Shakedown analysis for rolling and sliding contact problems

There is a range of problems where repeated rolling or sliding contact occurs. For such problems shakedown and limit analyses provides significant advantages over other forms of analysis when a global understanding of deformation behaviour is required. In this paper, a recently developed numerical method. Ponter and Engelhardt (2000) and Chen and Ponter (2001), for 3-D shakedown analyses is used to solve the rolling and sliding point contact problem previously considered by Ponter, Hearle and Johnson (1985) for a moving Herzian contact, with friction, over a half space. The method is an upper bound programming method, the Linear Matching Method, which provides a sequence of reducing upper bounds that converges to the least upper bound associated with a finite element mesh and may be implemented within a standard commercial finite element code. The solutions given in Ponter, Hearle and Johnson (1985) for circular contacts are reproduced and extended to the case when the frictional contact stresses are at an angle to the direction of travel. Solutions for the case where the contact region is elliptic are also given

The effects of positive affective priming on Māori mothers' attributions for children's misbehaviours and appropriate methods of discipline : a thesis submitted in partial fulfilment of the requirements for the degree of Master of Arts in Psychology at Massey University, Wellington, New Zealand

This study is a test-retest experimental design which sets out to determine if Māori mothers, exposure to emotive (positive) photographs of Māori people (children interacting with adults) would influence their attributions and disciplinary responses for child misbehaviour in a positive direction. I also hypothesised that the exposure to Māori visual icons or objects might have a similar but lesser affect. The participants were a group of 48 mothers of Māori descent living in the Porirua and Wellington areas. I recruited by approaching the principal from a local primary school and my previous employer, by attending a parent group, and by using a snowballing strategy. Cultural identity was assessed using a "Lifestyle Questionnaire" and results showed that the majority of participants were well integrated into both Māori and mainstream New Zealand culture. Participants were randomly divided into four equal groups of 12 participants. Each group was shown different sets of photographs that served as the emotional primes (i.e., Māori people. non-Māori people, Māori objects and non-Māori objects). The two experiment groups viewed the Māori people or Māori objects photographs. Conversely, the two control groups viewed the non-Māori people or non-Māori objects photographs. The participants undertook a pre-testing exercise prior to viewing the photographs, followed by a post-testing exercise. The pre-testing and post-testing exercises consisted of parent-child scenarios based on child misbehaviours where the child could be blamed for the misbehaviour, and ambiguous behaviours where the child could not be clearly blamed for the misbehaviour. Participants used 4-point Likert scales to rate their causal attributions for the parent-child scenarios and their likely disciplinary responses. The data were statistically analysed using a mixed between-within subjects analysis of variance (ANOVA). Most of the results were not statistically significant, apart from two of the positive causal attributions. Child misbehaviour scenarios showed a significant main effect for pre-test and post-test scores, with all groups being more forgiving or excusing the child when clearly the child was to blame. Ambiguous behaviour scenarios showed a significant interaction between Māori and non-Māori groups' pre-test and post-test scores (i.e., Māori groups were more forgiving or excusing the child and non-Māori groups were less forgiving or excusing the child). The majority of participants' scores showed their disciplinary responses were less harsh at pre-test and post-test. The most likely responses were talking to their child, followed by child apologises and then telling off. The least likely responses were smacking; next in order were doing nothing and ignoring. This study provided some insight into Māori mothers' causal attributions and disciplinary responses. Recommendations for future research, limitations and positive features are presented

A simplified creep-reverse plasticity solution method for bodies subjected to cyclic loading

An extension of the upper bound shakedown theorem to load histories in excess of shakedown has been applied recently to the evaluation of a ratchet limit and the varying plastic strain magnitudes associated with a varying residual stress field. Solutions were obtained by the Linear Matching Method. In the present paper, this technique is extended to the evaluation of creep-reverse plasticity mechanism for bodies subjected to thermal cyclic loading including creep effects. The accumulated creep strain, the varying flow stress and the corresponding varying residual stress field during a creep dwell time are evaluated as well as the elastic follow-up factor. Three alternative computational strategies are discussed with differing but related assumptions. The problem of a plate with a central circular hole is discussed, subjected to cyclic thermal load. All three methods provide similar values for the elastic follow-up factor, indicating that the result is insensitive to the range of assumptions made. The simplest method, Method 1, is suggested as the basis of a general purpose method for use in life assessment

Modelling of the behaviour of a welded joint subjected to reverse bending moment at high temperature

The paper is concerned with the modeling of the behaviour of welds when subjected to severe thermal and mechanical loads where the maximum temperature during dwell periods lies in the creep range. The methodology of the life assessment method R5 is applied where the detailed calculations are carried out using the linear matching method (LMM), with the objective of generating an analytic model. The linear matching method has been developed to allow accurate predictions using the methodology of R5, the UK life assessment method. The method is here applied to a set of weld endurance tests, where reverse bending is interrupted by creep dwell periods. The weld and parent material are both Type 316L(N) material, and data were available for fatigue tests and tests with 1 and 5 h dwell periods to failure. The elastic, plastic, and creep behavior of the weld geometry is predicted with the LMM using the best available understanding of the properties of the weld and parent material. The numerical results are translated into a semi-analytic model. Using the R5 standard creep/fatigue model, the predicted life of the experimental welds specimens are compared with experimental data. The analysis shows that the most severe conditions occur at the weld/parent material interface, with fatigue damage concentrated predominantly in the parent material, whereas the creep damage occurs predominantly in the weld material. Hence, creep and fatigue damage proceed relatively independently. The predictions of the model are good, except that the reduction in fatigue life due to the presence of the weld is underestimated. This is attributed to the lack of separate fatigue date for the weld and parent material and the lack of information concerning the heat affected zone. With an adjustment of a single factor in the model, the predictions are very good. The analysis in this paper demonstrates that the primary properties of weld structures may be understood through a number of structural parameters, defined by cyclic analysis using the linear matching method and through the choice of appropriate material data. The physical assumptions adopted conform to those of the R5 life assessment procedure. The resulting semi-analytic model provides a more secure method for extrapolation of experimental data than previously available

