An algorithm for incremental elastoplastic analysis using equality constrained sequential quadratic programming

Bilotta, Antonio; Leonetti, Leonardo; Garcea, Giovanni

doi:10.1016/j.compstruc.2012.03.004

Cited by 27 publications

(34 citation statements)

References 25 publications

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“…The main features of the model are its simplicity and ease of implementation within [10] 0.8006 exact 0.8000 existing computational tools. More importantly, the element proves to be accurate and robust for the plastic analysis of plane problems.…”

Section: Discussionmentioning

confidence: 99%

“…The mixed format makes an effective extension of the model to nonlinear analyses simpler. For application in plastic analysis [10], the method is expected to behave well as the discontinuous interpolation for the stress field addresses discontinuities in the plastic deformation field and the plastic admissibility is also imposed in a simple manner.…”

Section: The Stress Interpolationmentioning

confidence: 99%

“…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%

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: Discussionmentioning

confidence: 99%

Section: The Stress Interpolationmentioning

confidence: 99%

Section: The Discrete Equilibrium Equationsmentioning

confidence: 99%

See 1 more Smart Citation

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)

Self Cite

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“…In such a case, a Hu‐Washizu principle can be invoked, taking displacement, stress, and strain fields as primary variables . Alternatively, with the clue that a highly nonlinear spatial distribution of the strain field stems from a similar pattern of the plastic strain, a deeply explored strategy amounts at replacing the strain with the plastic multiplier, thus obtaining a complementary mixed formulation …”

Section: Introductionmentioning

confidence: 99%

A mixed finite element for the nonlinear analysis of in‐plane loaded masonry walls

Nodargi

Bisegna

2019

Numerical Meth Engineering

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Summary A mixed membrane eight‐node quadrilateral finite element for the analysis of masonry walls is presented. Assuming that a nonlinear and history‐dependent 2D stress‐strain constitutive law is used to model masonry material, the element derivation is based on a Hu‐Washizu variational statement, involving displacement, strain, and stress fields as primary variables. As the behavior of masonry structures is often characterized by strain localization phenomena, due to strain softening at material level, a discontinuous, piecewise constant interpolation of the strain field is considered at element level, to capture highly nonlinear strain spatial distributions also within finite elements. Newton's method of solution is adopted for the element state determination problem. For avoiding pathological sensitivity to the finite element mesh, a novel algorithm is proposed to perform an integral‐type nonlocal regularization of the constitutive equations in the present mixed formulation. By the comparison with competing serendipity displacement‐based formulation, numerical simulations prove high performances of the proposed finite element, especially when coarse meshes are adopted.

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“…The formulation is presented in the framework of elastic–perfectly plastic materials, where it is able to furnish the desired equilibrium path of multistorey buildings using a restricted number of total Newton‐Riks iterations to solve the global equilibrium equations. In this case, the approach can also be framed as a proximal point formulation with a dual decomposition strategy for a direct evaluation of the limit load according to the static theorem of the limit analysis . Due to the small iterative effort, the approach also compares well with specialized direct methods for limit analysis, with the advantage of providing the load‐displacement relationship.…”

Section: Introductionmentioning

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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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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An algorithm for incremental elastoplastic analysis using equality constrained sequential quadratic programming

Cited by 27 publications

References 25 publications

Composite Fem Models for Limit and Shakedown Analysis

Composite Fem Models for Limit and Shakedown Analysis

A mixed finite element for the nonlinear analysis of in‐plane loaded masonry walls

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

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