Frictionless contact formulation by mathematical programming technique

The object of the paper concerns a consistent formulation of the classical Signorini's theoryregarding the frictionless unilateral contact problem between two elastic bodies in the hypothesis ofsmall displacements and strains. A variational approach, employed within the symmetric BoundaryElement Method, leads to an algebraic formulation based on nodal quantities. The contact problemis decomposed into two sub-problems: one is purely elastic, and the other pertains to the unilateralcontact condition alone. Following this methodology, the contact problem, faced with symmetricBEM, is characterized by symmetry and sign definiteness of the coefficient matrix, thus admitting aunique solution.The solution of the frictionless unilateral contact problem can be obtained- through a step-by-step analysis utilizing generalized quantities as check elements in the zones ofpotential contact or detachment. Indeed, the detachment or the contact phenomenon may happenwhen the weighted traction or the weighted displacement is greater than the weighted cohesionor weighted minimum reference gap, respectively;- through a quadratic programming problem based on the minimum of the total potential energy.In the example, given in the paper, the detachment phenomenon is considered and somecomparisons of the solution between the step-by-step analysis and the direct approach which utilizesthe quadratic programming will be shown.