Abstract: A fundamental solution for half-plane problems which will play a key role in calculation of the stress concentration around a hole embedded in half-plane is derived by a method combining images with direct integrations. It is wore intuitive than the Fourier transform method used by Gladwell[6]. In addition, the principle and procedure of boundary element method to solve the half-plane problems are also presented by means of Betti’s reciprocal theorem in this paper.It is shown that the. computing procedure for half-plane problems is much more convenient using the fundamental solution presented here than the one adopted by C.A.

Key words: elastic tank-liquid coupling system, bifurcation equation, singularity theory, sloshing control