Equilibrium models for lower bound limit analyses of reinforced concrete slabs

Maunder, E. A. W.; Ramsay, A. C. A.

doi:10.1016/j.compstruc.2012.02.010

Cited by 20 publications

(4 citation statements)

References 15 publications

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“…For example, Anderheggen & Knopfel [8] were among the first to apply finite-element limit-analysis techniques to slabs, showing that rigorous lower bound solutions could be obtained providing a suitable element formulation was employed. More recently, it has been demonstrated that nonlinear optimization [9] and the second-order cone programming techniques [10][11][12] can be applied, obviating the need to linearize the yield surface. Meshless (element-free Galerkin) methods have also been applied to slab problems, and reasonably good approximations of the collapse load factor can be obtained rapidly [13].…”

Section: Introductionmentioning

confidence: 99%

Automatic yield-line analysis of slabs using discontinuity layout optimization

Gilbert

Smith

et al. 2014

Proc. R. Soc. A.

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The yield-line method of analysis is a long established and extremely effective means of estimating the maximum load sustainable by a slab or plate. However, although numerous attempts to automate the process of directly identifying the critical pattern of yield-lines have been made over the past few decades, to date none has proved capable of reliably analysing slabs of arbitrary geometry. Here, it is demonstrated that the discontinuity layout optimization (DLO) procedure can successfully be applied to such problems. The procedure involves discretization of the problem using nodes inter-connected by potential yield-line discontinuities, with the critical layout of these then identified using linear programming. The procedure is applied to various benchmark problems, demonstrating that highly accurate solutions can be obtained, and showing that DLO provides a truly systematic means of directly and reliably automatically identifying yield-line patterns. Finally, since the critical yield-line patterns for many problems are found to be quite complex in form, a means of automatically simplifying these is presented.

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Section: Introductionmentioning

confidence: 99%

Automatic yield-line analysis of slabs using discontinuity layout optimization

Gilbert

Smith

et al. 2014

Proc. R. Soc. A.

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“…They can, therefore, be used in the application of the lower bound theorem of limit analysis. This approach has been initiated in and also in , but in the latter, the equilibrium operators were derived from an initial upper bound yield line analysis. However, further research is necessary in order to guarantee the local enforcement of the yield condition.…”

Section: Discussionmentioning

confidence: 99%

A general degree hybrid equilibrium finite element for Kirchhoff plates

Almeida

Maunder

2013

Numerical Meth Engineering

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SUMMARYWe present a family of hybrid equilibrium finite elements for the quasistatic linear elastic analysis of plates governed by Kirchhoff theory. The moments are approximated by self‐balanced polynomial fields of general degree, and in order to impose strong codiffusivity, the normal boundary rotations are approximated with complete polynomials of the same degree, whereas the transverse deflections use polynomials one degree lower. Furthermore, it is also necessary to include an independent approximation of the vertex translations. We show that the triangular form of this element is stable, that is, free from spurious kinematic modes, and the formulation that we present allows these elements to be used as a standard displacement element. Examples of computed values and convergence of the solutions are presented, which demonstrate the performance of these elements. Copyright © 2013 John Wiley & Sons, Ltd.

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“…This criterion is naturally formulated as rotated quadratic cones , and recently, a formulation with two quadratic cones have been presented . Following the formulation presented in and , the elastic domain can be expressed by intersection of two cones

{boldZ}^{+} \in {bold-italicC}_{5}^{r}

and

{boldZ}^{-} \in {bold-italicC}_{5}^{r}

from and , respectively

{boldZ}^{i} - bold-italicA {boldt}^{i} = {boldb}^{i}

where

{boldZ}^{i} = {([], {boldZ}^{i +}, {boldZ}^{i -})}^{i} = {([], \begin{matrix} z_{0}^{+} \\ z_{1}^{+} \\ z_{2}^{+} \\ z_{3}^{+} \\ z_{4}^{+} \\ z_{0}^{-} \\ z_{1}^{-} \\ z_{2}^{-} \\ z_{3}^{-} \\ z_{4}^{-} \end{matrix})}^{i}, bold-italicA = ([], \begin{matrix} - 1 & 0 & 0 & 0 & 0 \\ 0 & - 1 & 0 & 0 & 0 \\ 0 & 0 & \sqrt{2} & 0 & 0 \\ 0 & 0 & 0 & ε & 0 \\ 0 & 0 & 0 & 0 & ε \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \end{matrix})

…”

Section: Plastic Collapse Analysismentioning

confidence: 99%

Plastic collapse analysis of Mindlin-Reissner plates using a composite mixed finite element

Leonetti

2015

Int. J. Numer. Meth. Engng

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Summary The paper proposes a mixed finite element model and experiments its capability in the analysis of plastic collapse Mindlin–Reissner plates. The model is based on simple assumptions for the unknown fields, ensuring that it is easy to formulate and implement. A composite triangular mesh is assumed over the domain. Within each triangular element, the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece‐wise constant description by introducing a subdivision of the element into three triangular regions. The plastic collapse analysis is formulated as quadratic and conic mathematical programming problem and is accomplished by an interior‐point algorithm, which furnishes both the collapse multiplier and the collapse mechanism. A series of numerical experiments shows that the proposed model performs well in plastic analysis, where it takes advantage of the absence of locking phenomena and the possibility of simply described discontinuities in the plastic deformation field within the element. Copyright © 2015 John Wiley & Sons, Ltd.

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Equilibrium models for lower bound limit analyses of reinforced concrete slabs

Cited by 20 publications

References 15 publications

Automatic yield-line analysis of slabs using discontinuity layout optimization

Automatic yield-line analysis of slabs using discontinuity layout optimization

A general degree hybrid equilibrium finite element for Kirchhoff plates

Plastic collapse analysis of Mindlin-Reissner plates using a composite mixed finite element

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