General Discussion and Conclusions

Abstract

The present work describes a way to transform domain integrals into boundary integrals in boundary element formulations. The transformation is presented for both potential and elasticity problems with detailed treatments of how they can be implemented numerically. The results tested term by term demonstrate the accuracy of this method. The transformation formulae are proved to be reliable using the numerical methods and the programs developed in this work. For the case of arbitrary source or Body force functions, the solutions obtained by the transformation technique are sufficiently accurate provided that enough number of terms are taken in the Fourier series. The examples presented demonstrate that this type of transformation technique is feasible for applications to Poisson’s or elasticity type problems including cases with arbitrary source or body force functions. The numerical solutions are accurate for engineering problems when a relatively low number of terms of Fourier series is taken. Therefore the transformation technique is also efficient in computer time.