带裂纹功能梯度材料薄板SIFs分析的广义参数Williams单元

Williams Element with Generalized Degrees of Freedom for SIFs Analysis in Functionally Graded Material Plate with Cracks

根据Williams级数位移场,仅考虑弹性模量E为坐标的函数,通过改变裂尖奇异区微单元刚度集成方式,推导建立了功能梯度材料薄板平面断裂分析的广义参数Williams单元新格式.结合含中心斜裂纹和边界裂纹的功能梯度材料薄板,分析了弹性模量E的分布形式、裂纹倾角及裂纹长度对裂尖应力强度因子的影响.算例结果表明:该方法能够直接且高效求解带裂纹功能梯度材料薄板的裂尖应力强度因子;当弹性模量E呈单调变化且其梯度与荷载方向平行或垂直时,分别会使中心斜裂纹两个裂尖的I型或II型应力强度因子值产生差异,而应力强度因子随裂纹倾斜角度的分布规律并不受弹性模量E的分布形式影响.

According to the Williams series displacement field,only considering the elastic modulus E as a function of coordinate,a new format of Williams element with generalized degrees of freedom for the thin plane fracture analysis in a functionally graded material plate is derived by changing the integration mode of the overall stiffness of the crack tip in the singular region.Combined with a inclined crack and an edge crack contained in a functionally graded material plate,the influence of the distribution form of the elastic modulus E,the crack inclination angle and the crack length on the stress intensity factor at the crack tip is analysed.The results show that the method can directly and efficiently solve the crack tip stress intensity factor of the functionally graded material with cracks.When the elastic modulus E changes monotonically and its gradient is parallel to or vertical to the load direction,the stress intensity factors of mode I or mode II at the two crack-tips of the central inclined crack are different,and the distribution of stress intensity factors with the crack inclination angle is not affected by the distribution form of elastic modulus E.