A Boundary Element Method for the Analysis of Thin Piezoelectric Solids

Piezoelectric films or coatings are applied widely as sensors and actuators in smart materials and micro-electro-mechanical systems (MEMS). Analysis of these delicate thin piezoelectric solids are very important for the design and evaluations of such advanced materials. In this thesis, based on the conventional boundary integral equation (CBIE) formulation for piezoelectricity, an efficient, reliable, convenient and consistent boundary element method (BEM) is developed for the analysis of two dimensional (2-D) thin piezoelectric solids with any small thickness. An efficient analytical method is developed to deal with the nearly-singular integrals in the CBIE for 2-D thin structures. The nearly-singular integrals, which are line integrals for 2-D problems and arise when two boundary curves are close to each other, are transformed into summations of integrals containing fractions of polynomials. For the test problems studied, very promising results are obtained with the thickness-to-length ratios in the order of 6 10 , which is sufficient for modeling most thin piezoelectric films and coatings in the micro-scale, as applied in smart materials and MEMS.