This paper presents a refined higher-order shear deformation theory for the geometrically nonlinear analysis of layered composite structures. The theory allows parabolic description of the transverse shear stresses and therefore the shear correction factors of the usual shear deformation theory are not required. The theory accounts for small strains but moderately large displacements (i.e., von Karman strains). A shell finite element with a variable number of nodes, from 4- to 9-nodes,has been derived in this work. A 9-node quadrilateral Lagrange finite element was used as the basic one, while a 4-node one was formulated on the basis of discrete Kirchhoff 's theory, which ensures C¹ continuity at discrete points on element boundaries. The formulation of this element was made in the domain of linear and geometrically nonlinear behaviour, including a critical or postcritical analysis. A resonable agreement between numerical results and experiments suggest a rational method for nonlinear analysis and predicting failure loads of complex aircraft and civil composite structures.

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