An efficient approximate solution method for predicting the buckling of axially compressed imperfect cylindrical shells

A theoretical investigation of an efficient numerical solution scheme to solve approximately the nonlinear Donnell equations for imperfect isotropic cylindrical shells with edge restraints and under axial compression was carried out. The nonlinear partial differential equations have been reduced to an equivalent set of nonlinear ordinary differential equations. The resulting two-point boundary value problem was solved, first, by using "Newton's Method of Quasilinearization" to obtain a set of linearized differential equations for the correction terms and, secondly, these differentials were approximated as finite differences to cast the linearized system of equations into the form of a block tridiagonal matrix equation. The Potters' Method solution scheme was used to solve efficiently the block tridiagonal matrix equation. By successive iterations a solution to the set of nonlinear ordinary differential equations was obtained. The use of this method makes it possible to investigate how the axial load level at the limit point is affected by the following factors: the choice of inplane boundary conditions, the prebuckling growth caused by the radial edge constraint, the orientation and shape of the axisymmetric and asymmetric imperfection components, and the finite length of the shell