Application of the differential quadrature method to the buckling analysis of cylindrical shells and tanks.

Abstract

The newly developed differential quadrature method (DQM) is applied to the problem of linear elastic budding of circular cylindrical shells and tanks. The Flugge theory serves as the basis of the analysis. For the first time the DQM is applied to the buckling problem of cylindrical shells and also for the first time the 2-dimensional DQM with two different test functions (polynomial and harmonic test functions) is applied to the structural mechanics problems with circumferential continuity. As well for the first time the nonsymmetrical form of the buckling equations is derived based on the Flugge theory and used for analyzing nonsymmetric buckling problem of tanks under quasi static earthquake loading. Both the 1-dimensional and 2-dimensional DQM are used. In the 1-dimensional part, the fields (U, V, W) are expressed as products of unknown functions along the axial direction and known trigonometric functions along the circumferential direction. In the 2-dimensional part, the displacement fields are represented by unknown functions in two directions. The derivatives in both the governing equations and the boundary conditions are discretized by the DQM. In this process the governing differential equations and boundary conditions are transformed into a set of algebraic equations, the eigenvalues of which are the buckling loads of the shell or the tank. In the 2-dimensional part, shells under single and combined loads are considered. The latter load represents the tanks containing liquid under quasistatic earthquake loading. The accuracy and efficiency of the DQM is examined by comparing the results with those in the literature. The results of 1-dimensional DQM are in good agreement with the work of other researchers. In the 2-dimensional problems, while an overall convergence is observed, in some cases a complete convergence is not obtained. The size of the matrices in the 2-dimensional DQM is an order of magnitude larger than those in one dimension, yet good results have been found for tanks under earthquake loading in the last part where more accurate equations and boundary conditions are used. The results show that the application of DQM to the tank and shell problems a successful.