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The use of static reduction in the finite element solution of two-dimensional frictional contact problems

In this paper, detailed instructions are given for performing static reduction on a finite element description of an elastic contact problem, thus reducing the dimensionality of the problem to the set of contact nodes alone. This significantly reduces the computational time for the solution to evolutionary contact problems and also gives the user greater control over the detailed implementation of the contact and friction laws. The reduced stiffness matrix is also an essential ingredient in the determination of the critical coefficient of friction for the problem to be well posed, and it facilitates the determination of the conditions under which a frictional system may shake down under periodic loading.