Mixed finite element method for contact problems with friction and initial gaps

A new iterative method—mixed finite element method,was proposed for contact problems with friction and initial gaps.Based on the characteristic of local nonlinearity for this problem,the system of forces acting on the contactor was divided into two parts: external forces and contact forces.The displacement of contactor was chosen as the basic variable and the nodal contact force in possible contact region was chosen as the iterative variable,so that the nonlinear iteration process was only limited in the possible contact surface.In this way,the sophisticated contact nonlinearity was shown by the variation of the contact forces.Moreover,in the case of multi-body contact problem,the flexibility matrix is symmetric and sparse.Thus the iterative procedure became easily to be carried out and much more economical.Firstly,the mechanical model for three-dimensional contact problems with friction and initial gaps was presented,and its finite element compliance equations were obtained.And then,the iteration process was given in detail.At last,the validity and accuracy of the proposed procedure was demonstrated with two numerical examples.