Shape optimisation by design of experiments and finite element methods—an application of steel wheels

Schäfer, Christina; Finke, Eckhard

doi:10.1007/s00158-007-0183-6

Cited by 20 publications

(9 citation statements)

References 17 publications

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“…Regarding the joint use of FEA and DOE, we found that they have been combined in several applications in non-lattice structures. The current work can be divided into three groups: (i) evaluation of material and mechanical properties, including metals [18], resins [19] and composite materials [20]; (ii) shape optimization of mechanical parts, including medical devices [21] and automobile parts [22]; and (iii) generation of meta-models to estimate the stress-strain responses in small lattice domains using DOE [5]. However, the produced meta-models are not used for any further analysis with large lattice domains.…”

Section: Modeling and Simulation Of Lattice Structuresmentioning

confidence: 99%

Approximation of the Mechanical Response of Large Lattice Domains Using Homogenization and Design of Experiments

et al. 2020

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Lattice-based workpieces contain patterned repetition of individuals of a basic topology (Schwarz, ortho-walls, gyroid, etc.) with each individual having distinct geometric grading. In the context of the design, analysis and manufacturing of lattice workpieces, the problem of rapidly assessing the mechanical behavior of large domains is relevant for pre-evaluation of designs. In this realm, two approaches can be identified: (1) numerical simulations which usually bring accuracy but limit the size of the domains that can be studied due to intractable data sizes, and (2) material homogenization strategies that sacrifice precision to favor efficiency and allow for simulations of large domains. Material homogenization synthesizes diluted material properties in a lattice, according to the volume occupancy factor of such a lattice. Preliminary publications show that material homogenization is reasonable in predicting displacements, but is not in predicting stresses (highly sensitive to local geometry). As a response to such shortcomings, this paper presents a methodology that systematically uses design of experiments (DOE) to produce simple mathematical expressions (meta-models) that relate the stress–strain behavior of the lattice domain and the displacements of the homogeneous domain. The implementation in this paper estimates the von Mises stress in large Schwarz primitive lattice domains under compressive loads. The results of our experiments show that (1) material homogenization can efficiently and accurately approximate the displacements field, even in complex lattice domains, and (2) material homogenization and DOE can produce rough estimations of the von Mises stress in large domains (more than 100 cells). The errors in the von Mises stress estimations reach 42 % for domains of up to 24 cells. This result means that coarse stress–strain estimations may be possible in lattice domains by combining DOE and homogenized material properties. This option is not suitable for precise stress prediction in sensitive contexts wherein high accuracy is needed. Future work is required to refine the meta-models to improve the accuracies of the estimations.

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Section: Modeling and Simulation Of Lattice Structuresmentioning

confidence: 99%

Approximation of the Mechanical Response of Large Lattice Domains Using Homogenization and Design of Experiments

et al. 2020

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“…To address these problems, this work proposes a deep learning method based on patchwise training to reconstruct the temperature field from limited observation. First, training data is generated via the finite element method (FEM) (Schäfer and Finke (2008)). Second, the observation and the temperature field of the domain are regarded as input and output images, respectively.…”

Section: Introductionmentioning

confidence: 99%

A deep learning method based on patchwise training for reconstructing temperature field

Peng¹,

Li²,

Gong³

et al. 2022

Preprint

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Physical field reconstruction is highly desirable for the measurement and control of engineering systems. The reconstruction of the temperature field from limited observation plays a crucial role in thermal management for electronic equipment. Deep learning has been employed in physical field reconstruction, whereas the accurate estimation for the regions with large gradients is still diffcult. To solve the problem, this work proposes a novel deep learning method based on patchwise training to reconstruct the temperature field of electronic equipment accurately from limited observation. Firstly, the temperature field reconstruction (TFR) problem of the electronic equipment is modeled mathematically and transformed as an image-to-image regression task. Then a patchwise training and inference framework consisting of an adaptive UNet and a shallow multilayer perceptron (MLP) is developed to establish the mapping from the observation to the temperature field. The adaptive UNet is utilized to reconstruct the whole temperature field while the MLP is designed to predict the patches with large temperature gradients. Experiments employing finite element simulation data are conducted to demonstrate the accuracy of the proposed method. Furthermore, the generalization is evaluated by investigating cases under different heat source layouts, different power intensities, and different observation point locations. The maximum absolute errors of the reconstructed temperature field are less than 1K under the patchwise training approach.

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“…Lee and Jung [7] developed metamodel for optimizing a connecting rod subjected to a certain fatigue life. Schafer and Finke [8] carried out a shape optimization of steel wheels by using design of experiment (DoE) and finite element method (FEM), aiming to reduce fatigue failure and increase durability. Kaya et al [9] re-designed a failed vehicle component subjected to cyclic loading using topology and shape optimization approach.…”

Section: Introductionmentioning

confidence: 99%

Multiobjective robust design optimization of fatigue life for a truck cab

Fang

Gao

Sun

et al. 2015

Reliability Engineering & System Safety

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Shape optimisation by design of experiments and finite element methods—an application of steel wheels

Cited by 20 publications

References 17 publications

Approximation of the Mechanical Response of Large Lattice Domains Using Homogenization and Design of Experiments

Approximation of the Mechanical Response of Large Lattice Domains Using Homogenization and Design of Experiments

A deep learning method based on patchwise training for reconstructing temperature field

Multiobjective robust design optimization of fatigue life for a truck cab

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