Effect of Inhomogeneity on the Stress in Pipes

The purpose of this paper is to investigate the influence of elastic inhomogeneity on the elastic field in solid circular cylinders, pipes, and also in a solid of infinite extent surrounding an internally pressurized cavity. The motivation for this research stems from recent interest in the use of laser technology and the vapor deposition of thin layers onto the surfaces of pipes. The present analysis extends previous treatments insofar as a more general form for the spatial variation of Young's modulus is used. An estimate for the optimal functional gradient within a pressurized pipe is presented.