New non-intrusive stochastic finite element method for plate structures

Huo, Hui; Xu, Wentao; Wang, Wenpei; Chen, Guohai; Yang, Dixiong

doi:10.1016/j.compstruc.2022.106812

Cited by 10 publications

(9 citation statements)

References 65 publications

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“…} k i=1 by Equation ( 19) 13: Calculate the ith original stochastic eigenvector 𝝋 i (𝜃) = D𝜼 i (𝜃) via Equation (17) to solve the stochastic solution q i (𝜃) corresponding to the ith stochastic mode. Compared to the stochastic dynamic case, both the random sample vector λi ( θ) ∈ R n s and fi ( θ) ∈ R n s are calculated once.…”

Section: Algorithm Implementationmentioning

confidence: 99%

“…Several improvements are presented to reduce the computational effort of PC-based methods, for example, the Krylov-based iteration and the sparse PC approach. 10,11 Other methods are also explored to efficiently and accurately perform stochastic structural static and dynamic analyses, for example, the stochastic collocation method, 12 the PGD-based method, 13,14 the ANOVA method, 15 the direct probability integral method 16,17 and so forth.…”

Section: Introductionmentioning

confidence: 99%

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Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

Zheng,

Beer,

Nackenhorst

2024

Numerical Meth Engineering

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This article presents unified and efficient stochastic modal decomposition methods to solve stochastic structural static and dynamic problems. We extend the idea of deterministic modal decomposition method for structural dynamic analysis to stochastic cases. Standard/generalized stochastic eigenvalue equations are adopted to calculate the stochastic subspaces for stochastic static/dynamic problems and they are solved by an efficient reduced‐order method. The stochastic solutions of both static and dynamic equations are approximated by stochastic bases of the stochastic subspaces. Original stochastic static/dynamic equations are then transformed into a set of single‐degree‐of‐freedom (SDoF) stochastic static/dynamic equations, which are efficiently solved by the proposed non‐intrusive methods. Specifically, a non‐intrusive stochastic Newmark method is developed for the solution of SDoF stochastic dynamic equations, and the element‐wise division of sample vectors is used to solve the SDoF stochastic static equations. All of these methods have low computational effort and are weakly sensitive to the stochastic dimension, thus the proposed methods avoid the curse of dimensionality successfully. Two numerical examples, including two‐ and three‐dimensional spatial problems with low and high stochastic dimensions, are given to show the efficiency and accuracy of the proposed methods.

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Section: Algorithm Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

Zheng,

Beer,

Nackenhorst

2024

Numerical Meth Engineering

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“…Therefore, if a non-intrusive method based on the Nastran software can be developed to calculate the aeroelastic characteristics of folding wings, it can simplify the flutter analysis process of folding wings and promote it to engineering applications. At present, non-intrusive methods are mostly used in the field of uncertainty quantification and propagation [19][20][21][22][23]. In recent years, some scholars have also begun to use non-invasive methods for research in the field of aeroelasticity [24,25].…”

Section: Introductionmentioning

confidence: 99%

Flutter Characteristics of a Modified Z-Shaped Folding Wing Using a New Non-Intrusive Model

Qi,

Wu,

Tian

2024

Aerospace

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Unmanned aerial vehicles (UAVs) with folding wings can serve in multiple mission profiles, usually accompanied by sudden changes in flight speed. These bring great challenges to the aeroelastic design of UAVs, especially in the calculation of flutter characteristics. This paper developed a new non-intrusive aeroelastic model to quickly calculate the flutter characteristics of Z-shaped folding wings at different folding angles. First, the original Z-shaped folding wing was designed to be enhanced. Beams and ribs were arranged inside each wing segment to enhance the structural strength performance. Control surfaces were arranged in the middle-wing and outer-wing to enhance the aerodynamic control performance. Second, a parametric aeroelastic model at any folding angle was reconstructed based on the input file of Nastran software for the flutter calculation of the folding wing in the unfolded state. Finally, the effects of parameters such as folding angle, hinge stiffness between different wing segments, and hinge stiffness of the control surfaces on the flutter characteristics of the folding wing were investigated. The results show that the enhancement scheme could significantly increase the flutter speed and flutter frequency of the folding wing. The hinge stiffness between each wing segment had a significant impact on the flutter characteristics of the folding wing, but flutter at the control surface basically did not occur.

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“…The reliability index was introduced because its value is easier for people to compare than the probability of failure, which in the case of civil engineering is very low. There are numerous methods that are used to estimate the reliability index, including approximation methods (FORM, SORM) [2][3][4], simulation methods (Monte Carlo, Subset Simulation) [5][6][7], Stochastic Finite Element Method (SFEM) [8][9][10], Response Surface Method [11][12][13] or Artificial Neural Networks [14][15][16]. The biggest problem with most of mentioned method is that they are appropriate for analysis of individual limit state functions.…”

Section: Introductionmentioning

confidence: 99%

The safety of steel space truss under fire conditions according to the system reliability analysis.

Kubicka

2023

Preprint

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The proposed paper focuses on the method of estimating the reliability index β (as a safety measure) of the spatial steel truss under fire conditions. The whole procedure connected with computation of temperatures of elements, effects of actions and bearing capacities is realised in author-designed C++ code, prepared according to Eurocode. The probabilistic model includes mechanical properties of steel (yield strength), geometrical characteristics of bar cross-sections and effect of actions. In the next step, the stiffness matrix spectral analysis is realized. The code prepared by the author is being developed to be useful for spatial structures. The program realization leads to finding so called cut-sets, i.e. possible ways of transforming the structure into mechanism. These sets of elements create a logical model, which will be introduced to the SYSREL module, which is part of STRUREL program. This is the software that was created in Munich University of Technology to solve reliability problems. SYSREL module is dedicated to conduct system reliability analysis connected with different reliability methods including, among others, the FORM,SORM, Monte Carlo and Subset Simulation method.

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New non-intrusive stochastic finite element method for plate structures

Cited by 10 publications

References 65 publications

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

Efficient stochastic modal decomposition methods for structural stochastic static and dynamic analyses

Flutter Characteristics of a Modified Z-Shaped Folding Wing Using a New Non-Intrusive Model

The safety of steel space truss under fire conditions according to the system reliability analysis.

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