No abstract

An application of the element-based Lagrangian formulation is described for large-deformation analysis of both single-layered and laminated shells. Natural co-ordinate-based stresses, strains and constitutive equations are used throughout the formulation of the present shell element which o ers signiÿcant implementation advantages compared with the traditional Lagrangian formulation. In order to avoid locking phenomena, an assumed strain method has been employed with judicious selection of the sampling points. Three strictly successive ÿnite rotations are used to represent the current orientation of the shell normal. The equivalent natural constitutive equation is derived using an explicit transformation scheme to consider the multi-layer e ect of laminated structures. The arc-length control method is used to trace complex load-displacement paths. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. ? 1998 John Wiley & Sons, Ltd.KEY WORDS: assumed strain method; element-based Lagrangian formulation; laminated shell; equivalent natural constitutive equation; three successive ÿnite rotations; arc-length control method