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

发布时间：2018-09-13 13:15

【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。
[Abstract]:In order to improve the accuracy of solving the fracture analysis of a cracked piezoelectric flexible arm, a mechanical analysis model of the piezoelectric flexible arm is established based on the theory of fracture mechanics of piezoelectric materials. The displacement field function and electric field function describing the singularity of crack tip are introduced into the traditional meshless Galerkin method, and the electromechanical coupled extended meshless Galerkin method is proposed. Compared with the traditional meshless Galerkin method, this method only needs a small influence domain to describe the crack tip singular field, and the node influence domain is not affected by the crack line. The energy release rate of piezoelectric materials is derived from the virtual crack closure method, and the effect of different Gao Si point density on the strength calculation results is discussed. Compared with the analytical solution, the result of the finite element method is better than that of the finite element method at the number of Gao Si points is 6 脳 6, and the calculation error of the extended meshless Galerkin method is 1.88, which is better than that of the finite element method. Numerical examples show that this method has high accuracy.
【作者单位】：吉林体育学院计算机教研室;吉林大学机械科学与工程学院;
【基金】：国家自然科学基金(51305157) 吉林省科技厅基金(20130305006GX;20160520064JH)
【分类号】：O346.1

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