Dual finite-element analysis using second-order cone programming for structures including contact

Boustani, Chadi El; Bleyer, Jérémy; Arquier, Mathieu; Ferradi, Mohammed-Khalil; Sab, Karam

doi:10.1016/j.engstruct.2019.109892

Cited by 11 publications

(18 citation statements)

References 57 publications

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“…It must be kept in mind that the discrete optimization problems associated with J stat,h and J kin,h are not dual to each other in the convex optimization sense since they are associated with different discretization strategies. They however offer a bracketing of the true solution since the accuracy of the discretized solution can be compared by computing J kin,h + J stat,h (see [17]). We later refer to this quantity as the primal-dual gap i.e.…”

Section: Variational Formulation For Elastoplasticitymentioning

confidence: 99%

“…With a von Mises material, both problems fall into the class of second-order cone programming problems for which interior-point algorithms are well suited. Let us mention that we can also add unilateral or associated frictional contact conditions to both formulations following the lines of [17] without changing the second-order cone nature of the problem.…”

Section: Variational Formulation For Elastoplasticitymentioning

confidence: 99%

“…in which the primal optimization variables arex = (∆û, ∆ε p , ∆γ). As mentioned previously, contact constraints can be added and enforced at all 6 nodes of each face following [17]. After introducing a proper change of variable, the contact conditions can be easily transformed into a standard second-order cone constraint using a Lorentz cone.…”

Section: Kinematic Approach 411 Continuous Discretizationmentioning

confidence: 99%

“…Some contributions also explored the use of this framework for other applications such as granular media [13,14], contact [15][16][17], viscoplastic flows [18,19] or elastoplastic computations [15,[20][21][22]. The latter case is of interest since limit analysis does not guarantee a unique solution as regards failure mechanisms nor does it enable to compute the structure displacements and total strains.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of the present manuscript is to provide a general framework for computing efficiently the ultimate state of complex steel assemblies including plasticity. Following on the ideas of [17], we will resort to a dual finite-element discretization involving kinematic displacement-based elements as well as static equilibrium-based elements providing, respectively, an upper and lower bounds estimate to the exact solution and, in particular, to the exact structure ultimate load. Both computations can be also be used to compute a constitutive error indicator which can be used in a remeshing algorithm.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Elastoplastic and limit analysis of 3D steel assemblies using second-order cone programming and dual finite-elements

Boustani

Bleyer

Arquier³

et al. 2020

Engineering Structures

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We investigate the use of a second-order cone programming (SOCP) framework for computing complex 3D steel assemblies in the context of elastoplasticity and limit analysis. Displacement and stress-based variational formulations are considered and appropriate finite-element discretization strategies are chosen, yielding respectively an upper and lower bound estimate of the exact solution. An efficient interior-point algorithm is used to solve the associated optimization problems. The discrete solution convergence is estimated by comparing both static and kinematic solutions, offering a way to perform local mesh adaptation. The proposed framework is illustrated on the design of a moment-transmitting assembly, its performance is assessed by comparison with classical elastoplastic computations using Abaqus and, finally, T-stub resistance and failure mechanisms when assessing the strength of a column base plate are compared with the Eurocodes design rules.

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Section: Variational Formulation For Elastoplasticitymentioning

confidence: 99%

Section: Variational Formulation For Elastoplasticitymentioning

confidence: 99%

Section: Kinematic Approach 411 Continuous Discretizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Elastoplastic and limit analysis of 3D steel assemblies using second-order cone programming and dual finite-elements

Boustani

Bleyer

Arquier³

et al. 2020

Engineering Structures

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A variational rigid‐block modeling approach to nonlinear elastic and kinematic analysis of failure mechanisms in historic masonry structures subjected to lateral loads

