Mechanics of Indentation for an Elastic Half-Space by Punches

The dynamic and static problems of finding stress components under four moving punches (a≤|X|≤b,c≤|X|≤d), located close to each other over an elastic half-plane (Y=0), are solved. Employing the Fourier integral transform, the problem is reduced to a set of integral equations in both cases. Using the Hilbert transform technique, the integral equations are solved to obtain the stress and displacement components. Finally, exact expressions for the stress components under the punches and the normal displacement component in the region outside the punches have been derived. Numerical results showing the variations in stress intensity factors (SIF) at the punch ends, and the 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.