Nonlinear analysis of doubly curved shells: An analytical approach

Abstract

Dynamic analogues of von Karman-Donnell type shell equations for doubly curved, thin isotropic shells in rectangular planform are formulated and expressed in displacement components. These nonlinear partial differential equations of motion are linearized by using a quadratic extrapolation technique. The spatial and temporal discretization of differential equations have been carried out by finite-degree Chebyshev polynomials and implicit Houbolt time-marching techniques respectively. Multiple regression based on the least square error norm is employed to eliminate the incompatibility generated due to spatial discretization (equations > unknowns). Spatial convergence study revealed that nine term expansion of each displacement in x and y respectively, is sufficient to yield fairly accurate results. Clamped and simply supported immovable doubly curved shallow shells are analysed. Results have been compared with those obtained by other numerical methods. Considering uniformly distributed normal loading, the results of static and dynamic analyses are presented.