BOUNDARY-VALUE PROBLEMS OF THE ELASTIC HALF-PLANE

In this investigation we employ a combination of complex potential and Fourier integral methods to solve problems of generalized plane stress of semi-infinite plates with one straight boundary. In the first part of this paper relations between the complex potentials Ω(z), ω(z) are obtained suitable for giving any desired conditions of stress or displacement along the real axis, thus reducing problems of the half-plane y ≥ 0 to the determination of the single potential function Ω(z). A simple method is given of obtaining Ω(z) from specified conditions along the real axis and at infinity. The method is applied to the solution of problems of the half-plane y ≥ 0 in equilibrium with specified stresses or displacements along the straight boundary and balancing stresses at infinity and to the problem of the half-plane subjected to an interior force and with the straight boundary free from displacement.