Derivation of an evolution model for nonlinearly elastic beams by asymptotic expansion methods

Abstract

The asymptotic expansion method has been shown to be a powerful tool in order to mathematically justify well-known mechanical models and obtain new ones. In this paper we justify the classical semi-linear evolution equation for the bending of an elastic beam submitted to axial forces at both ends. In addition to a theoretical study of this limit model, in the last section, we obtain a generalization of this model for more complete situations.