Analysis of Elastodynamic Problems Based on the Principle of Superposition (Extention of the Body Force Method to Elastodynamic Problems)

In this study, the body force method was extended to the analysis of elastodynamic problems. By inserting the region in question into the adjoint region, it was possible to reduce the given elastodynamic problem to an elastodynamic problem of an infinite body. The general integral formula was obtained based on superposition of the elastodynamic fields of a point force and a discrepancy in the time-space region. Therefore, analysis of the elastodynamic problem was reduced to a calculation of the unknown densities of force or discrepancy distributed along the imaginary boundary. The direct or indirect methods of BEM can be seen as special cases of the general formula proposed in this study. The effectiveness of the method was shown by analyzing an example of the elastodynamic problems of a half space with initial conditions subjected to uniform surface pressure.