Portioli

Godio

Calderini

et al. 2021

Earthq Engng Struct Dyn

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Displacement-based methods contained in recent standards for seismic safety assessment require the determination of the full nonlinear pushover curve for local failure mechanisms in historic masonry structures. This curve should reflect both the initial elastic behavior and the rigid body behavior after the activation of rocking. In this work, a rigid block model is proposed for the displacement-based seismic assessment of local collapse mechanisms of these structures. Masonry is modeled as an assemblage of two-dimensional rigid blocks in contact through frictional interfaces. Two types of contact models are formulated to capture, respectively, the pre and postpeak branches of the pushover curve: a unilateral elastic contact model, capturing the initial nonlinear behavior up to the force capacity of the structure, corresponding to the activation of the collapse mechanism, and a rigid contact model with finite friction and compressive strength, which describes the rigid-body rocking behavior up to the attainment of the displacement capacity of the structure. Tension-only elements are also implemented to model strengthening interventions with tie-rods. The contact problems associated with the elastic and rigid contact models are formulated using mathematical programming. For both models, a sequential solution procedure is implemented to capture the variation of the load multiplier with the increasing deformation of the structure (P-Δ effect). The accuracy of the modeling approach in reproducing the pushover curve of masonry panels subjected to horizontal seismic loads is evaluated on selected case studies. The solution is first tested against hand calculations, existing analytical models, and distinct element simulations. Then, comparisons against experimental tests follow. As a final application, the failure mechanism and pushover curve of a triumphal masonry arch are predicted by the model and its seismic assessment is performed according to codified force-and displacement-based methods, demonstrating the adequacy of the proposed tool for practice.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Numerical upper bounds to the ultimate load bearing capacity of three‐dimensional reinforced concrete structures

Vincent

Arquier²,

Bleyer

et al. 2020

Num Anal Meth Geomechanics

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This contribution is addressing the ultimate limit state design of massive three-dimensional reinforced concrete structures based on a finite-element implementation of yield design theory. The strength properties of plain concrete are modeled either by means of a tension cutoff Mohr Coulomb or a Rankine condition, while the contribution of the reinforcing bars is taken into account by means of a homogenization method. This homogenization method can either represent regions of uniformly distributed steel rebars smeared into the concrete domain, but it can also be extended to model single rebars diluted into a larger region, thereby simplifying mesh generation and mesh size requirements in this region. The present paper is mainly focused on the implementation of the upper bound kinematic approach formulated as a convex minimization problem. The retained strength condition for the plain concrete and homogenized reinforced regions are both amenable to a formulation involving positive semidefinite constraints. The resulting semidefinite programming problems can, therefore, be solved using state-of-the-art dedicated solvers. The whole computational procedure is applied to some illustrative examples, where the implementation of both static and kinematic methods produces a relatively accurate bracketing of the exact failure load for this kind of structures. K E Y W O R D S finite element, homogenization, reinforced concrete structures, semidefinite programming, tension cutoff Mohr-Coulomb strength condition, upper bound kinematic approach, yield design 1 INTRODUCTION Assessing the ultimate load bearing capacity of constructions involving massive three-dimensional reinforced concrete components requires a specific analysis, such as the widely acknowledged "strut-and-tie" model (see among many other Refs. 1-4), which can be related to the lower bound static approach of yield design. Indeed, such "D" (Disturbed or Discontinuity) regions, as opposed to "B" (Beam) regions, in the context of the strut-and-tie method cannot be modeled with enough accuracy using simple beam or plate/shell models. Such regions often require a fully 3D analysis, which is difficult to perform manually and therefore require some computational assistance. Typical examples are corbels, deep beams, pier or pile caps, footings, and so on. With a special attention to assessing the ultimate shear capacity of 2216

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Dual finite-element analysis using second-order cone programming for structures including contact

Cited by 11 publications

References 57 publications

Elastoplastic and limit analysis of 3D steel assemblies using second-order cone programming and dual finite-elements

Elastoplastic and limit analysis of 3D steel assemblies using second-order cone programming and dual finite-elements

A variational rigid‐block modeling approach to nonlinear elastic and kinematic analysis of failure mechanisms in historic masonry structures subjected to lateral loads

Numerical upper bounds to the ultimate load bearing capacity of three‐dimensional reinforced concrete structures

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