Abstract: An incremental method for contact problems, which are boundary value problems with variable constraints,is presented within the field of linear elasticity with small displacements. It is clarified that in some published papers it is not generally applicable to utilize the total amount variational method to solve the contact problems with friction. Instead, a numerical solution method derived from incremental variational principle is given with the corresponding normal condition of coulomb′s friction. Variable boundary conditions involved in the examples are relatively simple, which include only several discrete points, so the hit and miss method may be used to define the actual state of constraints. The numerical results show the satisfactory accuracy of the algorithm.

Key words: contact, variable constraint, incremental variational principle, normal condition, friction