无限长条功能梯度材料自由边界运动裂纹问题  

Moving crack problem in an infinite strip of FGM between free boundary

作　　者：毕贤顺[1] 刘宝良[1] 于丽艳[1] 李玉琳[1] 

机构地区：[1]黑龙江科技学院数力系,哈尔滨150027

出　　处：《黑龙江科技学院学报》2005年第6期352-354,共3页Journal of Heilongjiang Institute of Science and Technology

基　　金：黑龙江省教育厅科学技术研究资助项目(10551269)

摘　　要：假设剪切模量和密度沿厚度方向连续且为指数形式模型,研究了含有限长裂纹的无限长条功能梯度材料在反平面剪应力荷载作用下的运动裂纹问题。利用非局部线弹性理论和Fourier积分变换方法,将混合边界值问题简化为对偶积分方程,最后通过Schmidt方法对裂纹尖端的应力场和位移场进行了求解。与经典理论的解答不同,裂纹尖端应力为有限值,其最大值随长条高度和裂纹的运动速度的增加而增加。It is assumed that the shear moduli and mass density vary continuously in the thickness direction and is to be of exponential form, The study involves the moving crack problem in an infinite strip of FGM between free boundary subjected to an anti-plane shear loading in an infinite strip of functionally graded material （FGM）. The mixed boundary value problem is reduced to a dual integral equation by means of nonlocal linear elasticity theory and Fourier integral transform method. The stress field and displacement field for an infinite strip of FGM are solved near the tip of a crack by using Schmidt＇s method. Unlike the classical elasticity solution, the magnitude of stress at the crack tip is finite, and it is found that the maximum stress at the crack tip increase as the strip length and crack moving speed are increased.

关 键 词：功能梯度材料 非局部理论 断裂 对偶积分方程 积分变换 

分 类 号：O346.1[理学—固体力学]