含裂纹压电材料的Cell-Based光滑扩展有限元法
Cell-Based smoothed extended finite element method for piezoelectric materials with cracks

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 piezoelectric materials with cracks under the electromechanical coupling effect accurately and effectively, Cell-Based smoothed extended finite element method for piezoelectric materials containing cracks was put forward firstly by introducing complex potential function method, extended finite element method and smooth gradient technology into the problem of fracture mechanics for piezoelectric materials with cracks. Then, the intensity factors of piezoelectric materials with center cracks were simulated, and the simulated results were compared with the calculated results of extended finite element method and finite element method. The results of numerical examples show that Cell-Based smoothed extended finite element method has both the characteristics of extended finite element method and smoothed finite element method, not only the element meshes and crack surface are independent of each other, but also unnecessary to divide the element at crack tip precisely, at the same time, Cell-Based smoothed extended finite element method also has advantage such as the shape function is simple and does not require derivative, the mesh quality requirements are low and the solution precision is high, etc. The conclusions obtained show that Cell-Based smoothed extended finite element method is an effective numerical method for fracture analysis of piezoelectric materials. 国家自然科学基金(51305157);吉林省科技厅基金(20130305006GX,20160520064JH)