A dedicated Fourier analysis for the simulation of composite pipes with defects

Through the study of a linear problem, this paper introduces some of the ingredients that are needed in order to conduct efficient non-linear calculations on composite pipes under thermo-mechanical loading in the presence of defects. Based on the observation that the main degradation scenarios take place at the extremity of a pipe, a refined model is used to describe this end zone while the rest of the pipe is described using a beam model. This study focuses on the efficient resolution of the refined end zone. For that, a dedicated Fourier expansion is used. The initial 3D problem is then transformed in a set of coupled 2D ones. The questions of the expansion truncation and the resolution of the coupled problem are then tackled. The use of a preconditioned conjugate gradient method allows to treat quasi-industrial problems in a prototype code in Matlab. Copyright q 2006 John Wiley & Sons, Ltd