为对功能梯度材料( FGM) 板进行断裂力学分析，提出了施加温度场建立 FGM 板分层线性离散模型的方法．采用该方法、梯度有限元法和常规有限元法对 FGM 板的应力场和位移场进行对比分析，结果表明该方法简便可行．在所提方法的基础上，采用扩展有限元法求解含裂纹 FGM 板的位移场，再利用位移外推法计算裂纹尖端的应力强度因子，通过上述方法对不同材料梯度参数、裂纹尺寸、裂纹倾斜角的 FGM 板裂纹尖端应力强度因子进行数值模拟．计算结果表明，合理地选择 FGM 板的梯度参数并控制裂纹尺寸能有效降低裂纹尖端应力强度因子．所提出的方法可推广应用于材料梯度分布为任意连续变化的 FGM 板断裂力学分析．

In order to perform the fracture mechanics analysis of functionally graded material (FGM) plates,amethod for temperature field loading is proposed to establish a layered linear discrete model.Then,a comparativeanalysis of the proposed method,the gradient finite element method and the common finite element method is per-formed in terms of the stress field and the displacement field of the plates,which verifies the convenience and feasi-bility of the proposed method.Moreover,the displacement field of FGM plates with crack is calculated via the ex-tended finite element method based on the proposed method,and the stress intensity factors of crack tips are de-rived by the displacement extrapolation technique.Finally,by using the above- mentioned methods,the stress in-tensity factors of FGM plates with different gradient parameters.crack sizes and crack inclination angles are numeri-cally simulated.The results show that stress intensity factors can be effectively reduced by reasonably selecting thegradient parameter and controlling the crack size,and that the proposed method is applicable for the fracture me-chanics analysis of FGM plates with arbitrarily- distributed properties.