Mathematics - Colloquium
Friday, April 19, 2013
11:00 AM-12:00 PM
ABSTRACT: This work has been made in collaboration with Philippe G. Ciarlet of City University of Hong Kong. We study the Kirchhoff-Love model of nonlinearly elastic plates and we adopt an "intrinsic" approach by considering as the main unknowns (instead of the deformation itself) two 2x2 symmetric matrix fields derived from the deformation of a plate subjected to some volume forces. This approach allows us to describe the set of admissible forces for the pure traction problem, i.e. to find the necessary conditions that the forces must satisfy in order to have existence of a minimizer for the associated energy functional. The key role is played here by the rigidity properties of the new intrinsic unknowns. We also establish necessary and sufficient nonlinear compatibility conditions of Saint-Venant type for these unknowns. More precisely, these conditions ensure that two symmetric matrix fields satisfying them derive from a deformation.
Suggested Audiences: College, Adult
Last Modified: March 25, 2013 at 10:35 AM