Approximate Green's functions and a boundary element method for electro-elastic analyses of active materials
Abstract A boundary element method (BEM) for the analysis of two-dimensional, time independent problems of linear electro-elasticity is presented. Emphasis is given to the derivation of representation formulas and fundamental solutions as well as to the construction of an efficient numerical algorithm. The method is particularly suitable for studying the behavior of active materials such as electrostrictive, ferroelectric and piezoelectric ceramics. Two numerical examples with direct impact on the structural safety and reliability of piezoceramics are provided to demonstrate the virtues of the new BEM.
In this paper verification methods for Fredholm integral equations are considered. By these methods the numerical approximation is computed together with mathematically guaranteed error bounds of high quality. The foundations for such numerics is described and then applied to Fredholm integral equations. We conclude by some numerical examples demonstrating the effectiveness of such new numerical schemes.