A SOLUTION METHOD FOR PLANAR AND AXISYMMETRIC CONTACT PROBLEMS

SUMMARY A solution procedure for the analysis of planar and axisymmetric contact problems involving sticking, frictional sliding and separation under large deformations is presented. The contact conditions are imposed using the total potential of the contact forces with the geometric compatibility conditions, which leads to contact system matrices and force vectors. Some key aspects of the procedure arc the contact matrices, the use of distributed tractions on the contact segments for deciding whether a node is sticking, sliding or releasing and the evaluation of the nodal point contact forces. The solutions to various sample problems are presented to demonstrate the applicability of the algorithm. Much progress has been made during recent years in the development of computational capabilities for general analysis of certain nonlinear effects in solids and structures. In each of these developments, quite naturally, the first step was the demonstration of some ideas and possibilities for the analyses under consideration, and then the research and development for reliable and general techniques was undertaken. The second step proved in many cases much more difficult, and in the case of capabilities for analysis of contact problems has yielded few general results. Although some of the first complex contact problems have been solved using the finite element method quite some time ago,'- and much interest exists in the research and solution of contact problems (see, for example, References 4-1 5), there is still a great deaiwf effort necessary for the development of a reliable, general and cost-effective algorithm for the practical analysis of such problems. This is largely due to the fact that the analysis of contact problems is computationally extremely difficult, even for the simplest constitutive relations used. Much of the difficulty lies in that the boundary conditions of the bodies under consideration are not known prior to the analysis, but they depend on the solution variables. The aim in our research is the development of a solution algorithm for analysis of general contact conditions which shall include the possibilities to analyse: contact between flexible-flexible and rigid--flexible bodies; sticking or sliding conditions (with or without friction); large relative motions between bodies; repeated contact and separation between the bodies. Since the large deformation motion of the individual bodies can in many cases be analysed already quite effectively,'6 an algorithm of the above nature will certainly enlarge, very