6533b85bfe1ef96bd12ba566

RESEARCH PRODUCT

Frictionless contact formulation by mathematical programming technique

subject

description

The object of the paper concerns a consistent formulation of the classical Signorini's theory regarding the frictionless unilateral contact problem between two elastic bodies in the hypothesis of small displacements and strains. A variational approach, employed within the symmetric Boundary Element Method, leads to an algebraic formulation based on nodal quantities. The contact problem is decomposed into two sub-problems: one is purely elastic, and the other pertains to the unilateral contact condition alone. Following this methodology, the contact problem, faced with symmetric BEM, is characterized by symmetry and sign definiteness of the coefficient matrix, thus admitting a unique 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 of potential contact or detachment. Indeed, the detachment or the contact phenomenon may happen when the weighted traction or the weighted displacement is greater than the weighted cohesion or 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 some comparisons of the solution between the step-by-step analysis and the direct approach which utilizes the quadratic programming will be shown.