A generalised method for ratchet analysis of structures undergoing arbitrary thermo‐mechanical load histories

Abstract

This version is available at https://strathprints.strath.ac.uk/52828/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the University of Leicester, Leicester, LE1 7RH, UK AbstractA novel approach is presented based upon the Linear Matching Method framework in order to directly calculate the ratchet limit of structures subjected to arbitrary thermo-mechanical load histories. Traditionally, ratchet analysis methods have been based upon the fundamental premise of decomposing the cyclic load history into cyclic and constant components respectively, in order to assess the magnitude of additional constant loading a structure may accommodate before ratcheting occurs. The method proposed in this paper, for the first time, accurately and efficiently calculates the ratchet limit with respect to a proportional variation between the cyclic primary and secondary loads, as opposed to an additional primary load only. The method is a strain based approach and utilises a novel convergence scheme in order to calculate an approximate ratchet boundary based upon a predefined target magnitude of ratchet strain per cycle. The ratcheting failure mechanism evaluated by the method leads to less conservative ratchet boundaries compared to the traditional Bree solution. The method yields the total and plastic strain ranges as well as the ratchet strains for various levels of loading between the ratchet and limit load boundaries. Two example problems have been utilised in order to verify the proposed methodology.

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

“…Then Ponter and Carter [22,23] demonstrated an initial implementation of this technique and also provided a rigorous theoretical proof for the existence of the monotonically reducing upper bounds. Finally, a more generalized and practical code called the LMM [24,[55][56][57][58] was developed to be used for limit, shakedown and ratchet analyses of engineering structures by making full use of the commercial finite element software ABAQUS. Further, Garcea et al [25,26] propsoed an incremental-iterative solution method which has analogies with the Riks path-following algorithm to plane frames and two-dimensional flat structures.…”

A novel simulation for the design of a low cycle fatigue experimental testing programme

“…The calculation of the plastic and total strain range is performed through the first stage of the ratchet analyses of the LMM Direct Steady Cyclic Analysis (DSCA). This is a standalone component of the Linear Matching Method which obtains the steady cyclic stresses and strain rates for given combinations of loading through an iterative procedure which directly locates the ratchet limit [53]. This is explained further in Section 2.3.…”

Shakedown analysis of engineering structures under multiple variable mechanical and thermal loads using the stress compensation method

“…The first example is the Bree problem [37,40,46,48,49], which is a common benchmark example of shakedown analysis for structures under mechanical and thermal loads. As illustrated in Fig.…”

“…The plane stress Bree cases considering two loading paths ( Fig. 5a and b) have been studied numerically and analytically by some authors [40,49], and the two loading paths correspond to two types (Type-I and Type-II) of the Bree problem. Here, three different loading paths are considered for the purposes of comparison and verification.…”