摘 要

本文利用傅立葉轉換以及映射法來獲得由壓電材料所組成之全無窮域、半無窮域、雙異質以及單層平行域受點載荷作用下之反平面問題的理論解析解。施加之點載荷包含機械載荷如集中力與螺旋差排以及電載荷如點電荷與電壓，而所得到的理論解析解則包含壓電材料的位移場、應力場、電位移場與電場等，藉由理論解析解可以明白不同的邊界條件對於這些物理場的影響。最後將所得到的理論解析解配合實際的壓電材料係數將這些物理場繪製成圖形，除了可以驗證解函數的正確性之外，也可以用來了解壓電材料內物理場的分布特性。

關鍵詞：壓電材料、反平面問題、映射法

Abstract

Analytical solutions to the antiplane problem of the piezoelectric body subject to a point loading are obtained by Fourier transformation and image method in the study. The geometric configuration of the piezoelectric body includes infinite plane, half-plane, bimaterial, and single layer. The point loading consists of the antiplane shear force, screw dislocation, concentrated charge, and voltage. Based on these analytical solutions, the influence of boundary conditions on the field of displacement, stress, electric displacement, and electricity will be discussed. The numerical calculation with practical piezoelectric ceramics will be presented in figures in the paper. These figures will be used to verify the correctness of analytical solutions obtained in the study and explain the distribution of physical fields for the piezoelectric ceramics.

Keywords: Piezoelectric Body, Antiplane Problem, Image Method