Use of Fourier Expansions for the Simulation of Elastic 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 nonlinear calculations on composite pipes under thermomechanical 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.