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.
Parlavecchio, E., Salerno, M., & Zito, L. (2011). Frictionless contact formulation by mathematical programming technique. In International Association for Boundary Element Methods (IABEM 2011).
|Autori:||Parlavecchio, E.; Salerno, M.; Zito, L.|
|Titolo:||Frictionless contact formulation by mathematical programming technique|
|Data di creazione:||2011-09-10|
|Nome del convegno:||International Association for Boundary Element Methods (IABEM 2011)|
|Luogo del convegno:||Brescia|
|Anno del convegno:||10-12 Settembre 2012|
|Data di pubblicazione:||2011|
|Numero di pagine:||8|
|Citazione:||Parlavecchio, E., Salerno, M., & Zito, L. (2011). Frictionless contact formulation by mathematical programming technique. In International Association for Boundary Element Methods (IABEM 2011).|
|Tipologia:||0 - Proceedings (TIPOLOGIA NON ATTIVA)|
|Appare nelle tipologie:||0 - Proceedings (TIPOLOGIA NON ATTIVA)|