Computation of the stresses in a moving reference system in a half-space due to a traversing time-varying concentrated load

Abstract

An analytical approach is employed to investigate the transient and steady-state stresses in an isotropic, homogeneous half-space subjected to moving concentrated loads with subsonic speeds. Applying the Stokes–Helmholtz resolution to the Navier’s equation of motion for the half-space results in a system of wavetype partial differential equations. Based on the new moving coordinate system, a modified system of partial differential equations is obtained. Applying a concurrent two-sided and one-sided Laplace transformation, this system is modified to a system of ordinary differential equations, the solutions of which are obtained with respect to boundary conditions. The transformed transient stresses can be inverted by the Cagniard–de Hoop method. Special properties of Laplace transformation yield the steady-state stresses through an analytical approach. Numerical examples are presented to illustrate the methodology. Final results revealed the importance of considering the stresses related to the initial stages of the loading.