Analyses of piezoelectric plates with elliptical notches by special finite element

A novel special finite element with an elliptical notch, based on the complex potential theory and hybrid variational principle, is proposed for mechanical-electrical coupling analyses of piezoelectric plates with notches. The formulations are given and a variety of examples are analyzed. Comparisons are made with existing analytical or numerical data. It is shown that the proposed element is very efficient and accurate. Some new numerical results are given and discussed. It is found, perhaps for the first time according to the authors' knowledge, that the relationships between the logarithm concentration factor of tangential (θ=0) stress, electrical displacement, and electrical field at the notch tip and logarithm b/a are linear. Some conclusions are drawn based on the results reported herein.