In this paper the meshless local Petrov-Galerkin (MLPG) method is implemented to study the buckling of isotropic cylindrical shells under axial load. Displacement field equations, based on Donnell and first order shear deformation theory, are taken into consideration. The set of governing equations of motion are numerically solved by the MLPG method in which according to a semi-inverse method, a new variational trial-functional is constructed to derive the stiffness matrices and critical buckling loads are obtained in various boundary conditions.
The moving least squares interpolation is employed to construct both trial and test functions. The present method is a truly meshless method based on a number of randomly located nodes upon which no global background integration mesh is needed and no element matrix assembly is required. In the present MLPG formulation, a local variational form is constructed over a local sub-domain instead of using the conventional weighted-residual procedure. The influences of some commonly used boundary conditions and effects of shell geometrical parameters are studied. The results show the convergence characteristics and accuracy of the mentioned method.