动态载荷下功能梯度复合材料的圆币形裂纹问题

研究了动态载荷下功能梯度材料中的圆币形裂纹问题．假设材料为横观各向同性，并且含有多个垂直于厚度方向的裂纹，材料参数沿轴向（与裂纹面垂直的方向）为变化的，沿该方向将材料划分为许多单层，各单层材料参数为常数，利用Hankel变换祛，在Laplace域内推导出了控制问题的对偶积分方程组．利用Laplace数值反演，得出了裂纹尖端的动态应力强度因子和能量释放率．研究了含两个裂纹的功能梯度接头结构，分析了材料非均匀性参数对应力强度因子和能量释放率的影响．

DYNAMIC RESPONSE FOR FUNCTIONALLY GRADED MATERIALS WITH PENNY-SHAPED CRACKS

A method for studying the penny-shaped cracks configuration in functionally graded material (FGM) structures subjected to dynamic or steady loading is provided. It is assumed that the FGMs is transversely isotropic and all the material properties only depend on the axial coordinate z. In the analysis, the elastic region is treated as a number of layers. The material properties are taken to be constants for each layer. By utilizing the Laplace transform and Hankel transform technique,the general solutions for layers are derived. The Dual integral equations are then obtained by introducing the mechanical boundary and layer interface conditions via the flexibility/stiffness matrix approach. The stress intensity factors are computed by solving Dual integral equations numerically in Laplace transform domain. The solution in time domain is obtained by utilizing numerical Laplace inverse. The main advantage of the present model is its ability for treating multiple crack configurations in FGMs with arbitrarily distributed and continuously varied material properties by dividing the FGMs into a number of layers, the properties of each layer is slightly different from that of nergbouring ones.