Progressive deformation (ratcheting) can occur as a response to variable loads as soon as the elastic limit is exceeded. If this is the case, strains and displacements accumulate in the event of cyclic loading in each load cycle. Widely known as triggers for ratcheting and already being considered in some design codes are configurations, in which a structure is subjected to at least two different types of load, namely a constant load (the primary load) and a superimposed cyclic load. In this paper, another mechanism that generates ratcheting is introduced. It can be attributed solely to the effect of a single load. In the simplest case, this can be explained by the successive activation of (an infinite number of) plastic hinges if a load of constant magnitude is moved in space. The increments of strains and displacements can decrease or increase from cycle to cycle, when the material is hardening, or if elastic foundation is present, or if the equilibrium condition is formulated for the deformed system (second-order theory) or if ''large'' rotations are taken into account (third-order theory).
Cyclic and over-elastic loading can lead to an accumulation of plastic strains. If there is a cyclic load, which is driven by a single parameter, the lifecycle design can be very costly in terms of computational effort. If more than one cyclic load parameter is to be taken into account, which is then a multi-parameter loading, this task can become even more complex and costly. To solve this problem efficiently, different techniques are proposed. One of these techniques is based on step-by-step calculations of the strain ranges for a reduced set of loadings. Once these strain ranges are known, the accumulated state for each individual load case can be estimated using the Simplified Theory of Plastic Zones (STPZ), which requires just a few linear elastic analyses. It is shown that cyclic loads, which occur in intervals, can be replaced by interval-free calculations, which reduce the computational effort enormously. All these techniques lead to a procedure, which delivers good estimations in terms of post-shakedown quantities with very low computational effort compared to incremental step-by-step calculations. The results of the STPZ are presented by an example. A thick-walled cylinder is loaded with a constant axial force and subjected to cyclic shear and cyclic internal pressure. In general, for structures exhibiting ratcheting, hundreds or more load cycles must be analysed via step-by-step calculations until the shakedown state is reached. Using the STPZ, post-shakedown quantities, including strain ranges and accumulated strains can be estimated efficiently and the structure can be designed according to the rules of the ASME Codes. The computational effort and the quality of the results of the STPZ are compared with a step-by-step calculation.
After distinguishing material ratcheting and structural ratcheting, different phenomena related to structural ratcheting are gathered. Ratcheting of elastic–plastic structures observed with stationary position of loads is distinguished from ratcheting with moving loads. Both categories are illustrated by examples. The effect of evolution laws for the internal variables describing kinematic hardening on the accumulation of strain due to a ratcheting mechanism, and whether the ratcheting mechanism ceases with the number of cycles so that the accumulated strains are limited, is discussed. Some conditions are shown, under which the Chaboche model can lead to shakedown. Scenarios where shakedown is guaranteed at every load level, or where it may or may not occur at a specific load level, or where it definitely cannot occur at any load level, are distinguished. Correspondingly, the usefulness of shakedown analyses, which are searching for maximum load factors assuring shakedown, or direct (or simplified) methods to obtain postshakedown quantities by avoiding incremental cyclic analyses is discussed.
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