• Computational Structural Engineering
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• v.2 no.4
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• pp.99-109
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• 1989

Through a series of analyses of specific structures it is shown that incremental collapse may be the critical design criterion and that shakedown analysis can be used as a design tool. Using shakedown analysis technique, a nonlinear structural optimization program has been developed. This incorporates: (i) design constraints on elastic stresses and deflections: (ii) constraints for the prevention of incremental collapse and soft story failure: and (iii) the constraint on the fundamental period of structure. A five-step design procedure is proposed by using the program to obtain the optimum design that satisfies all the requirements of comprehensive earthquake-resistant design.

• Journal of Ocean Engineering and Technology
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• v.2 no.2
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• pp.71-77
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• 1988

For the collapse of structures due to the variable repeated load, two types of collapse mechanisms, i.e., incremental collapse and alternating plasticity, exist. Under the similar variable repeated loading conditions there exists shakedown state in the structures. In shakedown state, the number of plastic hinges are not increased and all further loading will be resulted in the elastic moment changes. Namely, under the shakedown state, structures do not collapse. In this investigation, shakedown analysis are performed by composing new computer programs. Basic theories employed to compose the programs are as follows. 1. Newton-Raphson methods are added to the existing matrix method for the plastic analysis. 2. An effort to construct the stiffness of axial and bending springs attached at both ends of the member has been made. By using the programs developed, it is possible to anticipate the collapse mechanisms (Incremental collapse, alternating plasticity). Lastly for the verification of performance of the program, demonstration examples have been solved and the results are compared with other sources.

• Structural Engineering and Mechanics
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• v.25 no.1
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• pp.107-126
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• 2007

The problem related to the computation of bounds on plastic deformations for structures in plastic shakedown condition (alternating plasticity) is studied. In particular, reference is made to structures discretized by finite elements constituted by elastic perfectly plastic material and subjected to a special combination of fixed and cyclic loads. The load history is known during the steady-state phase, but it is unknown during the previous transient phase; so, as a consequence, it is not possible to know the complete elastic plastic structural response. The interest is therefore focused on the computation of bounds on suitable measures of the plastic strain which characterizes just the first transient phase of the structural response, whatever the real load history is applied. A suitable structural model is introduced, useful to describe the elastic plastic behaviour of the structure in the relevant shakedown conditions. A special bounding theorem based on a perturbation method is proposed and proved. Such theorem allows us to compute bounds on any chosen measure of the relevant plastic deformation occurring at the end of the transient phase for the structure in plastic shakedown; it represents a generalization of analogous bounding theorems related to the elastic shakedown. Some numerical applications devoted to a plane steel structure are effected and discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1740-1747
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• 2000

Under repeated rolling, initial plastic deformation introduces residual stresses which render the steady cyclic state purely elastic. This is called the process of shakedown. Many studies have been done about the shakedown in semi-infinite half space using calculated Hertizian pressure. In this paper shakedown processes in a shaft are studied by finite element analyses of a two dimensional(plane strain) model with elastic-linear-kinematic-hardening-plastic material subjected to repeated, frictionless rolling contact. Symmetric and non-symmetric pressure distributions are obtained using a simplified model of the bearing-shaft assembly. The rolling contact is simulated by repeatedly translating both pressure distributions along the surface of the shaft. By the influence of the non-symmetric pressure, larger residual radial tensile stress is generated in the immediate subsurface layer, which may make a crack propagate and, the subsurface undergoes a zigzag plastic deformation during the shakedown process, which may lead to a crack initiation.

