The deformation of cylindrical shells subjected to radial loads - Madureira, M.L.R. (2010)
Cylindrical shells have a simple geometry and application in pressure vessels and piping engineering. The development of calculation algorithms in structural project is impelled by a constant challenge in the search of more accurate and fast design tools in engineering. The objective of this work is to contribute with a simple and reliable numerical tool for the stress analysis of cylindrical vessels subjected to generalized forces. A hybrid formulation in the definition of forces and displacements is proposed for cylindrical shells subjected to radial loads. Variational techniques coupled with functional analysis are used to obtain an optimized solution for the shell displacement and further stress field evaluation. As it is not possible to obtain exact solutions for the displacements or deformation field whenever the external loads are either concentrate or locally distributed, the solution here proposed deals with the combination of unknown analytic functions combined with Fourier expansions, where the former depend on the axial shell coordinate and the trigonometric terms are dependent upon the cylinder circumferential polar angle. These functions are expanded in Fourier series where displacement amplitudes are combined with trigonometric terms. The result is a system of ordinary differential equations where the solution is analytic after evaluation of eigenvalues and eigenvectors. The boundary conditions are then used to reach the final solution. As an example a large cylindrical shell subjected to pinching loads is considered. The results for the radial displacement and section ovalization are analyzed where the solution was obtained with three terms (nq=6) for the accuracy is acceptable in this case. The transverse displacement presents important dependence on the shell thickness vs radius, as the shell can be a thin-walled one (this case is included in the presented example) up to a moderately thick one, where the surface displacement ranges until the extreme edges, which is not the case analyzed. The proposed method leads to accurate results with a relatively low complexity input data. For conclusions of this work it is remarked that the definitions of the load system and boundary conditions are easily processed as the method has pre-defined possibilities for each load case or edge boundary conditions. An analytic solution is obtained and a low number of terms in the Fourier series show good accuracy. A comparison with finite element methods is presented.