Topology optimization of continuum structures under geometric uncertainty using a new extended finite element method

Rostami, Seyyed Ali Latifi; Ghoddosian, Ali; Kolahdooz, Amin; Zhang, Jian

doi:10.1080/0305215x.2021.1957860

Cited by 11 publications

(2 citation statements)

References 38 publications

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“…For RTO under uncertainty in material property, we can referred the following works: Tootkaboni et al [19], da Silva and Cardoso [20], Agrawal et al [21]. Zhang and Kang [22], Latifi Rostami and Ghoddosian [23,24], Latifi Rostami et al [25] and investigated the RTO problems with geometric uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Robust Topology Optimization of Continuum Structures under the Hybrid Uncertainties: A Comparative Study

Rostami

Kolahdooz

et al. 2023

Period. Polytech. Civil Eng.

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Due to the inevitable involvement of multisource uncertainties related to the load, material property and geometry in practical engineering designs, robust topology optimization (RTO) has recently attracted increasing attention to account for these uncertain effects. However, the majority of the existing RTO works are concerned with single source uncertainty, and very few studies have considered the multisource (hybrid) uncertainties simultaneously. To this end, a comparative study on the hybrid uncertainties (HU), i.e., material-loading, geometric-loading, material-geometric, and material-geometric-loading uncertainties, for RTO of continuum structures is presented in this paper. A truncated Karhunen-Loeve expansion is adopted for uncertainty representation and a sparse grid collocation method for uncertainty propagation of the objective function and constraints. Effects of the various HU on the compliance and robust design are comprehensively investigated and compared with the RTO models under individual component uncertainty using two continuum benchmarks. An important observation from the results is that the hybrid uncertainty model is a conservative state, and the resulting RTO designs tend towards those with loading uncertainty only.

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Section: Introductionmentioning

confidence: 99%

Robust Topology Optimization of Continuum Structures under the Hybrid Uncertainties: A Comparative Study

Rostami

Kolahdooz

et al. 2023

Period. Polytech. Civil Eng.

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“…Moreover, their random response is not well predicted by the deterministic tools of traditional analysis. To clearly understand the uncertain propagation and response of the mechanics-mathematical model during design and optimization, formally incorporating uncertainty into the design framework started to be taken into account in the topology optimization community (Latifi Rostami, et al, 2022;Latifi Rostami, et al, 2021;Rostami, et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Non‑intrusive polynomial chaos expansion for robust topology optimization of truss-like continua under random loads

Guo,

Zhou

2023

Preprint

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This paper dedicates to presenting an uncertain analysis framework for robust topology optimization (RTO) based on truss-like material model that integrates non-intrusive polynomial chaos expansion (PCE) approach. In this framework, the RTO problem is formulated as a bi-objective optimization one to simultaneously minimize the expectancy and its standard deviation of structural compliance with volume constraints. The magnitude and direction of load uncertainty are assumed to follow a Gaussian distribution independently. A standard non-intrusive PCE requires a large number of multivariate integrals to calculate the expansion coefficient. Therefore, response metrics such as structural compliance are efficiently characterized using the decoupling techniques based on the expansions of the uncertain parameters. The mechanical analysis and uncertainty analysis are separated, so that the number of simulations in the original PCE procedure is greatly reduced for linear structures by means of superposition. The optimization is achieved by gradient-based methods. The appreciable accuracy and efficiency are validated by the brutal Monte Carlo simulation. Three numerical examples are provided to demonstrate that the proposed method can lead to designs with completely different topologies and superior robustness.

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Robust topology optimization of continuum structures with smooth boundaries using moving morphable components

Rostami

Kolahdooz

Chung

et al. 2023

Struct Multidisc Optim

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Topology optimization of continuum structures under geometric uncertainty using a new extended finite element method

Abstract: The geometric uncertainty in the above Optimization problem is considered here. In the SIMP method, the boundary of the design domain is defined by threshold η in the Heaviside projection with the following equation tanh( ) tanh( ( ) tanh( ) tanh( (1 ) e e

Cited by 11 publications

References 38 publications

Robust Topology Optimization of Continuum Structures under the Hybrid Uncertainties: A Comparative Study

Robust Topology Optimization of Continuum Structures under the Hybrid Uncertainties: A Comparative Study

Non‑intrusive polynomial chaos expansion for robust topology optimization of truss-like continua under random loads

Robust topology optimization of continuum structures with smooth boundaries using moving morphable components

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