压电材料中切口/接头端部平面电弹性场奇异性有限元分析

为了对平面载荷作用下压电材料中切口或接头端部附近电弹性场奇异性问题进行分析，首先以应力平衡方程、Maxwell方程和和边界条件为基础，得到一种求解压电材料特征问题的弱式方程；其次，假定楔形切口或接头端部附近单元内位移和电势沿径向分布为指数形式，而周向方向分布则采用泡函数插值，将其代入弱式方程，建立一种只需对楔形切口或接头端部附近周边进行离散的一维简单有限元方法．压电材料的极化轴可以是任意方向．利用该有限元模型讨论了楔形切口角度、极化轴方向和边界条件对奇性场的影响．通过和其它特定情况下的现有解相比，证实了该文有限元数值方法的有效性，而且精度很高．

FINITE ELEMENT ANALYSIS OF SINGULAR ELECTRO ELASTIC FIELDS NEAR PIEZOELECTRIC WEDGES

To analyze singular electromechanical fields at a corner of wedge/junction in a piezoelectric media under inplane loading, as the first part of this work, stress equilibrium equations, Maxwell equation and boundary conditions are first employed to derive a new weak form for solving eigenpair problems in piezoelectric materials; then, with the asymptotic exponential assumption along the radial distribution and the bubble mode assumption along the circumferential distribution of the displacement and electric potential in a element around a tip of wedge/junction, a simple one-dimensional finite element formulation is established that only discretize the displacement and electric potential circumferentially. The polarization orientation of piezoelectric materials may be arbitrary. The finite element discretization formulation developed is employed to study numerically singular electroelastic fields near apices of wedges / junctions encountered often in smart structures. The dependences of wedge angle, material type, poling direction, and boundary and interface conditions on the singular behavior the electroelastic fields are examined. The effectiveness and the accuracy of the numerical algorithm are validated by comparing with other existing results in special cases.