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Abstract
Piezoelectric materials (PEM) are extensively used in modern technology to convert mechanical energy into electrical energy and vice versa. The importance of this unique characteristic is reflected in the growing number of cutting edge technologies using these materials in such industries as electronic packaging, medical instrumentation, automotive, aerospace and energy distribution.
In most of these applications the electrical and mechanical reliability of structures and devices has become a major concern. Indeed, severe loading conditions and the unavoidable presence of defects due to manufacturing processes have increased the likelihood of damage or failure of piezoelectric-based devices and structures. As a consequence, many researchers have been developing theoretical and experimental techniques to better understand the behavior of PEM under severe loading conditions. However, very few boundary value problems have been analyzed in closed form due to the inherent mathematical complexities resulting from material anisotropy and strong electro-elastic interactions. Thus the need for efficient computational techniques.
The present work introduces the boundary element method (BEM) as one computational alternative to address piezoelectric problems. In the process, we have derived new representation formulas, fundamental solutions (Green's functions) and boundary integral equations within the framework of two-dimensional electro-elastostatics. The mathematical developments have been implemented in a numerical algorithm which is tested for the solution of several boundary value problems of crucial importance in technology. The results show the excellent accuracy of the method and its economic features in terms of computer memory allocation and computational time.
