Preface

In the following case study, a mathematical analysis is made of nonmonotonic behaviour observed in the nondestructive testing of fibre-reinforced pressure vessels by the measurement of acoustic emissions. Although the pressure vessels are subjected to plastic deformation during their manufacture, it was possible to predict nonmonotonic behaviour using linear elasticity for the metal liners and a simple “tension band” model for the fibre wrapping. Not only was the qualitative behaviour predicted, but the mathematical model also gave quantitative results which compared well with experimental results.

Much of the algebraic manipulative work involved in the solution was carried out using the computer algebra software Maple. Familiarity with any one of the several such software packages is highly recommended for any mathematical modeler.

The problem considered was presented by Powertech Labs at the first Study Group with Industry meeting held in Canada under the sponsorship of the Pacific Institute of the Mathematical Sciences. The meeting took place in Vancouver at the University of British Columbia in 1997. Thanks are due to Dr A. Akhtar of Powertech for permission to include material on the testing of the pressure vessels.

Introduction

Metal cylinders overwrapped by continuous-filament fibre-reinforced plastic (FRP) are used for the storage of compressed gases in aerospace and terrestrial applications requiring lightweight pressure vessels. Examples of terrestrial applications are: breathing-air cylinders used by firefighters and vessels used for the storage of compressed gaseous fuels – in particular, natural gas (CNG) and hydrogen on natural gas vehicles (NGV) and hydrogen vehicles. To maximize the fuel efficiency of the vehicle, the fuel storage cylinder is designed to minimize its mass.