• Journal of KSNVE
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• v.2 no.2
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• pp.99-106
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• 1992

The complex Young's modulus of a viscoelastic material can be obtained as a function of frequency from the measurements of relative motion between the two ends of a bar-type specimen. Non-resonance method is usually used to obtain the complex Young's modulus over wide range of frequency including resonance points, while in resonance method information at resonance frequencies only is used. However, the complex Young's modulus obtained by the non-resonance method is often unreliable in the anti-resonance frequency regions because of the measurement noise problems. In this study, the effects of the random measurement errors on estimating the complex Young's modulus are studied in the aspect of sensitivity, and how to obtain the reliable frequency region for a given measurement error level is shown. The usable frequency regions in determining the complex Young's modulus are represented by a non-dimensional parameter formed with the wave length and specimen length.

• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.477-493
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• 2005

In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.

• Structural Engineering and Mechanics
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• v.6 no.6
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• pp.659-671
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• 1998

Exercise of complete control on all aspects of any manufacturing / fabrication process is very difficult, leading to uncertainties in the material properties and geometric dimensions of structural components. This is especially true for laminated composites because of the large number of parameters associated with its fabrication. When the basic parameters like elastic modulus, density and Poisson's ratio are random, the derived response characteristics such as deflections, natural frequencies, buckling loads, stresses and strains are also random, being functions of the basic random system parameters. In this study the basic elastic properties of a composite lamina are assumed to be independent random variables. Perturbation formulation is used to model the random parameters assuming the dispersions small compared to the mean values. The system equations are analyzed to obtain the mean and the variance of the plate natural frequencies. Several application problems of free vibration analysis of composite plates, employing the proposed method are discussed. The analysis indicates that, at times it may be important to include the effect of randomness in material properties of composite laminates.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.15 no.1
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• pp.21-26
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• 2005

In order to simulate the powder compaction process and to assess the effects of packing randomness and particle arrangement 2-dimensional model of rod array compaction using quasi-random multiparticle array is introduced. The elastic modulus of porous ceramics is computed by the homogenization method. With 3 Al₂O₃ and 3 Al particles the compaction processes associated with the porosities are simulated by the explicit finite element method, based on the elastic modulus found by the homogenization method. The simulation results are compared with both previous analytical ones and experimental measurements. Finally, in order to find the relationship between the friction coefficient of powder particles and the relative density, the sensitivity analysis is performed.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.471-502
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• 2016

This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.3
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• pp.127-132
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• 2018

In this paper, a scheme for the evaluation of variability in the eigen-modes of functionally graded material(FGM) beams is proposed within the framework of perturbation-based stochastic analysis. As a random parameter, the spatially varying elastic modulus of FGM along the axial direction at the mid-surface of the beam is chosen, and the thru-thickness variation of the elastic modulus is assumed to follow the original form of exponential variation. In deriving the formulation, the first order Taylor expansion on the eigen-modes is employed. As an example, a simply supported FGM beam having symmetric elastic modulus with respect to the mid-surface is chosen. Monte Carlo analysis is also performed to check if the proposed scheme gives reasonable outcomes. From the analyses it is found that the two schemes give almost identical results of the mean and standard deviation of eigen-modes. With the propose scheme, the standard deviation shape of respective eigen-modes can be evaluated easily. The deviated mode shape is found to have one more zero-slope points than the mother modes shapes, irrespective of order of modes. The amount of deviation from the mean is found to have larger values for the higher modes than the lower modes.

• The Journal of the Acoustical Society of Korea
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• v.11 no.4
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• pp.22-30
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• 1992

The propagation of coherent time-harmonic elastic SH waves in a medium with random distribution of cylindrical inclusions is studied for characterizing the dynamic elastic modulus and the attenuation property of fiber-reinforced composite materials. A multiple scattering theory using the single scattering coefficients in conjunction with the Lax's quasicrystalline approximation is derived and from which the dispersion relation for such medium is obtained. The pair-correlation functions between the cylinders which are needed to formulate the multiple scattering interaction between the cylinders are obtained by Monte Carlo simulation method.From the numerically calculated complex wavenumbers, the propagation speed of the average wave, the coherent attenuation coefficient and the effective shear modulus are presented as functions of frequency and area density.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.2
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• pp.153-158
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• 2017

In this paper, we take into account topology optimization problems considering spatial randomness in the material property of elastic modulus. Based on 88 lines MATLAB Code, Monte Carlo analysis has been performed for MBB(messerschmidt-$b{\ddot{o}}lkow$-blohm) model using 5,000 random sample fields which are generated by using the spectral representation scheme. The random elastic modulus is assumed to be Gaussian in the spatial domain of the structure. The variability of the volume fraction of the material, which affects the optimum topology of the given problem, is given in terms of correlation distance of the random material. When the correlation distance is small, the randomness in the topology is high and vice versa. As the correlation distance increases, the variability of the volume fraction of the material decreases, which comply with the feature of the linear static analysis. As a consequence, it is suggested that the randomness in the material property is need to be considered in the topology optimization.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.199-206
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• 2014

In this paper, a scheme to evaluate the response variability for functionally graded material (FGM) beam with varying sectional area is presented. The randomness is assumed to appear in a spatial domain along the beam axis in the elastic modulus. The functionally graded material categorized as composite materials, however without the drawbacks of delamination and occurrence of cracks due to abrupt change in material properties between layers in the conventional composite materials. The functionally graded material is produced by the gradual solidification through thickness direction, which endows continuous variation of material properties, which makes this material performs in a smooth way. However, due to difficulties in tailoring the gradients, to have uncertainty in material properties is unavoidable. The elastic modulus at the center section is assumed to be random in the spatial domain along the beam axis. Introducing random variables, defined in terms of stochastic integration, the first and second moments of responses are evaluated. The proposed scheme is verified by using the Monte Carlo simulation based on the random samples generated employing the spectral representation scheme. The response variability as a function of correlation distance, the effects of material and geometrical parameters on the response variability are investigated in detail. The efficiency of the proposed scheme is also addressed by comparing the analysis time of the proposed scheme and MCS.

• 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.