Frictional Contact Problems Involving Large Displacements Using B.E.M.

Abstract

A new algorithm is presented for the boundary element analysis of the static two-dimensional contact problem between elastic solids. The contact constraints are not applied node-on-node (node-pairs technique) but node-on-element, using quadratic shape functions for distributing the geometry, displacements and tractions on each element at the contact zone. Thus, the discretizations performed along the two surfaces in contact do not have to be the same. The solution procedure is based on the updated lagrangian approach and the resulting method is incremental. At least one increment of load must be done for each node changing its boundary condition, the geometry being updated after each increment Additional updatings must be done in order to notice any significant changes of the geometry that might occur during the loading process. The algorithm guarantees equilibrium and compatibility at the nodes in the final deformed configuration and allows us to deal with problems undergoing large displacements, with large slipping at the interface, without being necessary to change the initial discretization of the boundary of the bodies. The formulation is limited to elastic behaviour and a Coulomb friction law is assumed. Some special attention is devoted to the friction effects related with the type of interpolation used. One example is presented in order to check the validity and to show the applicability of the proposed algorithm. The results obtained, when the displacements are small, are in good agreement with the solutions obtained by other authors. When large displacements are considered, another non-linearity appears and its influence is going to be shown.