Indentation of an elastic half-space by four moving punches

Abstract

Abstract The dynamic and static problems of finding stress component under four moving punches (a ≤ |X| ≤ b, c ≤ |X| ≤ d), located closely to each other over an elastic half-plane (Y = 0), are solved. Employing the Fourier integral transform, the problem is converted to a set of integral equations. Using Hilbert transform technique, the integral equations are solved to obtain the stress and the displacement components. Finally, exact expressions for the stress components under the punches and the normal displacement component in the regions outside the punches have been derived. Numerical results showing the variations in stress intensity factors (SIF) at the punch ends and absolute value of torque applied over the contact regions with different values of the parameters used in the problems have been presented in the form of graphs.