基于线法的功能梯度材料断裂分析

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...

Method of lines for fracture analysis of functionally graded materials

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.