Contact algorithm for non-linear elastic problems with large displacementsand friction using the boundary element method

An efficient algorithm of contact is presented for the boundary element ana lysis of the static two-dimensional frictional contact problem between elas tic solids. The algorithm guarantees equilibrium and compatibility at the n odes in the final deformed configuration and it allows us to deal with prob lems undergoing large displacements, with large slipping at the interface a s the mismatching of contact nodes is allowed. The formulation is limited t o elastic behaviour with small strains and a Coulomb's friction law is assu med. The solution procedure, based on the Updated Lagrangian Approach, is i ncremental as the contact problem with friction is history-dependent. At le ast one load increment must be done for each node changing its boundary con ditions during the loading process. Additional increments are necessary to record any relevant modifications of the geometry that might appear. Quadra tic isoparametric boundary elements are used and the contact constraints ar e applied node-on-element, using the shape functions for distributing the g eometry, displacements and tractions on each element at the contact zone. S ome special attention is devoted to the frictional effects related to the t ype of interpolation used. Two representative examples are studied: a cylin der over a flat surface and a layer pressed against half-space. The compute d results, when the displacements are small and friction is not considered, are found to agree well with the analytical solutions. When friction is ta ken into account, no analytical solution is available and the results are c ompared to the numerical solutions obtained by other authors. When in addit ion large displacements appear, the problem becomes highly non-linear and t he most relevant aspects of those non-linearities will be shown in this pap er. (C) 1999 Elsevier Science S.A. All rights reserved.