The Deformation of Cylindrical Shells Subjected to Radial Loads Using Mixed Formulation and Analytic Solutions

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 using a mixed formulation. Variational techniques coupled with functional analysis are used to obtain an optimized solution for the shell displacement and further stress field evaluation using a combination of unknown analytic functions with Fourier expansions. A large cylindrical shell subjected to pinching loads is considered. These elements are intended to provide accurate modelling of the initially circular pipes response. Because of this behaviour, the bend's cross-section abandons its original roundness, turning into an oval or noncircular configuration. In addition, the initially plane cross-section, tends to deform out of its own plane. These two deformation patterns are termed ovalization and warping, respectively. In this work the results for the radial displacement and section ovalization are analysed where the solution has six terms for an acceptable accuracy. The transverse displacement presents important dependence on the shell thickness vs radius, where in the case of thin shells the ovalization is restricted to a local area and this is the case analysed. The proposed method leads to accurate results with low complex input data. The conclusions of this work are that the definition 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 as can be seen by a comparison with finite element methods.