Three field finite elements for the elastoplastic analysis of 2D continua

Bilotta, Antonio; Leonetti, Leonardo; Garcea, Giovanni

doi:10.1016/j.finel.2011.05.002

Cited by 29 publications

(46 citation statements)

References 23 publications

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“…It is worth noting that matrix, the single step of the elastoplastic analysis [6,21,10,22] can be seen as the solution of the mathematical problem (12) by adding the compliance matrix F that is block diagonal at the element (stress) level due to the constant interpolation adopted and its inverse F −1 can be directly assembled. In this way an inexpensive construction of the tangent stiffness matrix [6,10] is obtained.…”

Section: The Discrete Equilibrium Equationsmentioning

confidence: 99%

“…Table 1 reports a comparison of the computed values of the plastic collapse multiplier and the number of iterations spent on each analysis. The reference result [21] was obtained using a mesh having 1024 elements and 2178 dofs. [21] 0.3956…”

Section: Cook Membranementioning

confidence: 99%

“…The numerical values of the collapse multipliers, computed in plane stress condition and by using the Mises criterion, are compared in Table 2 for the three meshes. It is worth noting that the accurate reference results [21] were computed with 4802 dofs, 2304 elements and 9216 admissibility constraints. The exact collapse value has been computed with the analytical formula…”

Section: Square Plate With Circular Holementioning

confidence: 99%

See 2 more Smart Citations

Composite Fem Models for Limit and Shakedown Analysis

Leonetti¹,

Garcea²,

Nguyen‐Xuan³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The paper improved S-FEMs formulations with an enriched displacement field, making use of modified Allman's shape functions. This mixed interpolation is the natural context in performing lower bound strategy for shakedown, limit analysis and elastoplastic analysis. The model takes advantages from the simplicity and few addressed requirements for good performances in nonlinear analysis. The simple assumption made for the stress field regards the convenience of using self-equilibrated stress interpolations in Cartesian coordinates. In the proposed composite elements the stress is discontinuous on the element and across their sides and the mesh of the elements is coincident with the discretization of the geometry. This stress interpolation is able to address the discontinuities in the plastic strain and, in such a way, to define in their description a finer mesh with respect the basic grid.

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Section: The Discrete Equilibrium Equationsmentioning

confidence: 99%

Section: Cook Membranementioning

confidence: 99%

Section: Square Plate With Circular Holementioning

confidence: 99%

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Composite Fem Models for Limit and Shakedown Analysis

Leonetti¹,

Garcea²,

Nguyen‐Xuan³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…The algorithm we propose in Sections 3.3-3.5 is written in a format suitable for use in a generic finite element analysis context. In particular the plastic admissibility condition and the convex hull of the elastic stresses S H need to be defined at the local level of analysis that is: (i) the Gauss Point for standard compatible FE interpolations; and (ii) the finite element for more complex interpolations (see for example [35]). …”

Section: The Proposed Selection Rule Algorithm In a General Finite Elmentioning

confidence: 99%

Effective treatment of complex statical and dynamical load combinations within shakedown analysis of 3D frames

Leonetti

Casciaro

Garcea

2015

Computers & Structures

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“…In this paper, an extension of the MxTFA to the analysis of periodic composites characterized by linear isotropic hardening plasticity is presented. In particular, a mixed variational approach, originally proposed in [8] and recently implemented in [9,10], involving the weak form of compatibility and plastic admissibility equations is adopted to derive the evolution laws of the internal variables in the TFA framework. In fact, the literature shows how stress recovery techniques are able to produce very good results [11,12].…”

Section: Introductionmentioning

confidence: 99%

A Homogenization Technique for Elasto-Plastic Composites

Covezzi¹,

Miranda²,

Marfia³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The present study proposes a homogenization technique for the estimation of the overall behavior of composite materials characterized by a nonlinear behavior. A mixed nonuniform TFA procedure is proposed in order to study the mechanical response of periodic composites characterized by linear isotropic hardening plasticity. As the case of periodic composites is considered, the homogenization is performed on a repetitive unit cell that plays the equivalent role of representative volume element for random media. A numerical application is performed to test the effectiveness of the proposed technique. In particular, the homogenization results are compared with the ones carried out by micromechanical nonlinear finite element analyses. 2316

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Three field finite elements for the elastoplastic analysis of 2D continua

Cited by 29 publications

References 23 publications

Composite Fem Models for Limit and Shakedown Analysis

Composite Fem Models for Limit and Shakedown Analysis

Effective treatment of complex statical and dynamical load combinations within shakedown analysis of 3D frames

A Homogenization Technique for Elasto-Plastic Composites

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