• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.04a
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• pp.117-124
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• 1993

The Neumann Expansion method has been used for evaluating the response variability of three dimensional truss structure resulting from the spatial variability of material properties with the aid of the finite element method, and in conjunction with the direct Monte Carlo simulation methods. The spatial variabilites are modeled as three-dimensional stochastic field. Yamazaki 〔1〕 has extended the Neumann Expansion method to the plane-strain problem to obtain the response variability of 2 dimensional stochastic systems. This paper presents the extension of the Neumann Expansion method to 3 dimensional stochastic systems. The results by the NEM are compared with those by the deterministic finite element analysis and by the direct Monte Carlo simulation method

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.373-392
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• 2001

The main idea behind the paper is to present two alternative methods of homogenization of the heat conduction problem in composite materials, where the heat conductivity coefficients are assumed to be random variables. These two methods are the Monte-Carlo simulation (MCS) technique and the second order perturbation second probabilistic moment method, with its computational implementation known as the Stochastic Finite Element Method (SFEM). From the mathematical point of view, the deterministic homogenization method, being extended to probabilistic spaces, is based on the effective modules approach. Numerical results obtained in the paper allow to compare MCS against the SFEM and, on the other hand, to verify the sensitivity of effective heat conductivity probabilistic moments to the reinforcement ratio. These computational studies are provided in the range of up to fourth order probabilistic moments of effective conductivity coefficient and compared with probabilistic characteristics of the Voigt-Reuss bounds.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1920-1929
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• 1994

The stochastic finite element method(SFEM) based structural optimal design is presented. Random system response including uncertainties for the design variable is calculated with first order perturbation method. A method for calculating the sensitivity coefficients is developed using the equilibrium equation and first-order perturbed equation. Numerical results are presented for a truss, frame and plate structures with displacement and stress constraints. The sensitivity calculation proposed here is compared with finite difference method. A nonlinear programming technique is used to solve the problem. The procedure is easily incorporated with existing deterministic structural optimization.

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.311-325
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• 2020

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.10a
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• pp.351-358
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• 1999

The structural responses of underground structures are examined in probability by using the elasto-plastic stochastic finite element method in which the spatial distributions of material properties are assumed to be stochastic fields. In addition, the adaptive importance sampling method using the response surface technique is used to improve simulation efficiency. The method is found to provide appropriate information although the nonlinear Limit State involves a large number of basic random variables and the failure probability is small. The probability of plastic local failures around an excavated area is effectively evaluated and the reliability for the limit displacement of the ground is investigated. It is demonstrated that the adaptive importance sampling method can be very efficiently used to evaluate the reliability of a large scale stochastic finite element model, such as the underground structures located in the multi-layered ground.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.185-202
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• 2006

In this paper, using the Black-Scholes analysis, we will derive the partial differential equation of convertible bonds with both non-stochastic and stochastic interest rate. We also find numerical solutions of convertible bonds equation with known interest rate using the finite element method.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.4
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• pp.219-225
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• 2000

This paper presents the shape optimization considering the uncertainty of design variable to find robust optimal solution that has insensitive performance to its change of design variable. Stochastic finite element method (SFEM) is used to treat input data as stochastic variables. It is method that the potential values are series form for the expectation and small variation. Using correlation function of their variables, the statistics of output obtained form the input data distributed. From this, design considering uncertainty of design variables.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.1
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• pp.54-62
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• 1994

The expanding technique of the Stochastic Finite Element Method(SFEM) is proposed in this paper for adapting direct integration methods in stochastical dynamic analysis of structures. Grafting the direct integration methods and the SFEM together, one can deal with nonlinear structures and nonstationary process problems without any restriction. The stochastical central diffrence and stochastic Houbolt methods are introduced to show the expanding technique, and their adaptabilities are discussed. Results computed by the proposed method (the Stochastic Finite Element Method in Dynamics: SFEMD) for two degree-of-free- dom system are compared with those obtained by Monte Carlo Simulation.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.1-10
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• 1995

This study presents a methodology for the system reliability analysis of cracked structures with random material properties, which are modeled as random fields, and crack geometry under random static loads. The finite element method provides the computational framework to obtain the stress intensity solutions, and the first-order reliability method provides the basis for modeling and analysis of uncertainties. The ultimate structural system reliability is effectively evaluated by the stable configuration approach. Numerical examples are given for the case of random fracture toughness and load.

• Steel and Composite Structures
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• v.11 no.2
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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.