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**An edge-based smoothed finite element method for primal-dual shakedown analysis of structures.**
*(English)*
Zbl 1188.74073

Summary: An edge-based smoothed finite element method (ES-FEM) using three-node linear triangular elements was recently proposed to significantly improve the accuracy and convergence rate of the standard finite element formulation for static, free and forced vibration analyses of solids. In this paper, ES-FEM is further extended for limit and shakedown analyses of structures. A primal-dual algorithm based upon the von Mises yield criterion and a non-linear optimization procedure is used to compute both the upper and lower bounds of the plastic collapse limit and the shakedown limit. In the ES-FEM, compatible strains are smoothed over the smoothing domains associated with edges of elements. Using constant smoothing function, only one Gaussian point is required for each smoothing domain ensuring that the total number of variables in the resulting optimization problem is kept to a minimum compared with standard finite element formulation. Three benchmark problems are presented to show the stability and accuracy of solutions obtained by the present method.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |

### Keywords:

limit analysis; shakedown analysis; duality; non-linear programming; edge-based smoothed finite element method (ES-FEM); strain smoothing### Software:

XFEM
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\textit{T. N. Tran} et al., Int. J. Numer. Methods Eng. 82, No. 7, 917--938 (2010; Zbl 1188.74073)

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