Development of Geometrically Non-linear Formulation for the Analysis of Laminated Shells using Finite Elements

Abstract

Shell structures now days are widely used in constructing hall roofs with long spans, concrete roofs, pipe lines (gas and oil) and large water tanks. So the analysis of theses shell structures become of great interest for designing purposes. For this research lamination technique is adopted as one of the well known type of composite material. This research presents a finite element concept for geometrically linear and nonlinear analysis of laminated shell structures. Only static analysis is performed. At the beginning the theory of linear analysis is presented and then extended to include geometrically nonlinear analysis for large rotations and large displacements. The finite element formulation employed the 8-node degenerated curved shell element of (parabolic) shape. The element has five degrees of freedom per node, (three global translations X, Y & Z and two rotations α and β). Shear locking as one of the famous problem facing the application finite element method is discussed and some solutions are suggested. The nonlinear finite element formulation is based on Total Lagrangian approach using both Green and Geometric strains. The nonlinear equilibrium equations are solved using the Incremental and Newton-Raphson Method. Different seven numerical examples are performed to obtain the geometrically linear and nonlinear behaviour of laminated shell structures. The structures analysed are flat plate, cylindrical shell and spherical shell for different applied load types and various boundary condition. A FORTRAN computer programs are developed and implemented to analyse some laminated shell structures. Results obtained using Green’s strain is compared with those obtained when using Geometric strain. Good agreement was observed between the results obtained by the present formulation and those available in the literature.