| A finite element suitable for the nonlinear analysis of thin laminated shells is developed from three dimensional continuum theory through the use of assumptions associated with thin shell theory.; Accordingly, straight lines perpendicular to the undeformed reference surface are assumed to remain straight and unextended, but not necessarily perpendicular to the deformed reference surface in the deformed state (The Mindlin assumption). Thus, transverse normal strains are precluded, but transverse shearing strains are permitted. Because small strain theory is invoked, volume and area change due to deformation are considered negligible, but large displacements and rotations are permitted. Additionally, nonlinear contribution to curvature changes are discarded, and in-plane stresses and strains are assumed to vary linearly through the thickness, while transverse trains are uniform through the thickness.; Isoparametric thin shell finite elements are used to discretize the continuum. Integration through the thickness of the isoparametric element is accomplished on the basis of the thin shell assumptions described effectively reducing the inherently three dimensional problem to a two dimensional one. Because of the Mindlin assumption a C{dollar}sp0{dollar} continuous shell element was developed.; A Fortran 77 computer program was developed to test the efficacy of the new element. The nonlinear computational capacity of this program uses the Crisfield arc length procedure, displacement control procedure, and work control procedure as predictors and either the Newton-Raphson or the modified Newton-Raphson iterative procedure as a corrector. This predictor-corrector combination permits equilibrium path to be generated beyond limit points.; The numerical verification of the formulated element was performed in two stages. In the first stage several linear problems were solved to observe the behavior of the element for convergence, locking, and distortion sensitivity. In the next stage various nonlinear problems were considered. The large deflection and rotation capability was tested by the bending elastica and a cylindrical panel with a transverse concentrated load at the center. Nonlinear buckling capability was tested on plates and cylindrical panels with initial imperfections, finally several test problems involving orthotropic material cases were solved. |
