Mixed formulation for frictionless contact problems

Abstract

Simple mixed finite element models and a computational precedure are presented for the solution of frictionless contact problems. The analytical formulation is based on a form of Reissner's large rotation theory of the structure 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 element characteristic array 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 the determination of the contact area and the contact pressures.