Error on the constitutive relation in the nonlinear formulation of elastic beams: the plane case Original Research Article

The error measure we propose in this study is based on the mechanics concept of error on the constitutive relation. The error on the constitutive relation has already been used for the updating of elastic structures in dynamics, under the small perturbation assumption. Here, we extend this concept to the context of geometrically nonlinear elastic beams (large rotations and finite strains). It is shown that the proposed strategy, which uses measured experimental data, enables us to locate damaged substructures or, if the quality of the model is to be checked, the method provides the location of the zones of modelling errors. The formulation and its derivation are developed and a complete algorithmic treatment is presented. The implications of the formulation of the errors location discussed in this paper are illustrated through a set of numerical examples.