Non-probabilistic robust continuum topology optimization with stress constraints

Silva, Gustavo Assis da; Cardoso, Eduardo Lenz; Beck, André Teófilo

doi:10.1007/s00158-018-2122-0

Cited by 21 publications

(18 citation statements)

References 39 publications

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“…which are precisely the optimality conditions (18). As will be seen below, the algorithm may generate convergent subsequences which do not converge to stationary points for the Nash game.…”

Section: A Basic Convergence Resultsmentioning

confidence: 98%

“…For the worst-case compliance problem treated herein, the algorithm is not competitive with existing methods for solving the Stackelberg formulation, but algorithms of this type is of interest for other games in SO under uncertainty where it is difficult to find a numerically efficient Stackelberg formulation. [15][16][17][18][19][20] However, further development (to handle large-scale games for instance) and use of the algorithm should be combined with a search for practically verifiable conditions for existence of Nash equilibria.…”

Section: Discussionmentioning

confidence: 99%

“…Attractive features of such algorithms include very simple implementation and parallelization. Decomposition algorithms have previously been used for TO-games, [15][16][17][18][19][20]52,53 although not with the penalty terms used here.…”

Section: Numerical Solution Of Nash Gamesmentioning

confidence: 99%

“…For cases where numerically efficient Stackelberg formulations cannot be found, it is tempting to try staggered solution approaches where one alternates between (i) trying to find the best design for fixed uncertain data and (ii) trying to find the worst response for a fixed design. Recent works used variants of such algorithms, sometimes referred to as decomposition algorithms. In this paper, we consider one such algorithm and show (in Theorem later) that the algorithm, if it converges, converges to a stationary point of a Nash game.…”

Section: Introductionmentioning

confidence: 99%

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Game formulations for structural optimization under uncertainty

Thore

Grundström

Klarbring

2019

Numerical Meth Engineering

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Summary We consider structural optimization (SO) under uncertainty formulated as a mathematical game between two players –– a “designer” and “nature”. The first player wants to design a structure that performs optimally, whereas the second player tries to find the worst possible conditions to impose on the structure. Several solution concepts exist for such games, including Stackelberg and Nash equilibria and Pareto optima. Pareto optimality is shown not to be a useful solution concept. Stackelberg and Nash games are, however, both of potential interest, but these concepts are hardly ever discussed in the literature on SO under uncertainty. Based on concrete examples of topology optimization of trusses and finite element‐discretized continua under worst‐case load uncertainty, we therefore analyze and compare the two solution concepts. In all examples, Stackelberg equilibria exist and can be found numerically, but for some cases we demonstrate nonexistence of Nash equilibria. This motivates a view of the Stackelberg solution concept as the correct one. However, we also demonstrate that existing Nash equilibria can be found using a simple so‐called decomposition algorithm, which could be of interest for other instances of SO under uncertainty, where it is difficult to find a numerically efficient Stackelberg formulation.

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“…which are precisely the optimality conditions (18). As will be seen below, the algorithm may generate convergent subsequences which do not converge to stationary points for the Nash game.…”

Section: A Basic Convergence Resultsmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

Section: Numerical Solution Of Nash Gamesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Game formulations for structural optimization under uncertainty

Thore

Grundström

Klarbring

2019

Numerical Meth Engineering

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“…The source of uncertainty may be the variability of applied loads, spatial positions of nodes, material properties, and so on [2][3][4][5]. Various deterministic and stochastic approaches have been developed to account for different types of uncertainty in structural design and optimization methods to get robust solutions [6][7][8]. In addition, the reliability based topology optimization play important rule to handle uncertainties [9][10][11][12][13] in this research field.…”

Section: Introductionmentioning

confidence: 99%

Critical Investigation of the Combined Compliance Average and Spreading Measures in the Robust Topology Optimization with Uncertain Loading Magnitude and Direction

Csébfalvi

2020

Period. Polytech. Civil Eng.

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The paper critically investigates the role of the combined compliance average and spreading measures in the volume-constrained continuous robust topology optimization with uncertain loading magnitude and direction. In the robust topology optimization the generally expected and most popular robustness measure is the expected compliance, In the expectancy oriented approach, the compliance increment which is needed to get the robust design is an implicitly defined response variable. In order to open the possibility of the creative contribution of the designer to the best robust design searching process, this measure is sometimes combined with a spreading-oriented measure, which may be the variance or standard deviation. The best weighting schema can be done by a try-and-error-like algorithm in which the weights are design variables and the compliance-increment remains an implicitly defined response variable. In this paper, it will be shown that all of the compliance oriented approaches which are based on a single or combined statistical measure can be replaced by a new compliance-function-shape-oriented robust approach in which the allowed-compliance-increment will be an explicitly defined design variable and for a given increment value the robust solution will be the theoretically best one. A popular volume-constrained symmetric bridge problem with uncertain loading magnitude and direction will be presented to demonstrate the viability and efficiency of the proposed robust approach.

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On three concepts in robust design optimization: absolute robustness, relative robustness, and less variance

Kanno

2020

Struct Multidisc Optim

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Non-probabilistic robust continuum topology optimization with stress constraints

Cited by 21 publications

References 39 publications

Game formulations for structural optimization under uncertainty

Game formulations for structural optimization under uncertainty

Critical Investigation of the Combined Compliance Average and Spreading Measures in the Robust Topology Optimization with Uncertain Loading Magnitude and Direction

On three concepts in robust design optimization: absolute robustness, relative robustness, and less variance

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