Optimal Design of Plates, Shells, and Disks

Save, M.

doi:10.1007/978-1-4615-7921-2_6

Cited by 5 publications

(9 citation statements)

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“…For this case the exact collapse load multiplier was given in [8] as λ p = 24 m p qL 2 . When 20×20 nodes were used to model the slab, the corresponding normalized collapse multiplier was found to be 23.996, which is clearly in excellent agreement with the exact solution.…”

Section: Reinforced Concrete Slab Examplesmentioning

confidence: 99%

“…The exact collapse multiplier was given in [8] as λ p = 12 m p qR 2 , where R is the slab radius. The problem was solved using an irregular layout of nodes comprising 49 nodes laid out over the slab, as shown on Figure 9.…”

Section: Reinforced Concrete Slab Examplesmentioning

confidence: 99%

“…[1][2][3][4][5][6][7]. These procedures can provide good bounds on the exact collapse load (or 'load multiplier'), with the results in [1] remarkably providing the best lower-bounds available for plate problems for many years [8]. However, finite element based computational limit analysis methods have drawbacks, and have to date not found widespread use in engineering practice.…”

Section: Introductionmentioning

confidence: 99%

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Limit analysis of plates and slabs using a meshless equilibrium formulation

Gilbert

Askes

2010

Numerical Meth Engineering

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Published paperLe, Canh V., Gilbert, Matthew and Askes, Harm (2010) SUMMARYA meshless Element-Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems.

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Section: Reinforced Concrete Slab Examplesmentioning

confidence: 99%

Section: Reinforced Concrete Slab Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Limit analysis of plates and slabs using a meshless equilibrium formulation

Gilbert

Askes

2010

Numerical Meth Engineering

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“…Suivant [1,15], on fait l'hypothèse classique que les fibres normales à la surface moyenne de la plaque, < (x v x 2 , x 3 ) --< x 3 < -t, conservent leur longueur h et restent normales à la surface moyenne après déformation.…”

Section: Formulation Des Hypothèsesunclassified

“…A cette fin, nous introduisons les notations suivantes : Avec les notations ci-dessus et (3.1), le problème (3.3) s'écrit : 15) son dual est donc …”

Section: G*(e R) = H*(qr)dx Si (Qr)ek (37)unclassified

Étude dans $HB \times BD$ d’un modèle de plaques élastoplastiques comportant une non-linéarité géométrique

Hadhri

1985

ESAIM: M2AN

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Optimization of plastic shallow shells exhibiting nonstable behaviour

Lellep

Majak

1995

Structural Optimization

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An optimal design technique is suggested for axisymmetric shallow shells exhibiting nonstable behaviour in the post-yield point range. The material of the shells is ideally rigidplastic obeying the yon Mises yield condition, which is satisfied in the average and the associated deformation law. Spherical shells pierced with a hole and subjected to uniformly distributed transverse pressure are studied. Different cases of the support .conditions are considered. Making use of themethods of the optimal control theory the problem is transformed into a boundary value problem which is solved numerically.

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Optimal Design of Plates, Shells, and Disks

Cited by 5 publications

References 0 publications

Limit analysis of plates and slabs using a meshless equilibrium formulation

Limit analysis of plates and slabs using a meshless equilibrium formulation

Étude dans $HB \times BD$ d’un modèle de plaques élastoplastiques comportant une non-linéarité géométrique

Optimization of plastic shallow shells exhibiting nonstable behaviour

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