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磁电弹复合材料具有压电压磁的特点而被用于制作传感器等智能元件,在这些元器件中经常遇到界面端或切口问题,切口处由于易产生较高的奇异场而导致机械失效或电介击穿致使器件失效.本文主要研究磁电弹材料反平面切口的奇性问题.基于切口根部物理场的渐近展开假设,从应力平衡方程和电磁麦克斯韦方程组出发,导出了关于磁电弹材料反平面切口奇性指数的特征微分方程组,并将切口的力电磁学边界条件以及粘接材料的界面协调条件表达为奇性指数和特征角函数的组合.磁电弹材料切口反平面奇性指数的计算被转化为相应边界条件下常微分方程组特征值的求解问题,通过插值矩阵法计算出各阶奇性指数和相应的特征角函数.计算结果能提供减小切口奇性程度的切口角度和材料组合方案,更好地指导磁电弹智能元器件的结构设计.
Magnetoelectroelastic composites have the characteristics of piezoelectric pressure and are used to make intelligent components such as sensors. Interface elements or incisions are often encountered in these components. The incisions cause mechanical failure due to high singularity In this paper, we mainly study the singularity problem of anti-plane incision of magneto-electro-elastic material.According to the assumption of asymptotic development of the physical field of the incision root, from the stress balance equation and the electromagnetic Maxwell equations, The characteristic differential equations of the singularity index of the anti-plane incision of the elastic material are expressed, and the force-electromagnetism boundary conditions of the incision and the interfacial coordination condition of the adhesive material are expressed as the combination of the singularity index and the characteristic angle function. The calculation of singularity index is transformed into the problem of solving the eigenvalue of the ordinary differential equations under the corresponding boundary conditions. The singularity index and the corresponding characteristic angle function of each order are calculated by the interpolation matrix method. The calculation result can provide the method of reducing the degree of singularity The incision angle and material combination scheme can better guide the structural design of magnetoelectronic intelligent components.