  With the development of multi-layer elastic systems in the field of
engineering mechanics, the corresponding variational inequality theory and
algorithm design have received more attention and research. In this study, a
class of equivalent saddle point problems with interlayer Tresca friction
conditions and the mixed finite element method are proposed and analyzed. Then,
the convergence of the numerical solution of the mixed finite element method is
theoretically proven, and the corresponding algebraic dual algorithm is given.
Finally, through numerical experiments, the mixed finite element method is not
only compared with the layer decomposition method, but also its convergence
relationship with respect to the spatial discretization parameter $H$ is
verified.
