Frctionless contact: step by step analysis and mathematical programming technique

The object of the paper concerns a consistent formulation of the classical Signorini'stheory regarding the frictionless unilateral contact problem between two elastic bodies in thehypothesis of small displacements and strains. A variational approach employed in conjunctionwith the Symmetric Boundary Element Method (SBEM) leads to an algebraic formulation basedon generalized quantities [1]. The contact problem is decomposed into two sub-problems: one ispurely elastic, the other pertains to the unilateral contact conditions alone [2,3]. Following thismethodology, the contact problem, by symmetric BEM, is characterized by symmetry and signdefiniteness of the coefficient matrix, thus admitting a unique solution.The solution of the frictionless unilateral contact problem has been obtained:• by means of a quadratic programming problem [2], as optimization problem developed interms of discrete variables, by using Karnak.sGbem code [4] coupled with MatLab.• through a step by step analysis by using nodal quantities as the check elements. Indeed thedetachment or contact phenomenon occurs when the traction or the displacement is greaterthan the cohesion or reference gap, respectively [3].The innovative approach is given meanly by the only boundary discretization by using the SBEMapproach, by the elastic relation written for each bem-e involving the only quantities of the contact zone.In the examples some comparisons of the two strategies will be shown.