An nth high order perturbation-based stochastic isogeometric method and implementation for quantifying geometric uncertainty in shell structures

Ding, Chensen; Tamma, Kumar K.; Cui, Xiangyang; Ding, Yanjun; Li, Guangyao; Bordas, Stéphane P.A.

doi:10.1016/j.advengsoft.2020.102866

Cited by 29 publications

(5 citation statements)

References 84 publications

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“…In addition, a main limitation of the present method is that the structural-acoustic interaction effect is not taken into account, which will be studied by coupling FEM and BEM in an isogeometric analysis framework in the future work. We will also extend the present work to geometric uncertainly qualification [52][53][54] because IGABEM enables rapid sampling in stochastic analysis by allowing for numerical simulation directly from CAD.…”

Section: Modelmentioning

confidence: 97%

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

Lian¹,

Chen²,

Lin³

et al. 2022

Computer Modeling in Engineering &Amp; Sciences

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This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution. The geometries of the structures are represented by Catmull-Clark subdivision surfaces, which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometric modelling. The acoustic fields are simulated using the isogeometric boundary element method, and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces. The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needing meshing and volume parameterization, thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods. The effectiveness of the present method is demonstrated by three dimensional numerical examples.

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Section: Modelmentioning

confidence: 97%

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

Lian¹,

Chen²,

Lin³

et al. 2022

Computer Modeling in Engineering &Amp; Sciences

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“…A nth-order generalized perturbation isometric approach that is a steady-state heat transfer analysis simulation with material uncertainties was created by Rojas et al [43]. Ding et al [24] studied the nth-order perturbation method based on IGA to simulate the geometric uncertainty of shell structure. Cao et al [44] used uncertainty analysis to solve the equi-geometric bi-reciprocal finite element for non-Fourier transient heat transfer problems.…”

Section: Wave Numbermentioning

confidence: 99%

“…Among them, MCs is the most common and simplest method, but its accuracy is largely based on the quantity of samples, resulting in high-level computational costs [19][20][21]. Therefore, MCs is often used as a reference solution to validate other probabilistic methods [22][23][24]. The stochastic spectrum method is more efficient and takes advantage of generality, but it is still difficult to apply to large-scale problems.…”

Section: Introductionmentioning

confidence: 99%

A generalized isogeometric boundary element method for the uncertain analysis of infinite domain two-dimensional acoustic problems

Yang,

Huo,

Yuan

et al. 2023

Front. Phys.

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The key aim of this paper is to provide a new nth generalized order perturbed isogeometric fast multistage technique of boundary elements to compute the propagation of time harmonics in an infinite region. Structural geometry and boundary integral equations are constructed by using non-uniform rational B-splines. The source of system uncertainty is believed to be the incident plane wave number’s unpredictability. The actual field, depending on the input random variables, is simulated using the extended nth-order perturbation method. The field and kernel values for boundary integral formulas are generated via the nth-order generalized series of Taylor expansions using perturbation parameters. The fast multipole method (FMM) is utilized to speed up the process. The effectiveness and correctness of the proposed algorithm are verified by Monte Carlo simulations (MCs) with numerical examples.

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“…In attempts to develop advanced methods, isogeometric analysis [15] was proposed to solve mechanics problems with exact geometries and high accuracy. IGA has been developed for various types of structures, such as plates [16][17][18][19][20][21][22] and shells [23][24][25][26][27][28][29]. In particular, NURBS-based nonlinear inverse analyses of thin shells were performed not only for pure mechanical problems [30] but also for coupled problems [31].…”

Section: Introductionmentioning

confidence: 99%

Load-Carrying Capacity of Ultra-Thin Shells with and without CNTs Reinforcement

et al. 2022

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Isotropic ultra-thin shells or membranes, as well as cable–membrane structures, cannot resist loads at the initial state and always require a form-finding process to reach the steady state. After this stage, they can work in a pure membrane state and quickly experience large deflection behavior, even with a small amplitude of load. This paper aims to improve the load-carrying capacity and strength of membrane structures via exploiting the advantages of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) material. In this work, the load-carrying capacity and nonlinear behavior of membrane structures with and without CNTs reinforcement are first investigated using a unified adaptive approach (UAA). As an advantage of UAA, both form finding and postbuckling analysis are performed conveniently and simultaneously based on a modified Riks method. Different from the classical membrane theory, the present theory (first-order shear deformation theory) simultaneously takes into account the membrane, shear and bending strains/stiffnesses of structures. Accordingly, the present formulation can be applied adaptively and naturally to various types of FG-CNTRC structures: plates, shells and membranes. A verification study is conducted to show the high accuracy of the present approach and formulation. Effects of CNTs distribution, volume fraction, thickness, curvature, radius-to-thickness and length-to-radius ratios on the form-finding and postbuckling behavior of FG-CNTRC membranes are particularly investigated. In particular, equilibrium paths of FG-CNTRC membrane structures are first provided in this paper.

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An nth high order perturbation-based stochastic isogeometric method and implementation for quantifying geometric uncertainty in shell structures

Cited by 29 publications

References 84 publications

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

A generalized isogeometric boundary element method for the uncertain analysis of infinite domain two-dimensional acoustic problems

Load-Carrying Capacity of Ultra-Thin Shells with and without CNTs Reinforcement

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