Type 2 energy and bound analyses for the creep of smooth circular pipe bends under combined in-plane bending and internal pressure

Abstract

Using an energy method designated type 2, an approximate analysis is outlined for the stationary creep of a smooth circular cross-section constant thickness thin-walled pipe bend subject to combined internal pressure and in-plane bending. The analysis complements, but is independent of, the previous type 1 energy analysis. A simple n-power creep law is assumed relevant and direct optimization techniques are employed. Both analyses then prove useful in bounding techniques which allow the creep deformation rate to be bounded from above and below. Results are presented and discussed against the background of the type 1 work and, together, the analyses help to provide some confidence in predicting the bend behaviour in creep under combined loading. Some aspects of the type 2 theory are less satisfactory than the type 1 analysis but the outcome is simpler and, at the straight pipe end of the geometry range, the type 2 results are better.