Formulation and Computational Aspects of a Stress Resultant Geometrically Exact Shell Model

Abstract

This paper considers the formulation and numerical implementation of a geometrically exact resultant based shell model for the analysis of large deformations of thin and moderately thick shells. The model is essentially a single extensible director Cosserat surface. Variable thickness and thickness stretch effects are properly modeled via the extensibility condition on the director field. A simple linear elastic constitutive model is given which possesses the correct asymptotic limits as the thickness tends to zero and recovers the plane stress constitutive relations in the thin shell limit. On the computational side, a configuration update procedure for the director field is presented which is singularity free and exact regardless of the magnitude of the director (rotation and thickness stretch) increment. The performance of the shell model is assessed through an extensive set of numerical examples.