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

Leonetti, Leonardo; Casciaro, Raffaele; Garcea, Giovanni

doi:10.1016/j.compstruc.2015.06.002

Cited by 20 publications

(19 citation statements)

References 32 publications

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“…The beam finite element adopted (see the work of Leonetti et al) uses interpolations that satisfy the equilibrium equation on the element for zero body forces exactly, that is,

bold-scriptN,_{s} = bold0, bold-scriptM,_{s} + e_{1} \land bold-scriptN = bold0,

while body load effects are then included exactly as a “particular solution.”…”

Section: Elastoplastic Finite Element Analysis Of 3d Beamsmentioning

confidence: 99%

“…Following the works of Bleyer and De Buhan, Sessa et al, and Leonetti et al, we assume that the beam section domain Ω is the union of the n d subdomains Ω i in which the material is homogeneous (see Figure ) and elastic perfectly plastic. For each Ω i , the plastic admissibility condition is expressed in terms of normal stress only as − σ c i ≤ σ 11 ≤ σ t i , where σ t i is the ultimate normal stress in tension (positive) and σ c i in compression (negative).…”

Section: Elastoplastic Finite Element Analysis Of 3d Beamsmentioning

confidence: 99%

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Minkowski plasticity in 3D frames: Decoupled construction of the cross‐section yield surface and efficient stress update strategy

Magisano

Liguori

Leonetti

et al. 2018

Numerical Meth Engineering

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Summary This work makes the Minkowski sum of ellipsoids into a consolidated tool for the representation of the yield surface of arbitrarily shaped composite cross sections under axial force and biaxial bending and shows how best to use it within the incremental nonlinear analysis of three‐dimensional frames. A geometric interpretation of each term of the sum allows us to construct complex convex surfaces using a low number of ellipsoids, each of them evaluated in a robust and efficient decoupled manner. Specialized algorithms, which exploit the parameterization of the yield surface in terms of a cross‐section collapse mechanism, are proposed for an efficient stress update based on the elastic predictor–return mapping scheme on a three‐dimensional beam finite element. The derivation of the algorithmic tangent moduli for the Minkowski sum completes the elements required for an efficient path‐following nonlinear analysis. The proposed methodology is general and can be applied for the representation of any zonoid yield surface and the corresponding implicit stress integration to a variety of structural and plasticity models.

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“…The beam finite element adopted (see the work of Leonetti et al) uses interpolations that satisfy the equilibrium equation on the element for zero body forces exactly, that is,

bold-scriptN,_{s} = bold0, bold-scriptM,_{s} + e_{1} \land bold-scriptN = bold0,

while body load effects are then included exactly as a “particular solution.”…”

Section: Elastoplastic Finite Element Analysis Of 3d Beamsmentioning

confidence: 99%

Section: Elastoplastic Finite Element Analysis Of 3d Beamsmentioning

confidence: 99%

Minkowski plasticity in 3D frames: Decoupled construction of the cross‐section yield surface and efficient stress update strategy

Magisano

Liguori

Leonetti

et al. 2018

Numerical Meth Engineering

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show abstract

“…Structures, during their operational life, are subjected to a sequence of variable actions depicting, sometimes, a very complex loading scenario [2] In this context shakedown analysis furnishes, in a direct way, a reliable safety factor against plastic collapse, loss in functionality due to excessive deformation (ratcheting) or collapse due to low cycle fatigue (plastic shakedown), and also provides valuable information about the internal stress redistribution due to the plastic adaptation phenomenon. .…”

Section: Introductionmentioning

confidence: 99%

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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“…For instance, a thin-wall continuous beam with softening behavior under one-path loading was analyzed by [25] taking into account material non-linearity and local buckling. Sensitivity analysis of the stability problems of thin-walled structures presented in [17] The right approach is possible either by laborious analyzing of load history in time without any warranty of accounting for the worst histories of independent load cases, or for the entire class of loading as provided in the theory of shakedown analysis (SDA) [1,5,6,8,9,12,[14][15][16]19,20,22,26,27,[29][30][31][32]. The example of such shakedown approach to the steel frames confined with 1st class cross-sections was published in a paper by Atkočiūnas & Venskus [10]; a shakedown limit analysis of the reinforced concrete frames has been done by Alawdin & Bulanov [2]; an updated mathematical model for optimal shakedown analysis of plane reinforced concrete frames according to Eurocodes has been introduced by Alawdin & Liepa [3].…”

Section: Introductionmentioning

confidence: 99%

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

Alawdin

Liepa

2017

Civil and Environmental Engineering Reports

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Classical optimization problems of metal structures confined mainly with 1st class crosssections. But in practice it is common to use the cross-sections of higher classes. In this paper, a new mathematical model for described shakedown optimization problem for metal structures, which elements are designed from 1st to 4th class cross-sections, under variable quasi-static loads is presented. The features of limited plastic redistribution of forces in the structure with thin-walled elements there are taken into account. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members. Design formulae for Methods 1 and 2 for members are analyzed. Structures stiffness constrains are also incorporated in order to satisfy the limit serviceability state requirements. With the help of mathematical programming theory and extreme principles the structure optimization algorithm is developed and justified with the numerical experiment for the metal plane frames.

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

Cited by 20 publications

References 32 publications

Minkowski plasticity in 3D frames: Decoupled construction of the cross‐section yield surface and efficient stress update strategy

Minkowski plasticity in 3D frames: Decoupled construction of the cross‐section yield surface and efficient stress update strategy

Composite Fem Models for Limit and Shakedown Analysis

Optimal Shakedown of the Thin-Wall Metal Structures Under Strength and Stiffness Constraints

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