力电耦合扩展无网格伽辽金法在压电柔性臂断裂分析中的研究  

Mechanical-electrical coupling enriched element-free Galerkin method for fracture analysis of the piezoelectric flexible arm

作　　者：杨明泽[1] 周立明[2] 王晖[2] 

机构地区：[1]吉林体育学院计算机教研室,长春130022 [2]吉林大学机械科学与工程学院,长春130025

出　　处：《应用力学学报》2016年第4期560-564,732-733,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51305157);吉林省科技厅基金(20130305006GX;20160520064JH)

摘　　要：为提高含裂纹压电柔性臂在断裂分析中的求解精度,基于压电材料断裂力学理论,建立了压电柔性臂的力学分析模型。将描述裂纹尖端奇异性的位移场函数和电场函数引入到传统无网格伽辽金法中,提出了力电耦合扩展无网格伽辽金法。与传统无网格伽辽金法相比,本方法只需要较小的影响域来描述裂尖奇异场,并且节点影响域不会被裂纹线影响,不要可视准则和衍射准则,提高了计算精度。由虚拟裂纹闭合法推导了压电材料能量释放率,讨论了不同高斯点密度对强计算结果的影响。与解析解、有限元法的计算结果进行了比较,在高斯点个数为6×6时,扩展无网格伽辽金法的计算误差为1.88%,明显好于有限元的计算误差2.5%。数值算例结果表明本方法具有较高的计算精度。For improving the calculation precision of piezoelectric materials in the analysis of crack, based on the theory of fracture mechanics of piezoelectric materials, the extended terms are introduced into the approximation function of traditional element-free Galerkin method to describe the displacement field and electric field near the crack, and mechanical-electrical coupling enriched element-free Galerkin method is proposed. Compared with the traditional element-free Galerkin method, only a small domain is needed to describe the crack tip singular field, and the domain of the node is not affected by the crack, without the introduction of visibility method and the diffraction method, the computational efficiency can be improved. The energy release rate of piezoelectric materials is obtained by virtual crack closure method. Influence of the different number of nodes and different length of crack on the calculation precision of the intensity factor is discussed and the analytical solution and numerical results of finite element method are compared. When the number of gauss points is 6×6, the calculationerror of enriched element-free Galerkin method is 1.88%, it is much better than the calculation error of 2.5% by finite element method. Numerical example results indicate that the proposed method is feasible and possesses high precision.

关 键 词：扩展无网格法 压电材料 断裂力学 强度因子 

分 类 号：TP241[自动化与计算机技术—检测技术与自动化装置]