A Fast Fourier-Boundary Element Method for axisymmetric potential and elasticity problems with arbitrary boundary conditions

Abstract

This paper presents a new methodology, based on the Fast Fourier Transform (FFT), to solve axisymmetric potential and elasticity problems with arbitrary (non-axisymmetric) boundary conditions using the Boundary Element Method (BEM). The proposed technique is highly effective in cases where a large number of harmonics is required. The new feature concerns the efficient and reliable computation of the axisymmetric fundamental solutions. The methodology is applicable to any type of boundary elements, either continuous or discontinuous, for both direct and indirect BEM formulations. Numerical results are presented for constant boundary elements for typical potential and elasticity problems. Although the method is presented for static problems, it is general and can be applied to a wider class of boundary value axisymmetric problems, such as acoustics and elastodynamics in the frequency or the time domain.