功能梯度材料平面断裂中的一系列偏微分方程边值问题

A Series of Boundary Value Problem of Partial Differential Equation on Functionally Graded Materials Plane Fracture

当弹性模量按任意函数形式连续变化时,将各向同性、正交异性功能梯度材料平面断裂问题的Ⅰ型、Ⅱ型、Ⅰ+Ⅱ型裂纹的探讨归结为求解两类(6个)偏微分方程的边值问题。在此基础上进一步考虑当弹性模量按指数函数形式或按幂函数形式连续变化时,相应的Ⅰ型、Ⅱ型、Ⅰ+Ⅱ型裂纹的探讨可归结为求解另4类(12个)较为简单的偏微分方程边值问题。

The search for plane fracture problems of functionally graded materials with the elastic modulus variation represented in the arbitrary function form can be classified as solving two classes of boundary value problems of simple partial differential equation. Based on this, the search for plane fracture problems of functionally graded materials with the elastic modulus variation reprdsented in the exponential function or power function form can be classified as solving four classes of boundary value problems of simple partial differential equation.