Geometrically nonlinear FEM analysis of 6‐parameter resultant shell theory based on 2‐D Cosserat constitutive model

Abstract

We develop the elastic constitutive law for the resultant statically and kinematically exact, nonlinear, 6‐parameter shell theory. The Cosserat plane stress equations are integrated through‐the‐ thickness under assumption of the Reissner‐Mindlin kinematics. The resulting constitutive equations for stress resultant and couple resultants are expressed in terms of two micropolar constants: the micropolar modulus and the micropolar characteristic length l. Based on FEM simulations we evaluate their influence on the behaviour of shell models in the geometrically nonlinear range of deformations.