Structural integrity assessment of superheater outlet penetration tubeplate

In recent years, the Linear Matching Method (LMM) has been well developed for the integrity assessment of the component subjected to cyclic thermal and mechanical loads. In this paper, the fatigue damage of a superheater outlet penetration tubeplate is assessed in detail using the LMM with an ABAQUS 3D finite element model. The significant thermal transients of the component are due to the out of phase steam temperature oscillations. The primary loading on the component is from pressure (steam and gas) and system moment on the penetration and tail pipes. A transient thermal analysis is performed in the first step to determine the component temperature history during the cycle. Then these temperature solutions are used as an input to the structural analysis to obtain the elastic stress history caused by these temperature loads. A shakedown analysis is thereafter carried out and the evaluation of the steady cyclic behaviour of tubeplate during the steady state cycle is then achieved using the LMM. The elastic, plastic and total strain ranges over the steady state cycle are evaluated for the fatigue damage assessment. Both the constant and changing residual stress solutions associated with the steady state cycle are obtained. The comparisons of stress and strain range calculations for out of phase temperature oscillations by the LMM and other methodologies are given in the paper. Finally, a LMM ratchet limit analysis is carried out to assess the capacity of the component subjected to the existing thermal transients to withstand an additional primary loads including both pressure and moment. The temperature dependent elastic-plastic properties are adopted throughout the LMM assessment

The linear matching method applied to the high temperature life integrity of structures. Part 1. Assessments involving constant residual stress fields

Design and life assessment procedures for high temperatures are based on 'expert knowledge' in structural mechanics and materials science, combined with simplified methods of structural analysis. Of these R5 is one of the most widely used life assessment methods internationally with procedures based on reference stress techniques and shakedown calculations using linear elastic solutions. These have been augmented by full finite element analysis and, recently, the development of a new programming method, the Linear Matching Method (LMM), that allows a range of direct solutions that include shakedown methods and simplified analysis in excess of shakedown. In this paper LMM procedures are compared with calculations typical of those employed in R5 for cyclic loading problems when the assumption of a constant residual stress field is appropriate including shakedown and limit analyses, creep rupture analysis and the evaluation of accumulated creep deformation. A typical example of a 3D holed plate subjected to a cyclic thermal load and a constant mechanical load is assessed in detail. These comparisons demonstrate the significant advantages of linear matching methods for a typical case. For a range of cyclic problems when the residual stress field varies during the cycle, which include the evaluation of plastic strain amplitude, ratchet limit and accumulated creep strains during a high temperature dwell periods, the corresponding LMM and R5 procedures are discussed in an accompanying paper

Small scale monumental sculpture

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On creep-fatigue endurance of TIG-dressed weldments using the linear matching method

This paper is devoted to parametric study on creep-fatigue endurance of the steel type 316N(L) weldments at 550◦C identified as type 3 according to R5 Vol. 2/3 procedure classification. The study is implemented using a direct method known as the Linear Matching Method (LMM) and based upon the creep-fatigue evaluation procedure considering time fraction rule for creep-damage assessment. Seven configurations of the weldment, characterised by particular values of a geometrical parameter ρ, are proposed. Parameter ρ, which represents different grades of TIG dressing, is a ratio between the radius of the fillet of the remelted metal on a weld toe and the thickness of welded plates. For each configuration, the total number of cycles to failure N⋆ in creep-fatigue conditions is assessed numerically for different loading cases defined by normalised bending moment ˜M and dwell period t. The obtained set of N⋆ is extrapolated by the analytic function dependent on ˜M, t and parameter ρ. Proposed function for N⋆ shows good agreement with numerical results obtained by the LMM. Therefore, it is used for the identification of Fatigue Strength Reduction Factors (FSRFs) effected by creep, which are intended for design purposes, and dependent on t and ρ

A quantitative study of the relationship between academic achievement and the developmental study of vocal and instrumental music

The purpose of this study was to determine whether a quantitative relationship existed between academic achievement as measured by California Achievement Test scores and the involvement of high school students in the developmental study of vocal and instrumental music. The California Achievement Test Level 20 (CAT-5) scores of a cohort of 170 students were evaluated from grades nine and ten. Students were grouped according to whether they were involved in developmental vocal music, instrumental music, vocal and instrumental music programs, or no music study. Reading, Language, and Mathematics scores for students in music programs were compared to non-music students using the t - Test analysis to assess statistically significant differences. The p \u3c 0.05 level was chosen as the standard for statistical significance. Results indicated that students involved in developmental music study had marginally higher scores in grade nine and substantially higher scores in grade ten and that instrumental music study had the most profound positive influence upon these scores

A method for the evaluation of a ratchet limit and the amplitude of plastic strain for bodies subjected to cyclic loading

An extension of the upper bound shakedown theorem to load histories in excess of shakedown has been presented elsewhere in this issue. Here the minimisation process described therein is applied to the solutions of the ratchet limit as well as shakedown and limit load for a range of simple problems. The solutions provide an estimate of the maxima of the varying plastic strain magnitudes, which is compared with the Neuber approximate values. The position of the ratchet boundary is confirmed by comparison step-by-step analysis