无限长条功能梯度材料的非局部理论分析  

Research on infinite strip of functionally graded material using nonlocal theory

作　　者：刘宝良[1] 毕贤顺[1] 阎龙海[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3期182-184,共3页Journal of Heilongjiang Institute of Science and Technology

基　　金：黑龙江省自然科学基金资助项目(A01-10);黑龙江省教育厅基金项目(10551269)

摘　　要：假设剪切模量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裂纹问题。利用非局部线弹性理论和积分变换方法,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。结论表明,经典理论中的应力奇异性消失,在远离裂纹尖端的条件下的非局部解答和经典解答是一致的。A finite crack in an infinite strip of functionally graded material (FGM) under anti-plane shear loading is analyzed. It is assumed that the shear moduli varies continuously in the thickness direction and is to be of exponential form. The mixed boundary value problem is reduced to a dual integral equation by means of nonlocal linear elasticity theory and integral transform method. The stress field and displacement field near the tip of a crack for an infinite strip of FGM are solved by using Schmidt's method. The conclusion shows that the singularity of the solution of classical theory does not exist, and the solution of nonlocal theory accords with that of classical theory far from the tip of a crack.

关 键 词：功能梯度材料 非局部理论 裂纹 积分变换 对偶积分方程 

分 类 号：O346.1[理学—固体力学]