Green´s function for an elastic half space with a semi-cylindrical hill impacted by an out-plane linear source load

Based on the fundamental solution for a complete elastic space impacted by an out-plane harmonic linear source load, the Green´s function is obtained, which is the fundamental solution of displacement field for an elastic half space with a semi-cylindrical hill under an out-plane harmonic linear source load at an arbitrary point basal body. According to the idea ¿division¿, the whole model is divided, Part I is a circular domain including the boundary of the hill, and all the rest can be considered as Part II. The disturbance impacted by the out-plane harmonic linear source load can be considered as the incident wave, and the corresponding wave function can be constructed in two domains respectively. Considering the conditions of common boundary, the Green´s function suitable for the problem can be obtained. At last, the limitation of the Green´s function solved in the paper is discussed.