Analysis of Short Cylindrical Shell Under Internal Liquid Pressure Using Improved Finite Difference Method

ABSTRACT

This research work presents the static analysis of short cylindrical shell under internal liquid pressure with various boundary conditions and aspect ratios. Improved fourth order finite difference method was employed for the analysis and a MATLAB computer program was developed based on the matrix equations and models generated from the analysis. The following boundary conditions were covered in this research; short circular cylindrical shell simply supported at both edges(s-s), short cylindrical shell clamped at both edges(c-c) and short cylindrical shell clamped at one end and simply supported at the other edge(c-s). General differential equation for axisymmetrically loaded circular cylindrical shell as derived by previous researchers was reviewed. The general equation was combined with improved finite difference patterns developed from the application of Taylors and polynomial series on a computational grid of a short cylindrical shell for finite difference approximation, to develop finite difference equations for short cylindrical shell under internal liquid pressure. The finite different equation developed was used in the formulation of matrix equations which are the solutions for deformations and stresses for different boundary conditions. The deformations and stresses at various points of the short cylindrical shells were determined for cases of aspect ratio ranging from 1 to 4 for all the boundary conditions considered. Also hoop tension was calculated and its value tabulated for references, since it is a very important parameter used in analysis and design of liquid filled short cylindrical tanks. The maximum values of deflection, moment, slope and shear forces were also tabulated for 5, 7, 100, 150 and 200 nodal points. These maximum values were compared with the values obtained from exact method (Pasternaks theory) and found to be approximately the same.