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Based on the mathematical-physical model of pavement mechanics, a multilayerelastic system with interlayer friction conditions is constructed. Given thecomplex boundary conditions, the corresponding variational inequalities of thepartial differential equations are derived, so that the problem can be analyzedunder the variational framework. First, the existence and uniqueness of thesolution of the variational inequality is proved; then the approximation errorof the numerical solution based on the finite element method is analyzed, andwhen the finite element space satisfies certain approximation conditions, theconvergence of the numerical solution is proved; finally, in the trivial finiteelement space, the convergence order of the numerical solution is derived. Theabove conclusions provide basic theoretical support for solving thedisplacement-strain problem of multilayer elastic systems under the frameworkof variational inequalities.

Variational inequalities of multilayer elastic systems with interlayer  friction: existence and uniqueness of solution and convergence of numerical  solution