Frictionless contact with BEM using quadratic programming

The contact surface, with its accompanying load transfer, may well constitute the critical factor in a structural member. Thus it is essential to be able to perform contact stress analysis of a component accurately and efficiently. Considerable research effort is represented in the literature for contact analysis using finite elements. To obtain reliable results in the contact zone, it is necessary to provide a very fine discretization in that zone. Many distinct contact zones may exist, which may force the entire domain, and not just the contact zones, to be discretized finely. This generally leads to an excessive number of degrees of freedom (dof), resulting in an uneconomical, and sometimes intractable, analysis. The boundary element method (BEM), which deals with the discretization of only the boundary of the structure being analyzed, may be used to circumvent these difficulties and provide accurate, economical results. While a fine discretization of the contact zone is still unavoidable, the BEM leads to a smaller number of dof's because the rest of the boundary need not have a fine mesh. The problem of frictionless contact between an elastic body and a rigid surface is formulated as an optimization problem. Three distinct functions are defined in terms of the unknown variables (displacements and tractions) corresponding to the contact surface, and expressed as quadratic objective functions that are to be minimized. The solution is obtained using the standard quadratic programming techniques of optimization. A number of example problems with straight and curved contact boundaries were solved. The present formulations were validated through comparison of the test problems with existing alternative solutions.