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Three-dimensional analyses of stress singularities at the vertex of a piezoelectric wedge

机译：压电楔形顶点应力奇异性的三维分析

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摘要

The electroelastic singularities at the vertex of a rectilinearly polarized piezoelectric wedge are investigated using three-dimensional piezoelasticity theory. An eigenfunction expansion approach is combined with a power series solution technique to find the asymptotic solutions at the vertex of the wedge by directly solving the three-dimensional equilibrium and Maxwell's equations in terms of the displacement components and electric potential. This study is the first to address the problems in which the polarization direction of the piezoelectric material is not necessarily either parallel to the normal of the mid-plane of wedge or in the mid-plane. The correctness of the proposed solution is verified by convergence studies and comparison with the published results that are based on generalized plan strain assumption. The solution is further employed to study comprehensively the effect of the direction of polarization on the electroelastic singularities of wedges that contain a single material (PZT-5H), bounded piezo/isotropic elastic materials (PZT-5H/Si), or piezo/piezo materials (PZT-5H/PZT-4).
机译：利用三维压电弹性理论研究了直线极化压电楔形体顶点的电弹性奇点。本征函数展开方法与幂级数解技术相结合，通过直接求解位移分量和电势方面的三维平衡和麦克斯韦方程组，在楔形顶点处找到渐近解。这项研究首次解决了压电材料的极化方向不一定平行于楔形中平面的法线或中平面的问题。通过收敛性研究并与基于广义计划应变假设的已发布结果进行比较，验证了所提出解决方案的正确性。该解决方案还用于全面研究极化方向对包含单一材料（PZT-5H），有界压电/各向同性弹性材料（PZT-5H / Si）或压电/压电体的楔子的电弹性奇异性的影响材料（PZT-5H / PZT-4）。

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