Asymptotic solutions of axisymmetric laminated conical shells

Abstract

The three-dimensional (3D) solution of laminated conical shells subjected to axisymmetric loads is presented using the method of perturbation. The formulation begins with the basic 3D elasticity equations without making any static or kinematic assumptions in advance. After introducing a set of proper dimensionless variables, asymptotically expanding the field variables and then successively integrating the resulting equations through the thickness direction, we obtain the recursive sets of governing equations for various orders. The edge boundary conditions at each order level are derived as the resultant forms by following the variational approach. The method of differential quadrature (DQ) is used to determine the present asymptotic solution for various orders. For illustration purposes, the simply supported laminated conical shells under uniformly and sinusoidally distributed lateral pressure and the clamped laminated conical shells under edge torsion, are studied. It is shown that the present asymptotic DQ solution can be obtained order-by-order in a hierarchic and consistent manner and asymptotically approaches to the 3D elasticity solution.