• KSCE Journal of Civil and Environmental Engineering Research
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• 제26권2A호
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• pp.383-390
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• 2006

In this paper, a stochastic field that is compatible with Monte Carlo simulation is suggested for an expansion-based stochastic analysis scheme of weighted integral method. Through investigation on the way of affection of stochastic field function on the displacement vector in the series expansion scheme, it is noticed that the stochastic field adopted in the weighted integral method is not compatible with that appears in the Monte Carlo simulation. As generally recognized in the field of stochastic mechanics, the response variability is not a linear function of the coefficient of variation of stochastic field but a nonlinear function with increasing variability as the intensity of uncertainty is increased. Employing the stochastic field suggested in this study, the response variability evaluated by means of the weighted integral scheme is reproduced with high precision even for uncertain fields with moderately large coefficient of variation. Besides, despite the fact that only the first-order expansion is employed, an outstanding agreement between the results of expansion-based weighted integral method and Monte Carlo simulation is achieved.

• Structural Engineering and Mechanics
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• 제86권3호
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• pp.349-359
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• 2023

This paper presents a technique for determining the optimal number of elements in stochastic finite element analysis based on reliability analysis. Using the change-of-variable perturbation stochastic finite element approach, the probability density function of the dynamic responses of stochastic structures is explicitly determined. This method combines the perturbation stochastic finite element method with the change-of-variable technique into a united model. To further examine the relationships between the random fields, discretization of the random field parameters, such as the variance function and the scale of fluctuation, is also performed. Accordingly, the reliability index is calculated based on the explicit probability density function of responses with Gaussian or non-Gaussian random fields in any number of elements corresponding to the random field discretization. The numerical examples illustrate the effectiveness of the proposed method for a one-dimensional cantilever reinforced concrete column and a two-dimensional steel plate shear wall. The benefit of this method is that the probability density function of responses can be obtained explicitly without the use simulation techniques. Any type of random variable with any statistical distribution can be incorporated into the calculations, regardless of the restrictions imposed by the type of statistical distribution of random variables. Consequently, this method can be utilized as a suitable guideline for the efficient implementation of stochastic finite element analysis of structures, regardless of the statistical distribution of random variables.

• Computational Structural Engineering
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• 제8권1호
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• pp.127-136
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• 1995

In this paper the stochastic FE analysis considering the material and geometrical property of the plate structure is performed by the weighted integral method. To consider the stochasity of the material and geometrical property, the stochastic field is assumed respectively. The mean value of the stochastic field is 0 and the value of variance is assumed as 0.1. The characteristics of the assumed stochastic field is represented by auto-correlation function. This auto-correlation function is used in evaluating the response variability of the plate structure. In this study a new auto-correlation function is derived to concern the uncertainty of the plate thickness. The newly derived auto-correlation function is a function of auto-correlation function and coefficient of variation of the assumed stochastic field. The two results, obtained by proposed Weighted Integral method and Monte Carlo Simulation method, are coincided with each other and these results are almost equal to the theoretical result that is derived in this study. In the case of considering the variability of plate thickness, the obtained result is well coincide with those of Lawrence and Monte Carlo simulation.

• Structural Engineering and Mechanics
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• 제4권6호
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• pp.703-715
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• 1996

In stochastic analysis, the randomness of the structural parameters is taken into consideration and the response variability is obtained in addition to the conventional (mean) response. In the present paper the structural response variability of plate structure is calculated using the weighted integral method and is compared with the results obtained by different methods. The stochastic field is assumed to be normally distributed and to have the homogeneity. The decomposition of strain-displacement matrix enabled us to extend the formulation to the stochastic analysis with the quadratic elements in the weighted integral method. A new auto-correlation function is derived considering the uncertainty of plate thickness. The results obtained in the numerical examples by two different methods, i.e., weighted integral method and Monte Carlo simulation, are in a close agreement. In the case of the variable plate thickness, the obtained results are in good agreement with those of Lawrence and Monte Carlo simulation.

• Steel and Composite Structures
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• 제11권2호
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• pp.115-130
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• 2011

Considering the randomness of material parameters in the laminated composite plate, a scheme of stochastic finite element method to analyze the displacement response variability is suggested. In the formulation we adopted the concept of the weighted integral where the random variable is defined as integration of stochastic field function multiplied by a deterministic function over a finite element. In general the elastic modulus of composite materials has distinct value along an individual axis. Accordingly, we need to assume 5 material parameters as random. The correlations between these random parameters are modeled by means of correlation functions, and the degree of correlation is defined in terms of correlation coefficients. For the verification of the proposed scheme, we employ an independent analysis of Monte Carlo simulation with which statistical results can be obtained. Comparison is made between the proposed scheme and Monte Carlo simulation.

