Level set based robust shape and topology optimization under random field uncertainties

Chen, Shikui; Chen, Wei; Lee, Sanghoon

doi:10.1007/s00158-009-0449-2

Cited by 219 publications

(85 citation statements)

References 44 publications

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“…Since mid-2000 there has been increasing research on reliability based topology optimization (RBTO) considering uncertainties in loads, material, boundary geometry or fabrication. Since this work doesn't directly build on earlier RBTO contributions, we simply refer to Deaton and Grandhi (2014) for literature survey, and to select papers for further reading: Maute and Frangopol (2003), Kharmanda et al (2004), Jung and Cho (2004), Guest and Igusa (2008), Silva et al (2010), Chen et al (2010), Chen and Chen (2011), Lazarov et al (2012), Nguyen et al (2011), Rozvany and Maute (2011), Tootkaboni et al (2012), Wang et al (2006). However, as also pointed out by Jansen et al (2014), due to the binary nature of failure definition it is difficult to treat failsafe requirement within statistics based RBTO framework.…”

Section: Introductionmentioning

confidence: 99%

Fail-safe topology optimization

Zhou

Fleury

2016

Struct Multidisc Optim

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Fail-safe robustness of critical load carrying structures is an important design philosophy for aerospace industry. The basic idea is that a structure should be designed to survive normal loading conditions when partial damage occurred. Such damage is quantified as complete failure of a structural member, or a partial damage of a larger structural part. In the context of topology optimization fail-safe consideration was first proposed by Jansen et al. Struct Multidiscip Optim 49(4):657-666, (2014). While their approach captures the essence of fail-safe requirement, it has two major shortcomings: (1) it involves analysis of a very large number of FEA models at the scale equal to the number of elements; (2) failure was introduced in generic terms and therefore the fundamental aspects of failure test of discrete members was not discussed. This paper aims at establishing a rigorous framework for failsafe topology optimization of general 3D structures, with the goal to develop a computationally viable solution for industrial applications. We demonstrate the effectiveness of the proposed approach on several examples including a 3D example with over three hundred thousand elements.

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Section: Introductionmentioning

confidence: 99%

Fail-safe topology optimization

Zhou

Fleury

2016

Struct Multidisc Optim

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“…In this way spatially varying geometric imperfections can be easily represented. Similar models for level set approaches have been proposed in [30] and [31]. An additional study including spatially varying uncertainties in the material parameters is presented in [91].…”

Section: Topology Optimization Under Geometrical Uncertaintiesmentioning

confidence: 99%

Length scale and manufacturability in density-based topology optimization

2016

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Since its original introduction in structural design, density based topology optimization has been applied to a number of other fields like microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it can provide competitive designs in terms of cost, materials and functionality under a wide set of constraints. However, the optimized topologies are often considered as conceptual due to loosely defined topologies and the need of post processing. Subsequent amendments can affect the optimized design performance and in many cases can completely destroy the optimality of the solution. Therefore, the goal of this paper is to review recent advancements in obtaining manufacturable topology optimized designs. The focus is on methods for imposing minimum and maximum length scale, and ensuring manufacturable, well defined designs with robust performances. The overview discusses the limitations, the advantages and the associated computational costs. The review is completed with optimized designs for minimum compliance, mechanism design and heat transfer.

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“…Takezawa et al [Takezawa et al, 2011] proposed a topology optimization for a design problem formulated to minimize robust compliance defined as the maximum compliance induced by the worst load case of an uncertain load set. Chen et al [Chen et al, 2010] applied the random field process to evaluate a reduced set of random variables. Dunning and Kim [Dunning and Kim, 2013] developed robust topology optimization for a problem considering multiple loads.…”

Section: Introductionmentioning

confidence: 99%

Robust topology optimization of thin plate structure under concentrated load with uncertain load position

Nakazawa

Kogiso

Yamada

et al. 2016

JAMDSM

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This study investigates the robust topology optimization of a thin plate structure under a concentrated load with load position uncertainty. The effect of uncertain load direction, load magnitude, and load distribution in topology optimization problems has been investigated in previous research, but few studies have dealt with robust topology optimization considering load position uncertainty. In this study, load position uncertainty is modeled using the convex hull model, in which the load position uncertainty is confined within a circular area whose center is at the nominal load position. The worst load condition is defined as that when the applied load is at a position in the convex hull that gives the worst value of the mean compliance. Here, the robust objective function is formulated as a weighted sum of the mean compliance obtained from the mean load condition and the worst compliance obtained from the worst load condition, with a plate model based on Reissner-Mindlin plate theory. The robust topology optimization problem is formulated using a level set-based topology optimization method. Through numerical examples, robust optimum configurations are compared with deterministic optimum configurations and the validity of the proposed robust design method is then discussed.

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Level set based robust shape and topology optimization under random field uncertainties

Cited by 219 publications

References 44 publications

Fail-safe topology optimization

Fail-safe topology optimization

Length scale and manufacturability in density-based topology optimization

Robust topology optimization of thin plate structure under concentrated load with uncertain load position

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