A novel reliability‐based topology optimization framework for the concurrent design of solid and truss‐like material structures with unknown‐but‐bounded uncertainties

Wang, Lei; Liang, Jinxiong; Li, Dongliang; Chen, Wenpin

doi:10.1002/nme.6048

Cited by 13 publications

(4 citation statements)

References 52 publications

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“…The validation of their approach was carried out through aircraft structures. After that, Wang et al (2019a) developed a new RBTO framework for the concurrent design of solid and truss-like material structures with unknown but bounded uncertainties. In the same period, Wang et al (2019b) developed an RBTO approach for continuum structures under interval uncertainties.…”

Section: Classification According To Rbto Formulationsmentioning

confidence: 99%

Two decades review of reliability-based topology optimization developments

Kharmanda¹,

Mulki²

2022

IncertFia

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This review seeks to classify the different developments of the Reliability-Based Topology Optimization (RBTO) according to their formulations and methods. According to the RBTO formulations, two standpoints (topology and reliability standpoints) are generally treated, while according to methods, they are divided into loop and mixed methods. The different trends and gaps are discussed later. The selected publications over the last two decades (from December 2001 to December 2021) contain the term RBTO in their title and restricted to English language. There are several other publications, which have been written in other languages and some others containing the integration of the reliability analysis into topology optimization, but the RBTO was not included in their titles. These two types of publications are unfortunately not included in this review since it is the objective to provide the readers (especially the new researchers) a good guide (map) to the different RBTO developments and applications. Some additional publications considering other objective and constraint functions and dealing the RBTO with microstructural levels are also included since they were realized under the same period and containing the term of RBTO in their title. The first publication of the Reliability-Based Topology Optimization model was a technical report at Aalborg University in Denmark, published in December 2001. It was a new model where many critical discussions appeared between the topology optimization community and the reliability one during 2002 and 2003 (in several meetings and conferences). That led to delay the appearance of the first journal articles until 2004. According to the author's knowledge, more than 70 journal papers and more than 25 other publications (conference papers, chapters, reports... etc.) have been found during the last two decades. Almost 50% of journal papers have been published during the last four years which means that there is a strong interest to implement this model.

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Section: Classification According To Rbto Formulationsmentioning

confidence: 99%

Two decades review of reliability-based topology optimization developments

Kharmanda¹,

Mulki²

2022

IncertFia

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“…Due to the diffusion and reaction of oxygen and aluminum, an additional layer called TGO (thermally-grown oxide) is formed at the interface between TC and BC ( Figure 4). For the whole high-temperature oxidation, the oxides were primarily Al 2 O 3 and a small amount of Cr and Co oxides at the TC/BC (bond-coat) interface [47]. During the development of TGO, the local accumulation of TGO has a profound effect on the stress distribution near the interface.…”

Section: Tgomentioning

confidence: 99%

Research Progress of Failure Mechanism of Thermal Barrier Coatings at High Temperature via Finite Element Method

Liu

Wang

et al. 2020

Coatings

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In the past decades, the durability of thermal barrier coatings (TBCs) has been extensively studied. The majority of researches emphasized the problem of oxidation, corrosion, and erosion induced by foreign object damage (FOD). TBCs with low thermal conductivity are usually coated on the hot-section components of the aircraft engine. The main composition of the TBCs is top-coat, which is usually regarded as a wear-resistant and heat-insulating layer, and it will significantly improve the working temperature of the hot-section components of the aircraft engine. The application of TBCs are serviced under a complex and rigid environment. The external parts of the TBCs are subjected to high-temperature and high-pressure loading, and the inner parts of the TBCs have a large thermal stress due to the different physical properties between the adjacent layers of the TBCs. To improve the heat efficiency of the hot-section components of aircraft engines, the working temperature of the TBCs should be improved further, which will result in the failure mechanism becoming more and more complicated for TBCs; thus, the current study is focusing on reviewing the failure mechanism of the TBCs when they are serviced under the actual high temperature conditions. Finite element simulation is an important method to study the failure mechanism of the TBCs, especially under some extremely rigid environments, which the experimental method cannot realize. In this paper, the research progress of the failure mechanism of TBCs at high temperature via finite element modeling is systematically reviewed.

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“…Deng et al [50] investigated a RTO approach for the multiscale structure and multi porous with random field uncertainty. Wang et al [51,52] introduced two RBTO frameworks for the CTO of solid and truss-like structure considering unknown-but-bounded uncertainties. Besides, hybrid interval random model is also involved in the CTO.…”

Section: Introductionmentioning

confidence: 99%

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This paper studied a robust concurrent topology optimization (RCTO) approach to design the structure and its composite materials simultaneously. For the first time, the material uncertainty with imprecise probability is integrated into the multi-scale concurrent topology optimization (CTO) framework. To describe the imprecise probabilistic uncertainty efficiently, the type I hybrid interval random model is adopted. An improved hybrid perturbation analysis (IHPA) method is formulated to estimate the expectation and stand variance of the objective function in the worst case. Combined with the bi-directional evolutionary structural optimization (BESO) framework, the robust designs of the structure and its composite material are carried out. Several 2D and 3D numerical examples are presented to illustrate the effectiveness of the proposed method. The results show that the proposed method has high efficiency and low precision loss. In addition, the proposed RCTO approach remains efficient in both of linear static and dynamic structures, which shows its extensive adaptability.where J Y and J Y denote the lower and upper bounds of interval vector J Y . The symbol m J Y is the mean value of J Y , which can be calculated by averaging the lower and upper bounds value as shown in Eq. (16b). I J Y denotes the variation interval of J Y , which depends on the difference of the lower and upper bound values as shown in Eq. (16c). The deviation J Y  of the symmetrical interval can be acquired by averaging the upper and lower bounds of J Y as shown in Eq. (16d). In the combined form, the J-th hybrid interval random parameter( ) JJ X Y can be formulated as RCTO Volume fraction of solid: 95.6% Volume fraction of Phase 1: 70.3% DCTO Volume fraction of solid: 95.1% Volume fraction of phase 1: 70.7% 33 (b) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 93.0% Volume fraction of phase 1: 72.4% DCTO Volume fraction of solid: 92.7% Volume fraction of phase 1: 72.7% (c) Macrostructure Micro base-cell Composite material Phase 1 only RCTO Volume fraction of solid: 90.4% Volume fraction of phase 1: 74.9% DCTO Volume fraction of solid: 88.9% Volume fraction of phase 1: 76.3%JJ J ee JJ J J J J e J J e J J JJ J e e J J J J J J J J e J J e 2 2 J J J J JK J e e J J J J J J J J J J J J J e J J JJ JJ e J J J J JJ J J e J J J J e JJ e J J J J 3m d I e J J J J x X X e J J e J J e J J e J J e J J e J J e e e e J J J J e J J J J e J J J J H T A a J J J J H a J J J J pT A J J J J A e J J J J A e J J J J J J J J a i A Y J J J J p a i A Y J J J J a i J J J J a i A Y J J J J p a i A Y J J J J Ne ia A i J J J J a i J J J J Ne ia A i J J J J

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A novel reliability‐based topology optimization framework for the concurrent design of solid and truss‐like material structures with unknown‐but‐bounded uncertainties

Cited by 13 publications

References 52 publications

Two decades review of reliability-based topology optimization developments

Two decades review of reliability-based topology optimization developments

Research Progress of Failure Mechanism of Thermal Barrier Coatings at High Temperature via Finite Element Method

Robust concurrent topology optimization of structure and its composite material considering uncertainty with imprecise probability

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