The object of the paper concerns a consistent formulationudof the classical Signorini’s theory regarding the frictionlessudcontact problem between two elastic bodies in theudhypothesis of small displacements and strains. The employmentudof the symmetric Galerkin boundary element method,udbased on boundary discrete quantities, makes it possible touddistinguish two different boundary types, one in contact asudthe zone of potential detachment, called the real boundary,udthe other detached as the zone of potential contact, calledudthe virtual boundary. The contact-detachment problem isuddecomposed into two sub-problems: one is purely elastic,udthe other regards the contact condition. Following this methodology,udthe contact problem, dealtwith using the symmetricudboundary element method, is characterized by symmetry andudin sign definiteness of the matrix coefficients, thus admittinguda unique solution. The solution of the frictionless contact-uddetachment problem can be obtained: (i) through anuditerative analysis by a strategy based on a linear complementarityudproblem by using boundary nodal quantities as checkudquantities in the zones of potential contact or detachment;ud(ii) through a quadratic programming problem, based on audboundary min-max principle for elastic solids, expressed inudterms of nodal relative displacements of the virtual boundaryudand nodal forces of the real one.
展开▼
