C1 plate and shell finite elements for geometrically nonlinear analysis of multilayered structures

The aim of this work is to analyze the geometrically nonlinear mechanical behaviour of multilayered structures by a high order plate/shell finite element in order to predict displacements and stresses of such composite structures for design applications. Based on a conforming finite element method, a C1 triangular six node finite element is developed using trigonometric functions for the transverse shear stresses. The geometric nonlinearity is based on von-Karmann assumptions and only five generalized displacements are used to ensure:
• a cosine distribution for the transverse shear stresses with respect to the thickness co-ordinate, avoiding shear correction factors;
• the continuity conditions between layers of the laminate for both displacements and transverse shear stresses;
• the satisfaction of the boundary conditions at the top and bottom surfaces of the shells.