Mixed finite element formulation for frictionless contact problems

Simple mixed finite element models and a computational procedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large-rotation theory with the effects of transverse shear deformation included. The contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the internal forces (stress-resultants), the generalized displacements, and the Lagrange multipliers associated with the contact conditions. The elemental arrays are obtained by using a modified form of the two-field, Hellinger-Reissner mixed variational principle. The internal forces and the Lagrange multipliers are allowed to be discontinuous at interelement boundaries. The Newton-Raphson iterative scheme is used for the solution of the nonlinear algebraic equations, and for the determination of the contact region and the contact pressures.

Two numerical examples, axisymmetric deformations of a hemispherical shell and planar deformations of a circular ring, are presented. Both structures are pressed against a rigid plate. Detailed information about the response of both structures is presented. These examples demonstrate the high accuracy of the mixed models and the effectiveness of the computational procedure developed.