New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions<sup>#</sup>

Lógó, János

doi:10.1080/15397730701243066

Cited by 47 publications

(31 citation statements)

References 11 publications

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“…Since the mathematical nature of the problem (10) is similar to a classical topology optimization problem all the mathematical statements concerning convexity and differentiability are valid too (Rozvany [19], Lógó [11,13]). The penalization of the ground element thicknesses t g results in a more distinct material distribution indicating material or no material.…”

Section: Probabilistic Compliance Design In the Case Of Uncertain Loamentioning

confidence: 99%

“…(For sake of simplicity it is assumed, otherwise instead of Prekopa's theorem the original Kataoka-theorem is used.) By the use of a generalized compliance design concept (Lógó [13]) a new constraint…”

Section: Probabilistic Compliance Designmentioning

confidence: 99%

“…(10b-d)) can be solved by the use of a modified SIMP algorithm (Lógó [13]). The iterative algorithm is derived from the first order optimality conditions.…”

Section: Probabilistic Compliance Design In the Case Of Uncertain Loamentioning

confidence: 99%

“…Monte Carlo simulation together with second-order elastic analysis is used to verify that solutions offer improved performance in the presence of geometric uncertainties. Lógó [13] and Lógó et al [12,14] elaborated a rather powerful method for the stochastic topology optimization where the magnitude of the loads or the compliance bounds are given by their mean values, covariances and distribution functions. By the use of direct integration technique for the calculation of the uncertain bounds or applying an appropriate approximation for the loading uncertainties the stochastic expressions are substituted by an equivalent deterministic ones to make the optimization problem robust.…”

Section: Introductionmentioning

confidence: 99%

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SIMP type topology optimization procedure considering uncertain load position

Lógó

2012

Per. Pol. Civil Eng.

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IntroductionThe topology optimization has more than 100 years of history and still it is an expanding field in structural optimization. The numerical procedure for FE (finite element) based topology optimization of continuum type of structures was elaborated first by Rossow and Taylor [19] in 1973, but the real expansion started at the end of 80-s [4,20]. The majority of the papers still deal with deterministic problems. During these years several optimal topologies were numerically calculated but the analytical confirmations -which have come recently (Rozvany [21], Sokółet. al [22]) -are mostly missing. Until the end of the last century almost one could not find any publication on topology optimization considering uncertainties.During the last years before the millennium almost there were no publications in the topic of probability based topology optimization. The stochastic optimization works of Marti and Stöckl [16,17] provide early information about this topic. The paper of Duan et al. [5] is among the very first publications in the field of uncertainty based topology optimization. This work presents an entropy-based topological optimization method for truss structures by the use of iteration technique. Also a truss topology optimization (layout optimization) of the object of the paper of Alvarez and Carrasco [1] in case stochastic loading. They showed mathematically that a problem of finding the truss of minimum expected compliance (stability of the members are not considered) under stochastic loading conditions is equivalent to the dual of a special convex minimax problem. Dunning et al. [6,7] introduce an efficient and accurate approach to robust structural topology optimization for continuum type of problems. The objective is to minimize expected compliance with uncertainty in loading magnitude and applied direction, where uncertainties are assumed normally distributed and statistically independent. This approach is analogous to a multiple load case problem where load cases and weights are derived analytically to accurately and efficiently compute expected compliance and sensitivities. Illustrative examples using a level-set-based topology optimization method are then used to demonstrate the proposed approach.Topology optimization with uncertainty in the magnitude and

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Section: Probabilistic Compliance Design In the Case Of Uncertain Loamentioning

confidence: 99%

Section: Probabilistic Compliance Designmentioning

confidence: 99%

“…(10b-d)) can be solved by the use of a modified SIMP algorithm (Lógó [13]). The iterative algorithm is derived from the first order optimality conditions.…”

Section: Probabilistic Compliance Design In the Case Of Uncertain Loamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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SIMP type topology optimization procedure considering uncertain load position

Lógó

2012

Per. Pol. Civil Eng.

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“…[7] and [8]). To find the optimal operation scheme of a reservoir system there are several optimisation scheme too (see e.g.…”

Section: Optimisationmentioning

confidence: 99%

A simulation-optimisation methodology for designing the operation of emergency reservoirs in the Hungarian Tisza basin

Koncsos¹,

Balogh²

2010

Per. Pol. Civil Eng.

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This work reports the results of an investigation of reservoirs that were selected in Hungary in the framework of a new flood control strategy for the River Tisza, the largest tributary of the River Danube. Through a comprehensive analysis the optimal operation mode was identified, which would need to be applied to achieve the maximum decreasing effect on peak water levels. The flood waves were simulated using a 1D hydrodynamical model, which is based on the Saint-Venant equations. Both measured and synthetic discharge data were used as boundary conditions. The time lead as compared to the flood peak was determined for the reservoir system. On the Upper-Tisza the figures exceed the order of magnitude of the possible time lead of the realistic forecast, meaning that further research of the reconditioned discharge forecast is necessary. The investigation results of the interaction of two reservoirs showed that the sum of the decreasing effects on water levels when separated reservoirs work independently approaches the decreasing effect of the jointly operating reservoirs reasonably well. Therefore the joint impacts can be estimated using quick linear programming methods.Keywords flood control · reservoir systems · 1D hydrodynamic model Acknowledgement This work is connected to the scientific program of the "Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project.

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Robust topology optimization under loading uncertainties via stochastic reduced order models

Torres

Warner

Aguiló³

et al. 2021

Numerical Meth Engineering

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An efficient approach for topology optimization under uncertainty is presented.Stochastic reduced order models (SROMs) are leveraged for the modeling and propagation of uncertainties within a robust topology optimization (RTO) formulation. The SROM approach provides an alternative to existing uncertainty quantification methods and yields a substantial improvement in efficiency over a classical Monte Carlo based approach while retaining similar accuracy when representing the uncertainty in system parameters. In particular, random input parameters can be discrete or continuous and specified either analytically (standard distributions) or numerically (dataset samples). Furthermore, multiple random quantities need not be treated as uncorrelated; an SROM can seamlessly model random vectors with arbitrary correlation structure. The nonintrusive nature of the SROM method yields an implementation that can be seen as a drop-in replacement for a simple RTO approach that leverages Monte Carlo simulation and is therefore straightforward to implement in existing topology optimization software. The proposed approach is demonstrated in the context of structural topology optimization with uncertainty in applied loads. Several numerical results are presented, covering a range of uncertainty distributions that illustrate the flexibility afforded by the general SROM method, while highlighting the efficiency and accuracy achieved in uncertainty propagation.

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New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#

Cited by 47 publications

References 11 publications

SIMP type topology optimization procedure considering uncertain load position

SIMP type topology optimization procedure considering uncertain load position

A simulation-optimisation methodology for designing the operation of emergency reservoirs in the Hungarian Tisza basin

Robust topology optimization under loading uncertainties via stochastic reduced order models

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New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions#

Cited by 47 publications

References 11 publications

SIMP type topology optimization procedure considering uncertain load position

SIMP type topology optimization procedure considering uncertain load position

A simulation-optimisation methodology for designing the operation of emergency reservoirs in the Hungarian Tisza basin

Robust topology optimization under loading uncertainties via stochastic reduced order models

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New Type of Optimality Criteria Method in Case of Probabilistic Loading Conditions^#