Second-Order Cone and Semidefinite Representations of Material Failure Criteria

Bisbos, C.D.; Pardalos, Pãnos M.

doi:10.1007/s10957-007-9243-8

Cited by 50 publications

(50 citation statements)

References 36 publications

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“…More precisely, .˛; 1 ; : : : ; r / is optimal for problem (7) if and only if there exist 1 ; : : : ; r such that .˛; 1 ; : : : ; r ; 1 ; : : : ; r / is optimal for problem (9). Therefore, the optimal value of problem (9) coincides with the shakedown limit load multiplier.…”

Section: Reformulation To Semidefinite Programmingmentioning

confidence: 97%

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Ellipsoidal load-domain shakedown analysis with von Mises yield criterion: A robust optimization approach

Yamaguchi

Kanno

2016

Int. J. Numer. Meth. Engng

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SUMMARYThe static formulation of elastic shakedown analysis, based upon Melan's lower-bound theorem, can essentially be viewed as a robust optimization problem. This paper discusses an advantage that is enjoyed by taking this perspective. Specifically, we assume the von Mises yield criterion and an ellipsoidal load domain. In this setting, the shakedown analysis problem, which is viewed as robust second-order cone programming, can be recast as semidefinite programming.

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Section: Reformulation To Semidefinite Programmingmentioning

confidence: 97%

“…An example is the Ilyushin yield criterion, which can be represented as the intersection of two ellipsoids [9]. In that case, the resulting SDP has two positive semidefinite constraints for each l. Other examples may be found in [35,36].…”

Section: Remark 42mentioning

confidence: 99%

Ellipsoidal load-domain shakedown analysis with von Mises yield criterion: A robust optimization approach

Yamaguchi

Kanno

2016

Int. J. Numer. Meth. Engng

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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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“…Recent advances in mathematical programming have extended interior point algorithms to second-order cone programming (SOCP) problems [2,15,19,20]. SOCP encompasses a larger class of convex optimization problems and an important number of the usual strength criteria can be formulated using SOCP constraints [5,22], allowing us to obtain numerical estimates of limit loads with higher accuracy and small computation times. For these reasons, limit analysis using SOCP formulations has gained increasing attention and was successfully applied to 2D plane strain or plane stress problems [8,23,24,27] as well as plates in bending problems [6,17,18].…”

Section: Introductionmentioning

confidence: 99%

Yield surface approximation for lower and upper bound yield design of 3D composite frame structures

Bleyer

Buhan

2013

Computers & Structures

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surface approximation for lower and upper bound yield design of 3d composite frame structures. Computers and Structures, Elsevier, 2013, 129, pp. 86-98. <10.1016/j.compstruc.2013 AbstractThe present contribution advocates an up-scaling procedure for computing the limit loads of spatial structures made of composite beams. The resolution of an auxiliary yield design problem leads to the determination of a yield surface in the space of axial force and bending moments. A general method for approximating the numerically computed yield surface by a sum of several ellipsoids is developed. The so-obtained analytical expression of the criterion is then incorporated in the yield design calculations of the whole structure, using second-order cone programming techniques. An illustrative application to a complex spatial frame structure is presented.

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Second-Order Cone and Semidefinite Representations of Material Failure Criteria

Cited by 50 publications

References 36 publications

Ellipsoidal load-domain shakedown analysis with von Mises yield criterion: A robust optimization approach

Ellipsoidal load-domain shakedown analysis with von Mises yield criterion: A robust optimization approach

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

Yield surface approximation for lower and upper bound yield design of 3D composite frame structures

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