Axisymmetric Thin Shell Analyses With Reduced Degrees-of-Freedom

The formulation of a simple but effective unidimensional isoparametric displacement-based thin axisymmetric element is presented. The geometry is approximated by using cubic interpolation functions along the shell midsurface generatrix line and the element displacement field is represented by two spatial translation degrees-of-freedom only. The element kinematics incorporates membrane and bending strain components with the assumption of zero transverse shear deformations in the longitudinal and circumferential directions of the shell. This condition allows formulation of the element without using rotation as an independent degree-of-freedom, but continuity conditions between elements should be properly accounted for. The interaction effects between two adjoining elements or between an element and a rigid flange are modeled by using a penalty procedure to enforce continuity on the derivatives in the element midsurface radial displacements. The element formulation has been implemented and the results of various sample analyses are given to illustrate its effectiveness.