Size-controlled cross-scale robust topology optimization based on adaptive subinterval dimension-wise method considering interval uncertainties

Wang, Lei; Zhao, Xingyu; Li, Dongliang

doi:10.1007/s00366-022-01615-8

Cited by 19 publications

(3 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the convergence condition of the Neumann expansion in Equation (24), the convergence condition of the Neumann approximation of the inverse matrix K −1 ( a I ) is obtained as:…”

Section: Improved Neumann Expansionmentioning

confidence: 99%

“…Abdedou et al 22 proposed a non-invasive method based on B-splines Bezier polynomials. The multidimensional method 23,24 is also a novel approach to predict the structural response in various ranges of uncertainty. The accuracy of the collocation method relies on the number of order, however, the computation grows exponentially as the number of order and uncertain variables increase.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A novel univariate dimension‐reduction based interval finite element method for static response prediction of uncertain structures

Zhao

Feng

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

To eliminate the errors caused by the conventional interval perturbation finite element method due to classic interval arithmetic and neglect of higher-order terms, we propose a novel univariate dimension-reduction based interval finite element method to predict the static response bounds of structures with uncertain but bounded parameters. First, a univariate dimension-reduction algorithm is derived using the generalized Taylor expansion. The global stiffness matrix is expressed as the sum of the median and the univariate disturbance radius. Compared with Taylor expansion approximation, the univariate dimension-reduction approximation has higher accuracy and does not increase the amount of calculation. Then the inverse of the interval global stiffness matrix is approximated as an improved Neumann series. Higher-order terms are included by summing up the geometric terms in the Neumann series. Finally, the improved interval algorithm is used to solve the upper and lower bounds of the structural displacement response and the element stress response. The dependence between the interval parameters is accounted in comparison with the classic interval algorithm. The accuracy and effectiveness of the new method are validated by numerical cases on 2D truss, 3D frame and truck frame with multiple interval parameters.

show abstract

“…From the convergence condition of the Neumann expansion in Equation (24), the convergence condition of the Neumann approximation of the inverse matrix K −1 ( a I ) is obtained as:…”

Section: Improved Neumann Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel univariate dimension‐reduction based interval finite element method for static response prediction of uncertain structures

Zhao

Feng

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…As the necessary input conditions for the subsequent reliability assessment of the composite laminates, the achievement of the quantitative study with limited sample data is of great importance. Here, a total of two cases, namely, the static one under 16 groups of actual experimental samples corresponding to the engineering constants E 1 , E 2 , ν 12 , and G 12 of T300/QY8911 (as listed in Table 1, which is referred by [26]) and the dynamic one under six groups of virtual simulation histories subjected to external excitation F(t) (as shown in Figure 4, which is modified by [37,38]) are analyzed by utilizing the improved Grey system theory as above discussed. For ease of understanding, we take the longitudinal elastic modulus E 1 as an example, and its specific quantification procedure is summarized below.…”

Section: Cases Of Time-invariant and Time Variant Uncertainty Quantif...mentioning

confidence: 99%

Dynamic Uncertainty Quantification and Risk Prediction Based on the Grey Mathematics and Outcrossing Theory

Wang

Liu

2022

Applied Sciences

Self Cite

View full text Add to dashboard Cite

Embarked from the practical conditions of small samples in time-invariant and time-variant uncertainties, a complete non-probabilistic analysis procedure containing uncertainty quantification, uncertainty propagation, and reliability evaluation is presented in this paper. Firstly, the Grey systematic approach is proposed to determine the boundary laws of static intervals and dynamic interval processes. Through a combination of the policies of the second-order Taylor expansion and the smallest parametric interval set, the structural response histories via quantitative uncertainty results are further confirmed. Additionally, according to the first-passage idea from classical random process theory, the study on the time-dependent reliability measurement on the basis of the interval process model is carried out to achieve a more elaborate estimation for structural safety during its whole life cycle. A numerical example and one experimental application are eventually discussed for demonstration of the usage and reasonability of the methodology developed.

show abstract

On the Use of Fidelity Transformation Method for Stress‐Constrained Reliability‐Based Topology Optimization of Continuum Structure With High Accuracy

Meng,

Qian,

Hao

2024

Numerical Meth Engineering

View full text Add to dashboard Cite

Stress‐constrained reliability‐based topology optimization (RBTO) method has incurred considerable attention owing to its superiority of enhancing the structural safety. However, the traditional reliability methods encounter inaccurate issue for evaluating the failure probability of stress‐constrained structure. In this work, the failure mechanism of the stress‐constrained RBTO problem is analyzed for continuum structure, which reveals that the correlation between different stress constraints and utilization of aggregation function significantly impacts the accuracy. Then, a novel stress‐constrained system RBTO framework is suggested to enhance computational efficiency and accuracy for system reliability analysis. Furthermore, an accurate and efficient semi‐analytical method is suggested to approximate the performance functions through first‐order Taylor series expansion, in which the intricate implicit expressions are substituted by the straightforward analytic expressions. In addition, the fidelity transformation method is employed for converting the semi‐analytical RBTO method to classical RBTO method. To demonstrate the practicability of the proposed framework, three benchmark cases, including 2D and 3D problems, are tested. The results reveal that the proposed framework achieves high accuracy and efficiency.

show abstract

Size-controlled cross-scale robust topology optimization based on adaptive subinterval dimension-wise method considering interval uncertainties

Cited by 19 publications

References 46 publications

A novel univariate dimension‐reduction based interval finite element method for static response prediction of uncertain structures

A novel univariate dimension‐reduction based interval finite element method for static response prediction of uncertain structures

Dynamic Uncertainty Quantification and Risk Prediction Based on the Grey Mathematics and Outcrossing Theory

On the Use of Fidelity Transformation Method for Stress‐Constrained Reliability‐Based Topology Optimization of Continuum Structure With High Accuracy

Contact Info

Product

Resources

About