Efficient analytical solutions for heated, pressurized multi-layered cylinders

Abstract

Two independent sets of analytical solutions, one based on matrix inversion and one based on iteration, are derived for the displacement field and corresponding stress state in multi-layer cylinders subjected to pressure and thermal loading. Solutions are developed for cylinders that are axially free with no friction between layers (plane stress), for cylinders that are fully restrained axially (plane strain) and for axially loaded and spring-mounted cylinders, assuming that the combined two-layer cross-section remains plane after deformation (generalized plane strain). The analytical solutions are verified by means of detailed three-dimensional finite element analyses and comparisons between the two independent analytical solutions, which are easily implemented in, and suitable for, engineering applications.