功能梯度材料反平面裂纹问题的非局部理论解

Nonlocal Theory Solution for Functionally Grated Material under Antiplane Shear

用非局部线弹性理论研究了无限大功能梯度材料反平面的裂纹问题,通过Fourier积分变换使该问题的求解转化为对偶积分方程,然后利用Schmidt方法代替第二类Fredholm方法求解对偶积分方程,克服了Fredholm方法求解积分方程时积分核为奇异时遇到的困难。最后,计算出该问题裂纹尖端的应力场和位移场,并给出了裂纹尖端的应力解析表达式。

A crack problem is considered in an infinite mediums of functionally grated material (FGM) subjected to antiplane shear by using nonlocal linear elasticity theory. The solution of this problem can be transformed into dual integral equation, then a set of dual integral equation is solved by using the Schmidt' s method instead of using the second Fredholm integral equation method. This method overcomes the difficulty encountered in solving integral equation. The stress field and displacement field are presented at the crack tip and analytical solution is obtained.