Monte Carlo Simulation of Dynamic Problem Using Model Order Reduction Technique Highlighting on Tail Probability

Takano, Naoki; Asai, Mitsuteru; Okamoto, Kohta

doi:10.1299/jcst.6.169

Cited by 4 publications

(10 citation statements)

References 9 publications

(12 reference statements)

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“…However, the tail distribution, for instance, less or larger than , is not always predicted accurately. It is because the sampling points in the tail distribution of input parameters that may lead to the tail distribution of QoI are not dense enough, even though a reliable random generator such as Mersenne-Twister is employed (Takano, et al, 2012).…”

Section: Overall Flowmentioning

confidence: 99%

“…To obtain the tail distribution of QoI accurately but practically, a multi-step MC method has been proposed (Takano, et al, 2012, Susanto, et al, 2014, that can calculate the expected value and the tail probability. Instead of that, the whole probabilistic density function and accurate standard deviation are not obtained.…”

Section: Overall Flowmentioning

confidence: 99%

“…The convergence check of the expected value of QoI (Takano, et al, 2012) is described in the next section. The newly developed automated algorithm to find LSZ follows.…”

Section: Overall Flowmentioning

confidence: 99%

“…In the MC simulation, even if an accurate and reliable random number generator is employed and 10,000 total sampling points are used, the number of generated sampling points in the tail distribution is not always enough (Takano, et al, 2012). In the probabilistic fracture analysis of structures and materials, it is sometimes important to predict such cases that fracture occurs at lower load than expected.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, in the conventional MC simulation, more number of sampling points is needed to cover the tail region, which results in serious problem of higher computational cost. In this paper, a newly developed automated algorithm for multi-step MC simulation (Takano, et al, 2012, Susanto, et al, 2014 is proposed.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Numerical prediction of scattered initial fracture load of perforated thin plate under tension by Monte Carlo FEM simulation with stepwise limited sampling

Akimoto

Takano²

2016

Mechanical Engineering Letters

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For the probabilistic finite element analysis of structures and materials considering uncertainty parameters, the Monte Carlo (MC) simulation is often used. However, the accuracy to predict the tail distribution of the quantity of interest (QoI) is not always good enough. Therefore, this paper proposes a multi-step MC method focusing on the tail distribution. The first step aims at predicting the expected value of QoI accurately with least number of sampling points. By analyzing the results of sampling points in the first step, a region in the parameter space is determined whose sampling points may result in extreme value in the tail distribution of QoI. The next step employs the sampling points in the above limited region to obtain accurately the tail distribution. The main contribution of this paper is to present the newly developed automated algorithm to determine the above region in parameter space. Its usefulness has been shown in the simulation of tensile test of perforated thin plate considering the scattering of geometrical size of holes due to laser processing. Predicted scattered initial fracture load was compared with experimental results.

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Section: Overall Flowmentioning

confidence: 99%

Section: Overall Flowmentioning

confidence: 99%

“…The convergence check of the expected value of QoI (Takano, et al, 2012) is described in the next section. The newly developed automated algorithm to find LSZ follows.…”

Section: Overall Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical prediction of scattered initial fracture load of perforated thin plate under tension by Monte Carlo FEM simulation with stepwise limited sampling

Akimoto

Takano²

2016

Mechanical Engineering Letters

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Stochastic nonlinear multiscale computational scheme for short fiber reinforced composites to study the influence of microstructural variability on damage propagation

Hoang

Abe

Nakamura³

et al. 2020

SN Appl. Sci.

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In this paper, a stochastic nonlinear multiscale computational scheme is proposed to study the influence of the variability in both physical parameters of constituent materials and geometrical parameters such as fiber orientation, fiber arrangement of short fiber reinforced composites on the damage propagation. The aim is to predict many probable damage patterns in a huge number of scenarios under complex strain conditions and to discuss the influential level of variability in the physical and geometrical parameters for short fiber reinforced composites. The parameterization and numerical modelling for short fiber reinforced plastics made by injection molding are conducted. The random physical parameters are considered theoretically by the first-order perturbation based stochastic homogenization method, while sampling is used for the random geometrical parameters. When the scenario becomes huge in the stochastic nonlinear analysis, a computational scheme using sub-sampling is proposed. Moreover, the stochastic prediction of the homogenized properties of the composite material and their probable degradation are discussed. The stochastic computation of microscopic strains is analyzed though the damage propagation simulation. When the geometrical variability is considered, a definition of an average strain distribution among many samples is also presented. The efficiency of the accelerated element-by-element scaled conjugate gradient iterative solver is shown by solving many three-dimension random short fiber reinforced models with hundreds of thousands of degrees of freedom. The stochastic computational scheme provides a suitable reference to predict failure under specific reliability requirements of short fiber reinforced composites or other composite materials.

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Probabilistic prediction of mechanical behavior of additively manufactured product considering geometrical imperfections associated with building direction

Maruno

Takano

2021

Mechanical Engineering Journal

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Consideration of uncertainties in numerical simulations of materials and structures is required for their validation (ASME 2006). The uncertainties and variability to be taken into account for the modeling and simulation include the material property, geometry, constraint condition, loading condition and initial condition. To consider the variability in linear elastic material properties, many theoretical approaches based on the first-order perturbation (

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Monte Carlo Simulation of Dynamic Problem Using Model Order Reduction Technique Highlighting on Tail Probability

Cited by 4 publications

References 9 publications

Numerical prediction of scattered initial fracture load of perforated thin plate under tension by Monte Carlo FEM simulation with stepwise limited sampling

Numerical prediction of scattered initial fracture load of perforated thin plate under tension by Monte Carlo FEM simulation with stepwise limited sampling

Stochastic nonlinear multiscale computational scheme for short fiber reinforced composites to study the influence of microstructural variability on damage propagation

Probabilistic prediction of mechanical behavior of additively manufactured product considering geometrical imperfections associated with building direction

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