各向异性功能梯度材料弯曲断裂模型探讨

Model Analysis of Bending Fracture of Anisotropic Functionally Graded Materials

探讨各向异性功能梯度材料裂纹板受纯弯、纯扭、弯扭载荷作用下的弯曲断裂问题.根据弹性力学的基本方程以及断裂力学的有关理论及微积分方法,将材料常数(刚度系数)设为空间变量的任意函数,建立了各向异性功能梯度材料板弯曲断裂模型,即三类偏微分方程边值问题.再将材料常数依次设为空间变量的指数函数和幂函数,建立了相应的弯曲断裂模型,即一系列相关的偏微分方程的边值问题.这些模型是研究有关各向异性功能梯度材料板弯曲断裂问题的一个出发点和理论基础.

The bending fracture problems of cracked plate for anisotropic functionally graded materials under loads of pure bending, pure twisting or bending and twisting are discussed. From basic equations of elastic mechanics, related knowledge of fracture mechanics and frequent used methods of differential and integral calculus, bending fracture models of anisotropic functionally graded materials is established by assuming that material constants （stiffness matrix component）are expressed in arbitrary functions. Assume that material constants exponential functions or power functions of spatial variable ,the related bending fracture models are set,i, e. a series of boundary value problems of partial differential equations are established. These models are the threshold and theoretical basis to study on bending fracture problems for anisotropic functionally graded materials.