基于线法的功能梯度材料断裂分析  

Method of lines for fracture analysis of functionally graded materials

作　　者：燕秀发[1,2] 钱七虎[1] 方国强[3] 赵敏福[4] 郭延宝[5] 

机构地区：[1]解放军理工大学工程兵工程学院 [2]解放军91550部队 [3]海军装备部 [4]皖西学院 [5]装甲兵工程学院

出　　处：《解放军理工大学学报（自然科学版）》2011年第4期346-353,共8页Journal of PLA University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学创新研究群体科学基金资助项目(51021001);中国博士后科学基金资助项目(20080431344)

摘　　要：为了克服材料非均匀性引起的数值困难,一种半解析数值方法——线法,被引入功能梯度材料的断裂分析。通过有限差分将问题的控制方程半离散为定义在沿梯度方向离散节线上的常微分方程组,然后应用B样条高斯配点法求解该常微分方程组。为了演示线法功能梯度材料断裂分析的方法,给出了指数梯度含裂纹功能梯度材料板分别在恒定位移、弯曲载荷作用下应力强度因子的数值算例,同时给出了节线和配点局部加密、区间映射以及变间距离散等提高计算精度和效率的线法断裂分析技巧。与相关问题理论解的对比分析表明,该法的计算结果具有很高的精度。To overcome the numerical difficulties caused by material nonhomogeneity,a semi-analytical numerical method,method of lines（MOLs）,was introduced into the fracture analysis of functionally graded materials（FGMs）.The basic idea of that method was to semi-discretize the governing equations into a system of ordinary differential equations（ODEs） by means of finite difference approach.The ODEs were defined on the discrete lines along the gradation direction.By using B spline collocation method at Gaussian points,solutions to the problem were obtained.The computational examples of the stress intensity factors for the cracked plate of FGMs with an exponential gradation under constant displacement and bending loading were presented to demonstrate the fracture analysis method of FGMs.In such examples,some numerical techniques,including local refinement of discrete lines and collocation points,interval map and varying space discretization,were employed to improve the computational accuracy and the efficiency.Numerical results of the examples by MOLs are quite accurate compared with the theoretical solutions to the corresponding problems.

关 键 词：功能梯度材料 线法 非均匀性 断裂分析 半解析法 

分 类 号：O346.2[理学—固体力学]