Bounds to Shakedown Loads for a Class of Deviatoric Plasticity Models

Krabbenhøft, K.; Lyamin, A. V.; Sloan, Scott W.

doi:10.1007/s00466-006-0076-3

Cited by 43 publications

(16 citation statements)

References 32 publications

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“…We note that this upper bound actually corresponds to the static plastic shakedown limit as defined by Polizzotto (1993). The relationship of the plastic shakedown limit to other shakedown limits, for a variety of deviatoric plastic models, has been discussed by Krabbenhøft et al (2007b). Finally, a third type of upper bound on the elastic shakedown limit can be obtained by relaxing the yield constraints on the residual stress field but retaining the equilibrium conditions:…”

Section: Shakedown and The Constraints On The Residual Stress Fieldmentioning

confidence: 97%

Bounds for shakedown of cohesive-frictional materials under moving surface loads

Zhao

Sloan

Lyamin

et al. 2008

International Journal of Solids and Structures

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In this paper, shakedown of a cohesive-frictional half space subjected to moving surface loads is investigated using Melan's static shakedown theorem. The material in the half space is modelled as a Mohr-Coulomb medium. The sliding and rolling contact between a roller and the half space is assumed to be plane strain and can be approximated by a trapezoidal as well as a Hertzian load distribution. A closed form solution to the elastic stress field for the trapezoidal contact is derived, and is then used for the shakedown analysis. It is demonstrated that, by relaxing either the equilibrium or the yield constraints (or both) on the residual stress field, the shakedown analysis leads to various bounds for the elastic shakedown limit. The differences among the various shakedown load factors are quantitatively compared, and the influence of both Hertzian and trapezoidal contacts for the half space under moving surface loads is studied. The various bounds and shakedown limits obtained in the paper serve as useful benchmarks for future numerical shakedown analysis, and also provide a valuable reference for the safe design of pavements.

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Section: Shakedown and The Constraints On The Residual Stress Fieldmentioning

confidence: 97%

Bounds for shakedown of cohesive-frictional materials under moving surface loads

Zhao

Sloan

Lyamin

et al. 2008

International Journal of Solids and Structures

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“…The ratio D / L is chosen to be 0.2, for which the non‐shakedown state is known to be alternating plasticity. For a variation of the values D / L , the reader is referred to . Because of the symmetry of the system, only one quarter of the plate was considered.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The first example was the classical problem of a square plate with a circular central hole, which was used for validation by several authors, for example, [28,31,33,47,[82][83][84][85][86][87][88][89]. In addition, comparative studies were presented in, for example, [28,58,65,71,87]. The comparison with most of these was presented in [65].…”

Section: Square Plate With Circular Central Hole Under Biaxial Mechanmentioning

confidence: 99%

“…The corresponding running times are shown in Figure 6. [87] 0.430 Schwabe (2000) [90] 0.430 Belytschko (1972) [82] 0.431 Tran et al (2010) [31] 0.434 Garcea et al (2005) [47] 0.438 Groß-Weege (1997) [71] 0.446 Present solution [65] 0.458 Akoa et al (2007) [63] 0.466 Liu et al (2005) [28] 0.477 Chen et al (2008) [88] 0.480 Chen & Ponter (2001) [85] 0.492 Zhang & Raad (2002) [33] 0.494 Carvelli et al (1999) [84] 0.518…”

Section: Square Plate With Circular Central Hole Under Biaxial Mechanmentioning

confidence: 99%

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A selective strategy for shakedown analysis of engineering structures

Simon

Kreimeier

Weichert

2013

Numerical Meth Engineering

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SUMMARYDetermining the load‐bearing capacity of engineering structures is essential for their design. In the case of varying thermo‐mechanical loading beyond the elastic limit, the statical shakedown analysis constitutes a particularly suitable tool for this. The application of the statical shakedown theorem, however, leads to a nonlinear convex optimization problem, which is typically characterized by large numbers of variables and constraints. In the present work, this optimization problem is solved by a primal–dual interior‐point algorithm, which shows a remarkable performance due to its problem‐tailored formulation. Nevertheless, the solution procedure remains still a demanding task from computational point of view. Thus, the aim of this paper is to tackle the task of solving large‐scale problems by use of a new so‐called selective algorithm. This algorithm detects automatically the plastically most affected zones within the structure, which have the highest influence on the solution. The entire system is then reduced to a substructure consisting of these zones, based upon which a new optimization problem can be set up, which is solved with significantly less effort. Consequently, the running time decreases drastically, as is shown by application to numerical examples from the field of power plant engineering. Copyright © 2013 John Wiley & Sons, Ltd.

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“…This shakedown theory has been used for geotechnical applications including pavements (e.g. [27,28]), bearing capacity for shallow foundations [29] and laterally loaded piles [16]. The shakedown limit load is generally determined using lower and upper bound solutions based on Melan's static or Koiter's kinematic theorems.…”

Section: Introductionmentioning

confidence: 99%

Cyclic shakedown of piles subjected to two‐dimensional lateral loading

Levy

Einav

Hull

2009

Num Anal Meth Geomechanics

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SUMMARYPile foundations are frequently subjected to cyclic lateral loads. Wave and wind loads on offshore structures will be applied in different directions and times during the design life of a structure. Therefore, the magnitude and direction of these loads in conjunction with the dead loads should be considered. This paper investigates a loading scenario where a monotonic lateral load is applied to a pile, followed by two-way cycling in a direction perpendicular to the initial loading. This configuration is indicative of the complexity of loading that may be considered and is referred to in the paper as 'T-shaped' loading. The energy-based numerical model employed considers two-dimensional lateral loading in an elasto-plastic soil, with coupled behaviour between the two perpendicular directions by local yield surfaces along the length of the pile. The behaviour of the soil-pile system subjected to different loading combinations has been divided into four categories of shakedown previously proposed for cyclic loading of structures and soils. A design chart has been created to illustrate the type of pile behaviour for a given two-dimensional loading scenario.

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Bounds to Shakedown Loads for a Class of Deviatoric Plasticity Models

Cited by 43 publications

References 32 publications

Bounds for shakedown of cohesive-frictional materials under moving surface loads

Bounds for shakedown of cohesive-frictional materials under moving surface loads

A selective strategy for shakedown analysis of engineering structures

Cyclic shakedown of piles subjected to two‐dimensional lateral loading

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