Frictionless contact of elastic bodies by finite element method and mathematical programming technique
Résumé
The work presents an analysis of the contact problems between elastic bodies without friction. Extended variational principles in the contact problems constitute the theoretical foundations of the analysis. In fact, kinematically admissible displacement fields are subjected to the non-interpenetration conditions so that the contact problem being equivalent to a minimization of the potential energy with contraints on the displacements may be reduced to a particular case of the mathematical programming techniques. Applications are limited to plane state of stress or strain cases where small deformations are considered. The geometrical space is discretized into finite elements, namely the 12 degree of freedom hybrid triangles or the 16 degrees of freedom isoparametric bi-linear quadrangle elements. A special procedure of linearization is adopted to use the quadratic programming algorithm already prepared for large scale problems.
In these conditions, a computer program has been written in FORTRAN IV H and the results obtained from this present good agreement comparing to analytical solutions or other numerical solution in the literature. Finally, theoretical efforts have been performed to generalize the method by introducing a concept of fictitious locked material which represents the assumed contact space between the two bodies.
A general and new condition of non-interpenetration is proposed for general cases of two elastic solids in contact.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...