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为精确而有效地求解机电耦合作用下含裂纹压电材料的断裂参数,首先,通过将复势函数法、扩展有限元法和光滑梯度技术引入到含裂纹压电材料的断裂机理问题中,提出了含裂纹压电材料的Cell-Based光滑扩展有限元法;然后,对含中心裂纹的压电材料强度因子进行了模拟,并将模拟结果与扩展有限元法和有限元法的计算结果进行了对比。数值算例结果表明:Cell-Based光滑扩展有限元法兼具扩展有限元法和光滑有限元法的特点,不仅单元网格与裂纹面相互独立,且裂尖处单元不需精密划分,与此同时,Cell-Based光滑扩展有限元法还具有形函数简单且不需求导、对网格质量要求低且求解精度高等优点。所得结论表明Cell-Based光滑扩展有限元法是压电材料断裂分析的有效数值方法。
In order to solve the fracture parameters of cracked piezoelectric materials under electromechanical coupling accurately and effectively, firstly, by introducing the complex potential function method, the extended finite element method and the smooth gradient technique into the fracture mechanism of cracked piezoelectric materials, And the Cell-Based smoothing finite element method for the crack-containing piezoelectric material is established. Then, the strength factor of the piezoelectric material with the central crack is simulated and the simulation results are compared with the results of the finite element method and the finite element method Compared. The numerical example shows that the Cell-Based smoothing finite element method combines the characteristics of extended finite element method and smooth finite element method. Not only the element grid and crack surface are independent of each other, In the meantime, the Cell-Based smoothing finite element method has the advantages of simple shape function and no need of derivation, low requirement of grid quality and high solution accuracy. The results show that the Cell-Based smoothing finite element method is an effective numerical method for the fracture analysis of piezoelectric materials.