Modeling and computation of shakedown problems for nonlinear hardening materials

Stein, Erwin; Zhang, G.; Huang, Yifan

doi:10.1016/0045-7825(93)90048-3

Cited by 66 publications

(15 citation statements)

References 13 publications

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“…It is found that the number R of the basis vectors has little influence on the numerical accuracy of limit analysis when R 3. This has confirmed that the basis vectors generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis can ensure a good convergence of the reduced-basis technique [25,26]. The great advantage of such a technique is that it can decrease the optimal variables greatly and enable us to solve efficiently the related optimization problem of limit analysis.…”

Section: Thick-walled Cylindersupporting

confidence: 71%

“…It is obvious that small-or medium-sized discretized structures in general lead to a high dimension of mathematical programming so that the solution of this optimization problem is very difficult or even impossible. To overcome this difficulty, the reduced-basis technique is used here to simulate the self-equilibrium stress field [25,26].…”

Section: Mathematical Programming Of a Discretized Structurementioning

confidence: 99%

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Lower‐bound limit analysis by using the EFG method and non‐linear programming

Chen

Liu

Cen

2007

Numerical Meth Engineering

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SUMMARYIntended to avoid the complicated computations of elasto-plastic incremental analysis, limit analysis is an appealing direct method for determining the load-carrying capacity of structures. On the basis of the static limit analysis theorem, a solution procedure for lower-bound limit analysis is presented firstly, making use of the element-free Galerkin (EFG) method rather than traditional numerical methods such as the finite element method and boundary element method. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the domain under consideration. The reduced-basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. The self-equilibrium stress field is expressed by a linear combination of several self-equilibrium stress basis vectors with parameters to be determined. These self-equilibrium stress basis vectors are generated by performing an equilibrium iteration procedure during elasto-plastic incremental analysis. The Complex method is used to solve these non-linear programming sub-problems and determine the maximal load amplifier. Numerical examples show that it is feasible and effective to solve the problems of limit analysis by using the EFG method and non-linear programming.

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Section: Thick-walled Cylindersupporting

confidence: 71%

Section: Mathematical Programming Of a Discretized Structurementioning

confidence: 99%

Lower‐bound limit analysis by using the EFG method and non‐linear programming

Chen

Liu

Cen

2007

Numerical Meth Engineering

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“…To overcome this difficulty, a reduced-basis technique is used to simulate the self-equilibrium stress field (Stein et al, 1993).…”

Section: The Symmetric Galerkin Boundary Element Methodsmentioning

confidence: 99%

Lower bound shakedown analysis by the symmetric Galerkin boundary element method

LIU

2005

International Journal of Plasticity

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“…Firstly, the classical shakedown theorems, originally proved under the simplifying assumptions of geometric linearity and elastic-perfectly plastic constitutive relations obeying the associated flow law, have been extended to broader classes of problems accounting for the effects of high temperature, strain-or workhardening, nonlinear geometry, dynamics, damage and non-associated plastic constitutive relations, among others (Kö nig and Maier, 1981;Kö nig, 1987;Polizzotto, 1982;GrossWeege, 1990;Pham, 1992Pham, , 2001Pycko and Maier, 1995;Feng and Liu, 1996;Feng and Gross, 1999;Weichert and Maier, 2000;Bousshine et al, 2003;Nguyen, 2003). Secondly, various theoretical and numerical shakedown analysis methods have been established for solving technologically important problems, among which finite element and boundary element methods often play a significant role (e.g., Gross-Weege, 1997;Stein et al, 1993;Zouain et al, 2002;Vu et al, 2004;Abdel-Karim, 2005;Liu et al, 2005). Recently, considerable attention has been paid on damage and shakedown behavior of heterogeneous materials or composites using macro/micro or multiscale numerical approaches (Derrien et al, 1999;Zouain and Silveira, 1999;Li et al, 2003;Magoariec et al, 2004).…”

Section: Introductionmentioning

confidence: 99%