Recent Achievements in Constitutive Equations of Laminates and Functionally Graded Structures Formulated in the Resultant Nonlinear Shell Theory

The development of constitutive equations formulated in the resultant nonlinear shell theory is presented. The specific features of the present shell theory are drilling rotation naturally included in the formulation and asymmetric measures of strains and stress resultants. The special attention in the chapter is given to recent achievements: progressive failure analysis of laminated shells and elastoplastic constitutive relation for shells made of functionally graded material (FGM). The modified Hashin criterion is used to estimate failure initiation in laminates and stiffness degradation approach in the last ply failure computations. The numerical results obtained for axially compressed C-shaped column are compared with experimental load-deflection curve. The Cosserat plane stress assumption, Tamura-Tomota-Ozawa (TTO)model and improved method of shear correction factor calculation are applied in the elastoplastic constitutive relation for FGM shell. The proposed formulation is tested in numerical examples: rectangular compressed plate and channel section clamped beam. The influence of TTO model parameters and Cosserat characteristic length is investigated.