Fourier expansion based particular integral approach for non-boundary loadings in boundary-element method

The analysis of loads applied within the domain of a body cannot presently be done with the boundary-element method using a boundary-only discretization. Such load cases include patch loads applied over a part of the domain of the object, point loads and line loads. A treatment for such load cases is presented in this paper. The object being considered is embedded in a finite domain and the applied loading is first expressed in terms of a Fourier series expansion. The particular integral solution for the governing differential equation is next obtained at the boundary nodal points for the series expansion loading. These particular integrals at the boundary nodes completely represent the effect of the applied loading and contribute an addition to the 'force vector' in the standard boundary-element equations.