A simplified technique for shakedown load determination of a 90 degree pipe bend subjected to constant internal pressure and cyclic in-plane bending

In this paper a simple technique is presented to determine the shakedown load of a 90 degree pipe bend subjected to constant internal pressure and cyclic in-plane bending using the finite element method. Through the proposed technique, the shakedown load is determined without performing time consuming cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown load is determined through performing only two analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown load is determined through the calculation of the residual stresses developed in the pipe bend. In the elastic analysis, performed only once and stored, an in-plane closing moment is applied preserving structure stresses within the material elastic range. In the elastic-plastic analysis, a constant internal pressure, below the pressure to cause yielding, is applied in addition to an increasing moment magnitude that causes the material yield strength to be exceeded. For verification purposes, the results of the simplified technique are compared to the results of full cyclic loading finite element simulations where the pipe bend is subjected to constant internal pressure and cyclic in-plane closing moment loading. In order to have confidence in the proposed technique, it is applied beforehand on the Bree cylinder [1] subjected to constant internal pressure and cyclic high heat fluxes across its wall. The results of the proposed technique showed very good correlation with the, analytically determined, Bree diagram of the cylinder.