Isogeometric generalized n th order perturbation-based stochastic method for exact geometric modeling of (composite) structures: Static and dynamic analysis with random material parameters

Ding, Chensen; Hu, Xiaobin; Cui, Xiangyang; Li, Guangyao; Cai, Yong; Tamma, Kumar K.

doi:10.1016/j.cma.2018.09.032

Cited by 35 publications

(10 citation statements)

References 42 publications

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“…According to the above analysis, the expectation and variance of equation (6) with the uncertain distribution parameters are monotonous. Based on the monotonicity analysis, the vertex method is presented to quickly calculate the interval bounds of expectation and variance by equations (11) and (12).…”

Section: Calculation Of the Expectation And Variance Based Onmentioning

confidence: 99%

“…For the uncertainty analysis of structures, the probabilistic theory and the finite element method are combined to generate stochastic finite element analysis (SFEM) [9]. SFEM techniques include Monte Carlo simulation, perturbation method [10,11], and spectral stochastic finite element method [12,13]. However, constructing the precise probability model requires a large amount of experimental data which is impractical, especially for the complex engineering problem.…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

Xiao

Zhao

Wen

et al. 2020

Mathematical Problems in Engineering

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In practical engineering problems, the distribution parameters of random variables cannot be determined precisely due to limited experimental data. e hybrid uncertain model of interval and probability can deal with the problem, but it will produce extensive computation and it is difficult to meet the requirement of the complex engineering problem analysis. In this scenario, this paper presents a vertex method for the uncertainty analysis of the hybrid model. By combining the traditional finite element method, it can be applied to the structural uncertainty analysis. e key of this method is to demonstrate the monotonicity between expectation and variance of the function and distribution parameters of random variables. Based on the monotonicity analysis, interval bounds of the expectation and variance are directly calculated by means of vertex of distribution parameter intervals. Two numerical examples are used to evaluate the effectiveness and accuracy of the proposed method. e results show the vertex method is computationally more efficient than the common interval Monte Carlo method under the same accuracy. Two practical engineering examples are to show that the vertex method makes the engineering application of the hybrid uncertain model easy.

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Section: Calculation Of the Expectation And Variance Based Onmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

Xiao

Zhao

Wen

et al. 2020

Mathematical Problems in Engineering

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“…Hughes et al (2005) and Cottrell et al (2009) firstly introduced the concept of IGA by using the spline basis functions [such as non-uniform rational B-splines (NURBSs)] constructing the exact geometric models as interpolation functions in CAE analysis. Up to now, this approach has also gained widespread reception from the scientific community and many applications have been verified, for example, structural optimization (Cho and Ha, 2009;Qian, 2010;Ding et al, 2016;Ding et al, 2018c;Lian et al, 2017;Lian et al, 2016;Hao et al, 2018a;Hao et al, 2019;Hao et al, 2018b), plate and composite structures (Thai et al, 2014;Yu et al, 2018;Thai et al, 2015;Nguyen-Xuan et al, 2014;Chang et al, 2016;Yin et al, 2015;Thanh et al, 2019b;Phung-Van et al, 2019;Thanh et al, 2019a;Thanh et al, 2018;Phung-Van et al, 2018;Thai et al, 2018b;Thai et al, 2018a;Tran et al, 2017;Thai et al, 2016), isogeometric boundary methods (Simpson et al, 2013;Simpson et al, 2012;Peng et al, 2017;Scott et al, 2013), stochastic analysis (Ding et al, 2019a;Ding et al, 2018b;Ding et al, 2019b;Ding et al, 2019c), other splines based methods (Atroshchenko et al, 2018;Nguyen-Thanh et al, 2011;Gu et al, 2018a;Gu et al, 2018b), and especially the severa...…”

Section: Cae Modelmentioning

confidence: 99%

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Ding

2019

Self Cite

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Purpose This paper aims to provide designers/engineers, in engineering structural design and analysis, approaches to freely and accurately modify structures (geometric and/or material), and then quickly provide real-time capability to obtain the numerical solutions of the modified structures (designs). Design/methodology/approach The authors propose an isogeometric independent coefficients (IGA-IC) method for a fast reanalysis of structures with geometric and material modifications. Firstly, the authors seamlessly integrate computer-aided design (CAD) and computer-aided engineering (CAE) by capitalizing upon isogeometric analysis (IGA). Hence, the authors can easily modify the structural geometry only by changing the control point positions without tedious transformations between CAE and CAD models; and modify material characters simply based on knots vectors. Besides, more accurate solutions can be obtained because of the high order degree of the spline functions that are used as interpolation functions. Secondly, the authors advance the proposed independent coefficients method within IGA for fast numerical simulation of the modified designs, thereby significantly reducing the enormous time spent in repeatedly numerical evaluations. Findings This proposed scheme is efficient and accurate for modifying the structural geometry by simply changing the control point positions, and material characters by knots vectors. The enormous time spent in repeated full numerical simulations for reanalysis is significantly reduced. Hence, enabling quickly modifying structural geometry and material, and analyzing the modified model for practicality in design stages. Originality/value The authors herein advance and propose the IGA-IC scheme. Where, it provides designers to fasten and simple designs and modify structures (both geometric and material). It then can quickly in real-time obtain numerical solutions of the modified structures. It is a powerful tool in practical engineering design and analysis process for local modification. While this method is an approximation method designed for local modifications, it generally cannot provide an exact numerical solution and its effectiveness for large modification deserves further study.

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“…Zhang and Shibutani (2019) used polynomial chaos expansions to construct SIGA for uncertainty in shape. Ding et al (2019) considered higher-order Taylor series of functions of random variables to propose the Isogeometric generalized nth order perturbation-based stochastic method. Eckert et al (2020) developed a polynomial chaos method for an arbitrary random field in conjugate the standard isogeometric analysis for computational stochastic mechanics.…”

Section: Introductionmentioning

confidence: 99%

Perturbation based stochastic isogeometric analysis for bending of functionally graded plates with the randomness of elastic modulus

Nguyen

2020

Lat. Am. j. solids struct.

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We propose, in this paper, stochastic isogeometric analysis (SIGA) is a type of non-statistic approach in which combines the perturbation technique with the standard isogeometric analysis, in particular for static behavior of functionally graded plates with the uncertain elastic modulus. We assume that the spatial random variation of elastic modulus can be modeled as a two dimensional Gaussian random field in the plane of the plate. The random field is discretized to set of random variables using the integration point method. The system equations of SIGA are created using the NURBS functions for approximation displacement fields in conjunction with the first-order and second-order perturbation expansions of random fields, stiffness matrix, displacement fields. Besides the non-statistic approach, Monte Carlo simulation is presented for validation. The accuracy and appropriateness of the non-statistic approach are demonstrated via comparisons of the present results with those given by the stochastic finite element method in the literature and by the Monte Carlo analysis as well. The numerical examples are employed to investigate the effect of the randomness of elastic modulus and system parameters on the first and second statistical moments of displacement.

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Isogeometric generalized n th order perturbation-based stochastic method for exact geometric modeling of (composite) structures: Static and dynamic analysis with random material parameters

Cited by 35 publications

References 42 publications

Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

Isogeometric independent coefficients method for fast reanalysis of structural modifications

Perturbation based stochastic isogeometric analysis for bending of functionally graded plates with the randomness of elastic modulus

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