• Wind and Structures
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• 제16권5호
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• pp.433-455
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• 2013

A phase delay spectrum model towards the representation of spatial coherence of stochastic wind fields is proposed. Different from the classical coherence functions used in the spectral representation methods, the model is derived from the comprehensive description of coherence of fluctuating wind speeds and from the thorough analysis of physical accounts of random factors affecting phase delay, building up a consistent mapping between the simulated fluctuating wind speeds and the basic random variables. It thus includes complete probabilistic information of spatial stochastic wind fields. This treatment prompts a ready and succinct scheme for the simulation of fluctuating wind speeds, and provides a new perspective to the accurate assessment of dynamic reliability of wind-induced structures. Numerical investigations and comparative studies indicate that the developed model is of rationality and of applicability which matches well with the measured data at spatial points of wind fields, whereby the phase spectra at defined datum mark and objective point are feasibly obtained using the numerical scheme associated with the starting-time of phase evolution. In conjunction with the stochastic Fourier amplitude spectrum that we developed previously, the time history of fluctuating wind speeds at any spatial points of wind fields can be readily simulated.

• Journal of Mechanical Science and Technology
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• 제16권7호
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• pp.959-965
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• 2002

Effective hydraulic conductivity of a statistically anisotropic heterogeneous medium is obtained for steady two-dimensional flows employing stochastic analysis. Flow equations are solved up to second order and the effective conductivity is obtained in a semi-analytic form depending only on the spatial correlation function and the anisotropy ratio of the hydraulic conductivity field, hence becoming a true intrinsic property independent of the flow field. Results are obtained using a statistically anisotropic Gaussian correlation function where the anisotropy is defined as the ratio of integral scales normal and parallel to the mean flow direction. Second order results indicate that the effective conductivity of an anisotropic medium is greater than that of an isotropic one when the anisotropy ratio is less than one and vice versa. It is also found that the effective conductivity has upper and lower bounds of the arithmetic and the harmonic mean conductivities.

• Journal of the Computational Structural Engineering Institute of Korea
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• 제23권6호
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• pp.727-737
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• 2010

Together with the Young's modulus the Poisson's ratio is another independent material parameter that governs the behavior of a structural system. Therefore, it is meaningful to evaluate separately the influence of the parameter on the random response of the structural system. To this end, a formulation dealing with the spatial randomness in the Poisson's ratio in laminated composite plates is proposed. The main idea of the paper is to transform the fraction form of the constitutive coefficients into the expanded form in an ascending order of the stochastic field function. To validate the adequacy of the formulation, a square plate is chosen and the computation results are compared with those obtained using conventional Monte Carlo simulation. It is observed that the results show good agreement with those by the Monte Carlo simulation(MCS).

• Wind and Structures
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• 제19권4호
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• pp.421-441
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• 2014

With the assistance of typhoon field data at aerial elevation level observed by meteorological satellites and wind velocity and direction records nearby the ground gathered in Guangzhou Weather Station between 1985 and 2001, some key wind field parameters under typhoon climate in Guangzhou region were calibrated based on Monte-Carlo stochastic algorithm and Meng's typhoon numerical model. By using Peak Over Threshold method (POT) and Generalized Pareto Distribution (GPD), Wind field characteristics during typhoons for various return periods in several typical engineering fields were predicted, showing that some distribution rules in relation to gradient height of atmosphere boundary layer, power-law component of wind profile, gust factor and extreme wind velocity at 1-3s time interval are obviously different from corresponding items in Chinese wind load Codes. In order to evaluate the influence of typhoon field parameters on long-span flexible bridges, 1:100 reduced-scale wind field of type B terrain was reillustrated under typhoon and normal conditions utilizing passive turbulence generators in TJ-3 wind tunnel, and wind-induced performance tests of aero-elastic model of long-span Guangzhou Xinguang arch bridge were carried out as well. Furthermore, aerodynamic admittance function about lattice cross section in mid-span arch lib under the condition of higher turbulence intensity of typhoon field was identified via using high-frequency force-measured balance. Based on identified aerodynamic admittance expressions, Wind-induced stochastic vibration of Xinguang arch bridge under typhoon and normal climates was calculated and compared, considering structural geometrical non-linearity, stochastic wind attack angle effects, etc. Thus, the aerodynamic response characteristics under typhoon and normal conditions can be illustrated and checked, which are of satisfactory response results for different oncoming wind velocities with resemblance to those wind tunnel testing data under the two types of climate modes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 한국전산구조공학회 1993년도 가을 학술발표회논문집
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• pp.207-215
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• 1993

With the aid of finite element method, this paper deals with the problem of structural response variability of transmission tower subjected to the spatial variability of material properties, Young's modulus herein. The spatial variability of material property are modeled as two-dimensional stochastic field which has an isotropic auto-correlation function. Response variability has been computed based on two numerical techniques, such as the Neumann expansion method in conjunction with the Monte Carlo simulation method. The results by these numerical methods are compared with those by the deterministic approach.