Buckling of cylindrical shell panels: a MAEM solution

摘要

The meshless analog equation method, a purely mesh-free method, is applied to the buckling analysis of cylindrical shell panels. The method is based on the principle of the analog equation, which converts the three governing partial differential equations in terms of displacements into three uncoupled substitute equations, two Poisson's equations and one plate equation, under fictitious sources. The fictitious sources are represented by series of radial basis functions (RBFs) of multiquadric type, and the substitute equations are integrated. This integration allows the representation of the sought solution by new RBFs, which approximate accurately not only the displacements but also their derivatives involved in the governing equations. Then, by inserting the approximate solution in the original differential equations and the associated boundary conditions and collocating at a predefined set of mesh-free nodal points, a linear algebraic eigenvalue problem results, the solution of which gives the buckling loads and modes. The optimal value of the shape parameter of the RBFs is obtained as that minimizing eigenvalues. The method is illustrated by analyzing several shell panels. The studied examples demonstrate the efficiency and the accuracy of the presented method.