Steady-State Stresses in a Half-Space Due to Moving Wheel-Type Loads with Finite Contact Patch

In this paper, the steady-state stresses in a homogeneous isotropic half-space under a moving wheel-type load with constant subsonic speed, prescribed on a nite patch on the boundary, are investigated. Navier''s equations of motion in 2D case were modi ed via Stokes-Helmholtz resolution to a system of partial di erential equations. A double Fourier-Laplace transformation procedure was employed to solve the system of partial di erential equations in a new moving reference system, regarding the boundary conditions. The e ects of force transmission from the contact patch to the half-space have been considered in the boundary conditions. Utilizing a property of Laplace transformation leads to transformed steady-states stresses for which inverse Fourier transformation yielded the steady-state stresses. Considering two types of uniform and parabolic force transmission mechanism and a comparison between the pertaining results demonstrated that the parabolic load transmission induce lower stresses than the uniform one. Results of the problem for various speeds of moving loads showed that the stresses increase as the moving loads'' speeds increase to an extremum speed known as CIS. After the CIS speed, stresses'' absolute values decrease for higher speeds. Eventually CIS values for homogeneous half-spaces with di erent material properties were obtained.