Shakedown analysis of truss structures with nonlinear kinematic hardening

Leu, S.-Y.; Li, J.-S.

doi:10.1016/j.ijmecsci.2015.09.003

Cited by 10 publications

(3 citation statements)

References 27 publications

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“…They mostly concern the model of elastic perfectly plastic material and static load, for example [6,8]. Other material models are also taken in the same way as at paper [11].…”

Section: Introductionmentioning

confidence: 99%

Elastic shakedown limit of a steel lattice girder

Brzuzy

2021

iboa

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This paper presents a solution for the problem concerning the behaviour of a steel lattice girder subjected to dynamic load pulses. The theory of shakedown is used in the analysis. It is assumed that such loads cause a non-elastic response which includes dissipation of energy causing deformations and residual forces developed in the structural members of the girder. At a certain intensity of these forces, the girder can react to subsequent load pulses without further dissipation of energy, behaving in the elastic region after shakedown. This condition is referred to as adaptation of the structure to assumed cyclic loading. Elastic shakedown limit is determined through a direct analysis of the girder's dynamic behaviour, i.e. by checking if energy dissipation decreases with loading cycles. This gives the number of load applications after which no further increase of the energy dissipation is observed. The existing permanent deformations persist and residual forces remain in the same state. The analysis takes into account the possibility that compressed members can buckle which may result in non-elastic, longitudinal and transverse vibrations of these members. Non-linear geometry of members is taken into account. Then a perfectly elastic-viscoplastic model of the material is used. The main goal is to determine the state of the non-elastic movements of the girder joints and the residual internal forces developed in the girder members after each load application. The values obtained in this way serve as the basis for describing the next loading cycle. It is possible to use the approach presented in the paper to evaluate the effects of accidental loads. Then it is checked whether a small number of repetitions of accidental load would result in exceeding the serviceability limit state criteria of the maximum permanent deformation or displacement and/or strain amplitudes. If so, the magnitude of accidental load is greater than the elastic shakedown limit. Some examples are given to illustrate the application of the theory of shakedown.

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“…They mostly concern the model of elastic perfectly plastic material and static load, for example [6,8]. Other material models are also taken in the same way as at paper [11].…”

Section: Introductionmentioning

confidence: 99%

Elastic shakedown limit of a steel lattice girder

Brzuzy

2021

iboa

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“…Since the two classical shakedown theorems [3,4] were established, the studies on shakedown analysis have attracted broad attention in structural engineering and academic circles (see Refs. ), mainly involving the theoretical extensions [5][6][7][8][9][10][11][12][13][14][15][16] and development of numerical methods [7, for shakedown analysis.…”

Section: Introductionmentioning

confidence: 99%

“…In some engineering situations, these assumptions may be unrealistic. To extend the theory to make it applied in more practical applications, some researchers [6][7][8][9][10][11][12][13][14][15][16] got rid of some coercive assumptions. The shakedown problems of non-associated flow rules [6,7], geometrical nonlinearities [8], dynamic effects [9,10], damaging inelastic material [11,13] and nonlinear kinematic hardening material [12][13][14][15][16] have been investigated.…”

Section: Introductionmentioning

confidence: 99%

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

Peng

Liu

Chen

et al. 2018

International Journal of Mechanical Sciences

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The determination of shakedown load or shakedown domain is an important task in structural design and integrity assessment. In this paper, a novel numerical procedure based on the Stress Compensation Method (SCM) is developed to perform shakedown analysis of engineering structures under multiple variable mechanical and thermal loads. By applying the compensation stress on the yield regions that occur at every load vertex of the prescribed loading domain to adjust the total stress to the yield surface and resolving the equilibrium equations, the statically admissible residual stress field for static shakedown analysis is constructed. A robust and effective iteration control technique with some convergence parameters is used to check the change of the compensation stress in the inner loop and to update the shakedown load multiplier in the outer loop. For the purpose of general use, the method is implemented into ABAQUS platform. The shakedown problems for the Bree plate, a square plate with a central circular hole and a practical thick vessel with nozzles under some two-dimensional and three-dimensional loading domains are effectively solved and analyzed. Both alternating plasticity mechanism and ratcheting mechanism to determine the shakedown boundary of these structures are revealed. Numerical applications show that the proposed method has good numerical stability, high accuracy and efficiency, and is well suited for shakedown analysis of large-scale practical engineering structures.

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