Formula omitted]-matrix formulation applied to the Hertz contact problem with finite friction

Abstract

In this paper, we are concerned with coupled Volterra integral equations for rigid bodies in the frame of the Hertz contact model. Considering an appropriate integral operator as the variable of the matrix polynomial, a λ-matrix corresponding to the Hertz model is determined. Knowledge of the Smith decomposition forms of the λ-matrices enables us to characterize a single integral equation which recovers the normal stress as well as the compliance factor. The presented model shows a reliable behavior and an acceptable accuracy of the λ-matrix approach in comparison to the recent results in the literature.