Authors: Sebastien Lachance-Barrett and Vincent Prantil Hoop, Axial and Radial Stresses in Thick-Walled Pressure Vessels Created using ANYS 14.0 Problem Specification Consider the following pressurized thick-walled hydraulic cylinder. The following figure shows a section through the mid-plane. Stress directions in cylindrical coordinates: σ hoop is in the circumferential direction (out of the plane here) a = inner radius = 1.5 in b = outer radius = 2 in Assume the cylinders are 18 inches long and the vessel is pressurized to 1000 psi.

Here, we will be interested in finding the hoop, axial and radial stresses at the mid-length of the cylinders (@ 9 inches), to neglect the local effects of the end caps. Compare the finite element results obtained from axisymmetric analysis to those calculated with the theoretical formulae for both thin-wall and thick-wall approximations.

Note: For this problem, the material choice will not affect the stresses; it will only affect the displacements and strains. Learning Goals The purpose of this tutorial is to showcase, in a relatively simple situation, where thin-wall pressure vessel theory is no longer as valid as it is in the limit of large radius-to-thickness ratios. The point is that inadequate theory should not be used for validation purposes in the limit that the physical assumptions on which the theory is based break down. In this problem, this happens gradually as the vessel walls become thicker. This tutorial is meant to highlight where it is relatively straightforward to apply axisymmetric FEA and resolve a solution correctly that disprove analytical treatment with simple formulae derived for thin-walled vessels.

This tutorial is an educational tool designed to assist those who wish to learn how to use the ANSYS finite element software package. It is not intended as a guide for determining suitable modelling methods or strategies for any application. The authors of this tutorial have used their best efforts in preparing the tutorial. These efforts include the development, research and testing of the theories and computational models shown in the tutorial. The authors make no warranty of any kind, expressed or implied, with regard to any text or models contained in this tutorial.

ANSYS - Pressure Vessel; Pressure Vessel. Export to PDF Export to Word. Go to all ANSYS Learning Modules. Design & Stress Analysis of a Cylinder with Closed ends using ANSYS A. Iseki Hydraulic Manual Press on this page. Pressure vessel as in case of steam boilers or it may.

The authors shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of the text and models provided in this tutorial. There is no gaurantee that there are no mistakes or errors in the information provided and the authors assume no responsibility for the use of any of the information contained in this tutorial. In this tutorial you will examine the expansion of a pressure vessel due to an internal pressure using ANSYS.

The problem is adapted from case study E on page 327 of the textbook Practical Stress Analysis with Finite Elements (2nd Ed) by Bryan J. You will determine the principal stresses in the pressure vessel due to the applied loading and boundary conditions. A two-dimensional plane strain element will be used for this analysis. We will use SI system units for this tutorial: length = m, mass = kg, time = sec, force = N, stress/pressure = Pa. In this case the vessel is made from steel (E = 207 Gpa, v = 0.27) and the internal pressure is 10,000 Pa. Figure 1: Details of the Pressure Vessel - all dimensions in mm.

There are standard theories available for the behaviour of thin and thick walled cylinders subjected to internal pressure. These equations can be found in any text book on mechanics of solids or in any reference book. We can use these theories to predict the expected stresses in the pressure vessel due to the applied loading. The calculations for the various stresses is shown on pages 328 to 329 of Practical Stress Analysis with Finite Elements (2nd Ed) by Bryan J. Mac Donald and is summarised in the table below. Figure 2 shows an overview of the plane strain model of the pressure vessel. The model on the left hand side is a full plane strain model of a slice through the pressure vessel.