Explicit analytical solutions for heated, pressurized two-layer cylinders

Abstract

Closed-form analytical expressions are derived for the displacement field and corresponding stress state in two-layer cylinders subjected to pressure and thermal loading. Solutions are developed both for cylinders which 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). It is proven formally that the classical Lamé displacement field for a pressurized thick-walled cylinder is exact for layered cylinders under generalized plane strain conditions. The analytical solutions are verified by means of detailed three-dimensional finite element analyses, and they are easily implemented in, and suitable for, engineering applications. The chosen axial boundary conditions are demonstrated to be particularly relevant for pipeline and piping applications. By applying the exact solutions derived in the present study to typical offshore lined or clad pipelines, it is demonstrated that thermal expansion of the liner or clad layer causes higher tensile hoop stresses in the pipe steel wall than accounted for in current engineering practice. Moreover, it is shown that repeated cycles of start-up and shut-down phases for lined or clad pipelines cause significant stress cycles in the liner or cladding. This may pose a risk to the integrity of such pipelines.