Non-cyclic shakedown/ratcheting boundary determination – Part 1: Analytical approach

From the practical point of view, the classical elastic shakedown methods are not very useful for design, since in most components the stresses can safely exceed the elastic limit locally. This paper generalizes the static shakedown theorem (Melan’s theorem) to allow the analysis of plastic shakedown. Since the method is derived from a lower bound formulation in shakedown, it is very useful for the design purposes (safe). The ratchet boundary is analytically determined using the proposed method for several examples with uniform stress distributions. The numerical implementation of the method along with several examples is discussed in an accompanying paper.