Yield design of reinforced concrete slabs using a rotation-free meshfree method

Le, Canh V.; Ho, Phuc L.H.; Nguyen, Phuong H.; Chu, Thang Q.

doi:10.1016/j.enganabound.2014.09.001

Cited by 14 publications

(5 citation statements)

References 21 publications

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“…Finally, an arbitrary concrete slab, as shown in Figure , will be analysed by considering isotropic yield moment conditions

M_{x}^{+} = M_{y}^{+} = M_{x}^{-} = M_{y}^{-} = m_{p} = 1.0

and the parameter ε = 1/100. Collapse multipliers for three different meshes were reported in Table , showing that present numerical solutions are in good agreement with those obtained in .…”

Section: Numerical Resultssupporting

confidence: 81%

“…Finally, an arbitrary concrete slab, as shown in Figure 17 Table XI, showing that present numerical solutions are in good agreement with those obtained in [25,49].…”

Section: Arbitrary Geometric Concrete Slabsupporting

confidence: 81%

“…The Nielsen criterion is currently used to evaluate yield state of reinforced concrete slabs. It is formulated as function of moments and classically is used for the analysis of Kirchhoff plates

\frac{1}{2} m^{T} H + m^{T} G_{1} \leq M_{x}^{+} M_{y}^{+}

\frac{1}{2} m^{T} H - m^{T} g_{2} \leq M_{x}^{-} M_{y}^{-}

- M_{x}^{-} \leq M_{x} \leq M_{x}^{+}

- M_{y}^{-} \leq M_{y} \leq M_{y}^{+}

where

bold-italicH = ([], \begin{matrix} \cdot & - 1 & \cdot \\ - 1 & \cdot & \cdot \\ \cdot & \cdot & 2 \end{matrix}), {bold-italicg}_{1} = ([], \begin{matrix} M_{x}^{+} \\ M_{y}^{+} \\ 0 \end{matrix}) {bold-italicg}_{2} = ([], \begin{matrix} M_{x}^{-} \\ M_{y}^{-} \\ 0 \end{matrix})

…”

Section: Constitutive Equations and Yield Criteriamentioning

confidence: 99%

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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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“…Finally, an arbitrary concrete slab, as shown in Figure , will be analysed by considering isotropic yield moment conditions

M_{x}^{+} = M_{y}^{+} = M_{x}^{-} = M_{y}^{-} = m_{p} = 1.0

and the parameter ε = 1/100. Collapse multipliers for three different meshes were reported in Table , showing that present numerical solutions are in good agreement with those obtained in .…”

Section: Numerical Resultssupporting

confidence: 81%

“…Finally, an arbitrary concrete slab, as shown in Figure 17 Table XI, showing that present numerical solutions are in good agreement with those obtained in [25,49].…”

Section: Arbitrary Geometric Concrete Slabsupporting

confidence: 81%

\frac{1}{2} m^{T} H + m^{T} G_{1} \leq M_{x}^{+} M_{y}^{+}

\frac{1}{2} m^{T} H - m^{T} g_{2} \leq M_{x}^{-} M_{y}^{-}

- M_{x}^{-} \leq M_{x} \leq M_{x}^{+}

- M_{y}^{-} \leq M_{y} \leq M_{y}^{+}

where

bold-italicH = ([], \begin{matrix} \cdot & - 1 & \cdot \\ - 1 & \cdot & \cdot \\ \cdot & \cdot & 2 \end{matrix}), {bold-italicg}_{1} = ([], \begin{matrix} M_{x}^{+} \\ M_{y}^{+} \\ 0 \end{matrix}) {bold-italicg}_{2} = ([], \begin{matrix} M_{x}^{-} \\ M_{y}^{-} \\ 0 \end{matrix})

…”

Section: Constitutive Equations and Yield Criteriamentioning

confidence: 99%

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

Leonetti

2015

Int. J. Numer. Meth. Engng

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“…Methods for constructing stress and displacement fields in reinforced concrete slabs are considered in [18]. The proposed algorithm based on the Nielsen criterion, using a rotationfree meshless model and a second-order cone as a strength criterion, is in good agreement with these calculations by other methods.…”

Section: Introductionmentioning

confidence: 82%

Research of the stress-strain state of a reinforced concrete beamless floor

2021

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In the article, the authors present the results of a study of a flat reinforced concrete beamless floor of an existing building. The experiment consisted of loading a slab in span with water tanks. There were 15 loading stages in total, on average 4 kN. During the experiment, data was obtained on the relative deformations of concrete and reinforcement in the span and on the support. Also, observations of the growth of vertical deformations and the growth of cracks in the span were introduced.

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“…In this section, fundamentals of yield design theory are recalled, more details can be found in [45,[51][52][53][54]. Consider a elastic-plastic body of area Ω ∈ R 2 with fixed boundary Γ u and free portion Γ t , satisfying Γ u ∪ Γ t = Γ, Γ u ∩ Γ t = ⊘, and is subjected to body forces f and surface tractions t. Let Σ denotes a space of a statically admissible stress state, whereas Y is a space of a kinematically admissible displacement state.…”

Section: Fundamentals Of Yield Design Theorymentioning

confidence: 99%

Displacement and equilibrium mesh-free formulation based on integrated radial basis functions for dual yield design

Tran-Cong

2016

Engineering Analysis with Boundary Elements

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This paper presents displacement and equilibrium mesh-free formulation based on integrated radial basis functions (iRBF) for upper and lower bound yield design problems. In these approaches, displacement and stress fields are approximated by the integrated radial basis functions, and the equilibrium equations and boundary conditions are imposed directly at the collocation points. In the paper it has been shown that direct nodal integration of the iRBF approximation can prevent volumetric locking in the kinematic formulation, and instability problems can also be avoided. Moreover, with the use of the collocation method in the static problem, equilibrium equations and yield conditions only need to be enforced at the nodes, leading to the reduction in computational cost. The mean value of the approximated upper and lower bound is found to be in excellent agreement with the available analytical solution, and can be considered as the actual collapse load multiplier for most practical engineering problems, for which exact solution is unknown.

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Yield design of reinforced concrete slabs using a rotation-free meshfree method

Cited by 14 publications

References 21 publications

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

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

Research of the stress-strain state of a reinforced concrete beamless floor

Displacement and equilibrium mesh-free formulation based on integrated radial basis functions for dual yield design

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