A similarity law for stressing rapidly heated thin-walled cylinders

Abstract

When a thin cylindrical shell of uniform thickness is very rapidly heated by hot high-pressure gas flowing inside the shell, the temperature of material decreases steeply from a high temperature at the inside surface to ambient temperatures at the outside surface. Young's modulus of material thus varies. The purpose of the present paper is to reduce the problem of stress analysis of such a cylinder to an equivalent problem in conventional cylindrical shell without temperature gradient in the wall. The equivalence concept is expressed as a series of relations between the quantities for the hot cylinder and the quantities for the cold cylinder. These relations give the similarity law whereby strains for the hot cylinder can be simply deduced from measured strains on the cold cylinder and thus greatly simplify the problem of experimental stress analysis.