On the Finite Element Solution of Fractional Contact Problems Using Variational Inequalities

This article is devoted to the development and implementation of a variational inequalities approach to treat the general frictional contact problem. Unlike earlier studies which adopt penalty methods, the current investigation uses Quadratic Programming and Lagrange’s multipliers to solve the frictional contact problem and to identify the candidate contact surface. The proposed method avoids the use of user defined penalty parameters, which ultimately govern the convergence and accuracy of the solution. To establish the validity of the method, a number of test cases are examined and compared with existing solutions where penalty methods are employed.