A direct method for deriving a fundamental solution of half-plane problems (Q1096467)

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 more intuitive than the Fourier transform method used by \textit{G. M. L. Gladwell} [Contact problems in the classical theory of elasticity (1980; Zbl 0431.73094)]. 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. It is shown that the computing procedure for half-plane is much more convenient using the fundamental solution presented here than the one adopted by \textit{C. A. Brebbia} [The boundary element method for engineers (1978; Zbl 0414.65060)].