Shakedown Analysis of Plate Bending Under Stochastic Uncertainty by Chance Constrained Programming

Trần, Ngọc Trình; Tran, Thanh Ngoc; Matthies, Hermann G.; Stavroulakis, Georgios Ε.; Staat, Manfred

doi:10.7712/100016.2012.11106

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…. Based on the methodology of chance constrained programming, problem (3.4) can be converted into a equivalent deterministic program as shown in [10], [11]:…”

Section: Static Approach With Chance Constrained Programmingmentioning

confidence: 99%

“…Problem (4.7) is a stochastic program, which can be converted into an equivalent deterministic program by using a chance constrained programming technique [10], [11]. 1…”

Section: Kinematic Approach With Chance Constrained Programmingmentioning

confidence: 99%

“…Limit analysis of plates in bending has been studied analytically and numerically [11]- [23]. Due to limitations of analytical methods, alternative numerical approaches such as finite element methods (FEM), meshfree methods or isogeometric analysis (IGA) have been developed.…”

Section: Introductionmentioning

confidence: 99%

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Fem Shakedown Analysis of Kirchoff-Love Plates Under Uncertainty of Strength

Trần¹,

Staat²

2021

4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

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A new formulation to calculate the shakedown limit load of Kirchhoff plates under stochastic conditions of strength is developed. Direct structural reliability design by chance constrained programming is based on the prescribed failure probabilities, which is an effective approach of stochastic programming if it can be formulated as an equivalent deterministic optimization problem. We restrict uncertainty to strength, the loading is still deterministic. A new formulation is derived in case of random strength with lognormal distribution. Upper bound and lower bound shakedown load factors are calculated simultaneously by a dual algorithm.

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“…. Based on the methodology of chance constrained programming, problem (3.4) can be converted into a equivalent deterministic program as shown in [10], [11]:…”

Section: Static Approach With Chance Constrained Programmingmentioning

confidence: 99%

“…Problem (4.7) is a stochastic program, which can be converted into an equivalent deterministic program by using a chance constrained programming technique [10], [11]. 1…”

Section: Kinematic Approach With Chance Constrained Programmingmentioning

confidence: 99%

See 1 more Smart Citation

Fem Shakedown Analysis of Kirchoff-Love Plates Under Uncertainty of Strength

Trần¹,

Staat²

2021

4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

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FEM Shakedown of uncertain structures by chance constrained programming

Trần

Tran

Matthies

et al. 2016

Proc Appl Math and Mech

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We present a new primal‐dual numerical algorithm of the shakedown problem under uncertainty in which the material strength is considered as a normally distributed random variable. Using chance constrained programming, we obtain deterministic equivalent formulations based on upper bound and lower bound theorems which are dual to each other. The proposed algorithm is tested in numerical examples which are applied to civil engineering structures. The obtained solutions show good performance. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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