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为提高含裂纹压电材料结构分析的求解精度,基于压电材料断裂力学理论,在传统无网格伽辽金法近似函数中引入扩展项来描述裂纹处不连续位移场及电场,提出了含裂纹压电材料的扩展无网格伽辽金法.该方法能很好地模拟裂纹尖端奇异性,并且节点影响域的连续性不受裂纹线的影响,无须引入可视准则与衍射准则,易于编程实现.讨论了不同节点分布、不同裂纹长度对强度因子计算结果的影响,与解析解、常规无网格伽辽金法及有限元法的计算结果进行了比较,数值算例结果表明本方法正确可行且具有较高的精度.
Based on the fracture mechanics theory of piezoelectric materials, an extension term is introduced into the approximation function of traditional meshless Galerkin method to describe the discontinuous displacement field and electric field at the crack site. In order to improve the resolution accuracy of cracked piezoelectric material, The crack-free piezoelectric material has a mesh-free Galerkin method, which can well simulate the singularity of the crack tip and the continuity of the influence area of the node is not affected by the crack line, and it is easy to be easy to introduce the visual criterion and the diffraction criterion The effects of different nodes’ distributions and different crack lengths on the calculation of strength factor are discussed, which are compared with the analytical solutions and the results of the conventional meshless Galerkin method and finite element method. Numerical results show that this method Correct and feasible and with high precision.