Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches

The object of the paper concerns a consistent formulationof the classical Signorini’s theory regarding the frictionlesscontact problem between two elastic bodies in thehypothesis of small displacements and strains. The employmentof the symmetric Galerkin boundary element method,based on boundary discrete quantities, makes it possible todistinguish two different boundary types, one in contact asthe zone of potential detachment, called the real boundary,the other detached as the zone of potential contact, calledthe virtual boundary. The contact-detachment problem isdecomposed into two sub-problems: one is purely elastic,the other regards the contact condition. Following this methodology,the contact problem, dealtwith using the symmetricboundary element method, is characterized by symmetry andin sign definiteness of the matrix coefficients, thus admittinga unique solution. The solution of the frictionless contact-detachment problem can be obtained: (i) through aniterative analysis by a strategy based on a linear complementarityproblem by using boundary nodal quantities as checkquantities in the zones of potential contact or detachment;(ii) through a quadratic programming problem, based on aboundary min-max principle for elastic solids, expressed interms of nodal relative displacements of the virtual boundaryand nodal forces of the real one.