A simplified technique for shakedown limit load determination

In this paper, a simplified technique is presented to determine the shakedown limit load of a structure using the finite element method. The simplified technique determines the shakedown limit load without performing lengthy time consuming full elastic-plastic cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit load is determined by performing two analyses namely: an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit load is determined through the calculation of the residual stresses developed within the structure. The simplified technique is applied and verified using two bench mark shakedown problems namely: the two-bar structure subjected to constant axial force and cyclic thermal loading, and the Bree cylinder subjected to constant internal pressure and cyclic high temperature variation across its wall. The results of the simplified technique showed very good correlation with the, analytically determined, Bree diagrams of both structures. In order to gain confidence in the simplified technique, the shakedown limit loads output by the simplified technique are used to perform full elastic-plastic cyclic loading simulations to check for shakedown behavior of both structures.