求解得到级数形式位移场解析解的系数,同时获得应力场和切口尖端应力强度因子。将数值建模和数值计算统一到一个平台,提高了数值分析的效率;避免了等几何分析断裂问题的网格敏感问题,且无需后处理程序即可直接求解应力强度因子,同时避免了等几何方程计算难以收敛的问题。In this paper,an isogeometric analysis method is proposed to obtain the notch tip stress intensity factor for the plane fracture problem with V-notch.Based on the isogeometric analysis,which discretizes the overall structure and constructs the stiffness matrix of the structure,obtains the equilibrium equation,and simultaneously obtains the coordinate information of the nodes.Combined with the displacement expression of the plane with sharp notch in polar coordinate system,the node coordinate information of the whole field is substituted into the analytical expression after coordinate conversion to obtain a transformation matrix,and the isogeometric equilibrium equation is converted into a smaller-dimensional equation.The coefficients of the analytical solution of the displacement field can be calculated,and the stress field and the stress intensity factor of the notch are obtained at the same time.This method unifies numerical modeling and numerical calculation into one platform,which improves the efficiency of numerical analysis;avoids the grid-sensitive problem of iso-geometric analysis fracture problems,and the stress intensity factors can be directly solved without any post-processing program,and avoids the problem of inconsistency in the calculation of isogeometric equations.

关 键 词：应力强度因子 等几何分析 V型切口平面 位移场 应力场 

分 类 号：O346.1[理学—固体力学]