• Structural Engineering and Mechanics
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• v.1 no.1
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• pp.31-46
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• 1993

The motivations of the application of shakedown analysis to the earthquake-resistant design of ductile moment-resisting steel structures are presented. The problems which must be solved with this application are also addressed. The illustrative results from a series of static and time history nonlinear analyses of one-bay three-story steel frame and the related discussions have shown that the incremental collapse may be the critical design criterion in case of earthquake loading. Based on the findings, it was concluded that the inelastic excursion mechanism for alternation load pattern, such as in earthquake, should be the sidesway mechanism of the whole structure for the efficient mobilization of the structural energy dissipating capacity and that the shakedown analysis technique can be used as a tool to ensure this mechanism.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1989.10a
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• pp.51-58
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• 1989

Through a series of analyses of specific structures it is shown that incremental collapse may be the critical design criterion and that shakedown analysis can be used as a design tool. Using shakedown analysis technique, a nonlinear structural optimization program has been developed. This incorporates : (ⅰ) design constraints on elastic stresses and deflections ; (ⅱ) constraints for the prevention of incremental collapse and soft story failure ; and (ⅲ) the constraint on the fundamental period of structure. A five-step design procedure is proposed by using this program to obtain the optimum design that satisfies all the requirements of comprehensive earthquake-resistant design.

• Structural Engineering and Mechanics
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• v.30 no.6
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• pp.665-678
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• 2008

The beams components subjected to the loading such as axial, bending and cyclic thermal loads were studied in this research. The used constitutive equations are those of elasto-plasticity coupled to ductile and/or creep damage. The nonlinear kinematic hardening behavior was considered in elastoplasticity modeling. The unified damage law proposed for ductile failure and fatigue by the author of Sermage et al. (2000) and Kachanov's creep damage model applied to cyclic creep and low cycle fatigue of beams. Based on the results of the analysis, the shakedown limit loads were determined through the calculation of the residual strains developed in the beam analysis. The iterative technique determines the shakedown limit load in an iterative manner by performing a series of full coupled elastic-plastic and continuum damage cyclic loading modeling. The maximum load carrying capacity of the beam can withstand, were determined and imposed on the Bree's interaction diagram. Comparison between the shakedown diagrams generated by or without creep and/or ductile damage for the loading patterns was presented.

• Structural Engineering and Mechanics
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• v.13 no.1
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• pp.35-52
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• 2002

It was shown in the previous study (Lee and Bertero 1993) that incremental collapse can lead to the exhaustion of the plastic rotation capacity at critical regions in a structure when subjected to the number of load cycles and load intensities as expected during maximum credible earthquakes and that this type of collapse can be predicted using the shakedown analysis technique. In this study, a minimum-weight design methodology, which takes into account not only the prevention of this incremental collapse but also the requirements of the serviceability limit states, is proposed by using the shakedown analysis technique and a nonlinear programming algorithm (gradient projection method).

• Transactions of the Korean Society of Machine Tool Engineers
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• v.14 no.3
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• pp.103-109
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• 2005

Since fretting fatigue damage accumulation occurs over relatively small volumes, the role of the microstructure is quite significant in fretting fatigue analysis. The heterogeneity of discrete grains and their crystallographic orientation can be accounted for using continuum crystallographic cyclic plasticity models. Such a constitutive law used in parametric studies of contact conditions may ultimately result in more thorough understanding of realistic fretting fatigue processes. The primary focus of this study is to explore the influence of microstructure as well as the magnitude of the normal force and tangential force amplitude during the fretting fatigue process. Fretting maps representing cyclic plastic strain behaviors are also developed to shed light on the cyclic deformation mechanisms.

• Tribology and Lubricants
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• v.17 no.6
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• pp.417-426
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• 2001

The effect of silver particle introduction on the rolling friction of AISI 52100 steel pairs has been investigated. Experiments ware performed in dry conditions using a thrust bearing-type rolling test rig at a load range of 12-960 N and a sliding velocity range of 8-785 mm/sec with pure (99.99%) silver particles. Results showed that introduced silver particles formed transfer layers, which protected the virgin bearing surfaces and resulted in the low lolling friction. By changing the quantity of silver particles, transitions in the rolling friction were found. Results also showed that the variations in normal load and rolling speed also affected the rolling friction behavior. Analyses of SEM and EPMA showed that the formation the transfer layer was mainly governed by the silver particle quantity, normal load and rolling speed, and this resulted in the different behavior of rolling friction. In this study, it was found that the low and stable rolling friction was resulted from the, shakedown phenomena occurred at the silver transfer layer.