Integral Equation Method For Cylindrical Shell Under Axisymmetric Loads

Abstract

This paper is concerned with the development of the integral equation method for the analysis of a cylindrical shell under axisymmetric loads. The governing equations of the shell are traditionally described as a set of two ordinary differential equations with two unknown variables. These equat ions are normalized by eliminating their first derivatives, and then multiplied by a weighting function that is a selected Green's function. Finally, they are repeatedly integrated by parts until their differential operator is shifted from acting on the state variables to the weighting function. Consequently, the differential equations are transformed into a set of integral equations. To complete the analysis procedures, efforts are made to insert various boundary conditions of a shell into the kernels of the integral equations, and to express the internal forces, moments, and displacements of a shell in terms of the state variables. Thus, the integrals are readily available for the analysis of a cylindrical shell. A structure is selected to demonstrate how to apply the method in shell analysis. Three different types of construction are used for the shell; one has a constant thickness, the second has piecewise constant thickness and the third has piecewise linearly varying thickness. The solutions so obtained are compared with the corresponding ones found by the finite element method. They are also compared against the theoretical solutions whenever possible. A good agreement is attained.