Sequentially linear modelling of local snap-back in extremely brittle structures

Invernizzi, Stefano; Trovato, Daniele; Hendriks, Max A.N.; Graaf, A.V. Van de

doi:10.1016/j.engstruct.2011.01.031

Cited by 20 publications

(10 citation statements)

References 10 publications

(14 reference statements)

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“…The latter concepts correspond well to the concepts of reinforced and post-tensioned concrete beams. A lot of work has been performed in this field [1][2][3][4][5][6][7][8][9][10][11]. This information is not included in this paper, however some important references on this topic are included at the end of this work.…”

Section: Introductionmentioning

confidence: 94%

Development of composite glass beams – A review

Martens

Caspeele

Belis

2015

Engineering Structures

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Section: Introductionmentioning

confidence: 94%

Development of composite glass beams – A review

Martens

Caspeele

Belis

2015

Engineering Structures

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“…It has been a proven alternative to traditional incremental‐iterative methods for NLFEA of quasi‐brittle structures. SLA, thus far, has had contributions in the contexts of mesh‐objectivity, saw‐tooth laws for extremely brittle materials with snap‐back at constitutive level like glass, extension to non‐proportional loading situations, stepwise secant Coulomb friction laws, creep‐induced cracking, combined incremental‐total approaches like Non‐Iterative Energy‐based Method (NIEM) and the automatic method, combining SLA with a crack tracking technique and non‐proportional loading strategies for three‐dimensional (3D) stress states.…”

Section: Introductionmentioning

confidence: 99%

Two solution strategies to improve the computational performance of sequentially linear analysis for quasi‐brittle structures

Pari

Swart

Gijzen

et al. 2020

Numerical Meth Engineering

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Summary Sequentially linear analysis (SLA), an event‐by‐event procedure for finite element (FE) simulation of quasi‐brittle materials, is based on sequentially identifying a critical integration point in the FE model, to reduce its strength and stiffness, and the corresponding critical load multiplier (λcrit), to scale the linear analysis results. In this article, two strategies are proposed to efficiently reuse previous stiffness matrix factorisations and their corresponding solutions in subsequent linear analyses, since the global system of linear equations representing the FE model changes only locally. The first is based on a direct solution method in combination with the Woodbury matrix identity, to compute the inverse of a low‐rank corrected stiffness matrix relatively cheaply. The second is a variation of the traditional incomplete LU preconditioned conjugate gradient method, wherein the preconditioner is the complete factorisation of a previous analysis step's stiffness matrix. For both the approaches, optimal points at which the factorisation is recomputed are determined such that the total analysis time is minimised. Comparison and validation against a traditional parallel direct sparse solver, with regard to a two‐dimensional (2D) and three‐dimensional (3D) benchmark study, illustrates the improved performance of the Woodbury‐based direct solver over its counterparts, especially for large 3D problems.

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“…SLA is thus an event‐by‐event approach, ie, one linear analysis is performed at a time to identify a critical integration point and the method thereby avoids the problem associated with the regular incremental‐iterative procedures with respect to convergence as it traces through every event, ie, a jump or snap back, that may occur in the response of the structure. The method is a proven alternative for applications in masonry, reinforced concrete, and glass . Advancements in SLA include contributions to make the procedure mesh objective,() saw‐tooth laws for extremely brittle materials with snap back at constitutive level like glass, extension to non‐proportional loading situations,() stepwise secant Coulomb friction laws, combined incremental‐total approaches like non‐iterative energy–based method and the automatic method, SLA in a stochastic setting, combining SLA with crack tracking technique, and mesh‐free SLA .…”

Section: Introductionmentioning

confidence: 99%

Non‐proportional loading in sequentially linear analysis for 3D stress states

Pari

Hendriks

Rots

2019

Numerical Meth Engineering

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Summary Sequentially linear analysis (SLA), a non‐incremental‐iterative approach towards finite element simulation of quasi‐brittle materials, is based on sequentially identifying a critical integration point in the model, to reduce its strength and stiffness, and the associated critical load multiplier (λcrit), to scale the linear analysis results. In this article, two novel methods are presented to enable SLA simulations for non‐proportional loading situations in a three‐dimensional fixed smeared crack framework. In the first approach, the cubic function in the load multiplier is analytically solved for real roots using trigonometric solutions or the Cardano method. In the second approach, the load multiplier is expressed as a function of the inclination of a potential damage plane and is deduced using a constrained optimization approach. The first method is preferred over the second for the validation studies due to computational efficiency and accuracy reasons. A three‐point bending beam test, with and without prestress, and an RC slab tested in shear, with and without axial loads, are used as benchmarks. The proposed solution method shows good agreement with the experiments in terms of force‐displacement curves and damage evolution.

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Sequentially linear modelling of local snap-back in extremely brittle structures

Cited by 20 publications

References 10 publications

Development of composite glass beams – A review

Development of composite glass beams – A review

Two solution strategies to improve the computational performance of sequentially linear analysis for quasi‐brittle structures

Non‐proportional loading in sequentially linear analysis for 3D stress states

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