A Nonlinear Shell Theory with Through-The-Thickness Stretch

Abstract

This paper summarizes the important features of a geometrically exact resultant based shell model which incorporates through-the-thickness stretch. The shell is modeled as a single extensible director Cosserat surface where variable thickness and thickness stretch effects are accounted for through the extensibility of the director field. Even though thickness effects are included, the resulting equations are numerically well-conditioned in the thin shell limit and a simple linear elastic constitutive model is given which possesses the correct asymptotic behavior as the thickness tends to zero and identically recovers the plane stress constitutive relations in the thin shell limit. The performance of the theory is demonstrated by two numerical examples.