Formulation and solution of some plasticity problems as conic programs

Krabbenhøft, K.; Lyamin, A. V.; Sloan, Scott W.

doi:10.1016/j.ijsolstr.2006.06.036

Cited by 277 publications

(176 citation statements)

References 24 publications

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“…A primal-dual interior-point SOCP algorithm can efficiently solve problems involving linear or conic constraints. This algorithm is of particular interest in the field of limit analysis since most plasticity problems can be formulated as conic programming problems [22].…”

Section: Numerical Examplesmentioning

confidence: 99%

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Limit analysis of plates using the EFG method and second‐order cone programming

Gilbert

Askes

2009

Numerical Meth Engineering

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Published paperLe, Canh V., Gilbert, Matthew and Askes, Harm (2009) SUMMARYThe meshless Element-Free Galerkin (EFG) method is extended to allow computation of the limit load of plates. A kinematic formulation which involves approximating the displacement/velocity field using the moving least squares technique is developed. Only one displacement variable is required for each EFG node, ensuring that the total number of variables in the resulting optimization problem is kept to a minimum, with far fewer variables being required compared with finite element formulations. A stabilized conforming nodal integration scheme is extended to plastic plate bending problems. The evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions. Difficulties imposing essential boundary conditions are overcome by enforcing directly displacements at the nodes. The formulation can be expressed as the problem of minimizing a sum of Euclidean norms subject to a set of equality constraints. This non-smooth minimization problem can be transformed into a form suitable for solution using Second-Order Cone Programming (SOCP). The procedure is applied to several benchmark problems and is found in practice to generate good upper bound solutions for benchmark problems.

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Section: Numerical Examplesmentioning

confidence: 99%

“…One of the most efficient algorithms to overcome this difficulty is the primal-dual interior-point method presented in [19,20] and implemented in commercial codes such as the Mosek software package. The limit analysis problem involving conic constraints can then be solved by this efficient algorithm [16,21,22].…”

Section: Introductionmentioning

confidence: 99%

Limit analysis of plates using the EFG method and second‐order cone programming

Gilbert

Askes

2009

Numerical Meth Engineering

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“…The yield function f σ ( ) i is checked in the m points to ensure a safe stress field. For concrete, the Mohr-Coulomb yield criterion is commonly used which can be expressed as conic constraints [21,22].…”

Section: Acknowledgmentmentioning

confidence: 99%

Test and lower bound modeling of keyed shear connections in RC shear walls

Sørensen

Herfelt

Hoang

et al. 2018

Engineering Structures

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A R T I C L E I N F O Keywords:Keyed shear connections Precast concrete Push-off tests Rigid-plasticity Lower bound solutions A B S T R A C T This paper presents an investigation into the ultimate behavior of a recently developed design for keyed shear connections. The influence of the key depth on the failure mode and ductility of the connection has been studied by push-off tests. The tests showed that connections with larger key indentations failed by complete key cut-off. In contrast, connections with smaller key indentations were more prone to suffer local crushing failure at the key corners. The local key corner crushing has an effect on the load-displacement response, which is relatively more ductile. In addition to the tests, the paper also presents lower bound modeling of the load carrying capacity of the connections. The main purpose of the lower bound model is to supplement an already published upper bound model of the same problem and thereby provide a more complete theoretical basis for practical design. The two models display the same overall tendencies although identical results are not possible to obtain, due to differences in the basic assumptions usually made for upper and lower bound analysis of connections. It is found that the test results, consistent with the extremum theorems of plasticity, are all lying within the gap between the upper and the lower bound solution. The obtained results finally lead to a discussion of how the two models can be used in practice. The primary merit of the upper bound model lies in its simplicity (a closed-form equation). On the other hand, the lower bound model provides safe results, but is more complicated to apply. It is therefore argued that the upper bound model may be used in cases, where calibration with tests has been carried out. The lower bound model should be applied in situations, where the design deviates significantly from the configurations of the available tests.

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“…It was recognized in [28] that most commonly used yield criteria can be cast in the form of conic constraints, and optimization problems involving such constraints can be solved using highly efficient solvers [15]. Consequently, several numerical limit analysis procedures which involve the use of cone programming techniques have been reported recently [9,29,30].…”

Section: Second-order Cone Programming (Socp)mentioning

confidence: 99%

“…It is assumed that the slab is isotropic with positive and negative yield moments m p in both directions (constant reinforcement). For this case, the yield criterion (2) may be represented as a square yield locus in the plane of the principal moments [28,34], and the exact solution has been identified by Fox [35] as…”

Section: Numerical Examplesmentioning

confidence: 99%

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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Formulation and solution of some plasticity problems as conic programs

Cited by 277 publications

References 24 publications

Limit analysis of plates using the EFG method and second‐order cone programming

Limit analysis of plates using the EFG method and second‐order cone programming

Test and lower bound modeling of keyed shear connections in RC shear walls

Limit analysis of plates and slabs using a meshless equilibrium formulation

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