A NEW TEST ERROR METHOD TO SOLVE THE CONTACT PROBLEMS
求解接触问题的一种新的实验误差法

The control equations of the displacements and the contact force can be obtained when the contact status is given by the test error method. In the paper, a modified UZAWA algorithm with relaxation parameter is introduced to solve the control equations. The method to choose the parameter is as same as the two-point step gradient algorithm. According to the distribution characteristics of the candidate contact boundary, one can divide the domain into different subdoamins. By use of the domain decomposition method, one can divide the subdo-mains by finite element mesh respectively, and use different interpolation functions and different displacement models in different subdomains. In the paper, the conjugate gradient method with a modified incomplete factorization preconditioner is presented to solve the displacement equations of different subdomains. It has been proved that the incomplete factorization will yield a positive definite preconditioner matrix. In addition, the new test error method introduced in the paper is naturally parallel, for example, one can use different slave computers to calculate the element stiffness matrix and to solve the displacement field for different subdomains.