• Journal of the Korean Statistical Society
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• 제10권
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• pp.140-144
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• 1981

This paper approximates to a kernel density estimate by a truncated series of expansion involving Hermite polynomials, since this could ease the computing burden involved in the kernel-based density estimation. However, this truncated series may give a multimodal estimate when we are estiamting unimodal density. In this paper we will show a way to insure the truncated series to be positive and unimodal so that the approximation to a kernel density estimator would be maeningful.

• Structural Engineering and Mechanics
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• 제34권6호
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• pp.779-799
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• 2010

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.

• Korean Journal of Hydrosciences
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• 제6권
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1996년도 가을 학술발표회 논문집
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• pp.55-61
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• 1996

In the present study, a numerical formulation procedure fer free vibration analysis of thin-walled horizontally curved multi-girder bridges is presented. The presented finite element procedure consists of curved and straight beam elements including warping degree of freedom. The homogeneous solutions of curved beam equations were used for shape functions in numerical formulation to achieve good convergence. In the straight beam element, the third order hermite polynomials were used fer shape functions. The Gupta method was used to solve the eigenvalue problem efficiently. The developed numerical procedure was applied to investigate the characteristics of free vibration of horizontally curved multi-girder bridges with varing subtended angle.

• 대한기계학회논문집B
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• 제27권7호
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• pp.867-876
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• 2003

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Four points Hermite interpolation in the homogeneous direction and Chebyshev polynomials in the inhomogeneous direction is adopted to simulate the fluid particle dispersion. An inhomogeneity of Lagrangian statistics in turbulent boundary layer is investigated by releasing many particles at several different wall-normal locations and tracking those particles. The fluid particle dispersions and Lagrangian structure functions of velocity are scaled by the Kolmogorov similarity. The auto-correlations of velocity and acceleration are shown at the different releasing locations. Effect of initial particle location on the dispersion is analyzed by the probability density function at the several downstreams and time instants.

• Structural Engineering and Mechanics
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• 제23권5호
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.

• 오토저널
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• 제12권2호
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• pp.29-42
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• 1990

Three dimensional frame structures with such nonlinearities as large displacements, medium rotations, plastic hinges and local defects are efficiently analyzed by introducing the nonlinear rotational spring. Formulations are based on the incremental updated Lagrangian descriptions and the virtual work principle, Axial displacement and twisted angle in beam elements are interpolated linearly, while bending displacements are approximated by the Hermite polynomials. The modified are length method is used as a solution method. The moment-angle of rotation relationship obtained analytically or experimentally can be easily incorporated into the solution procedure. Several examples tested show that the present method can be used efficiently in analyzing nonlinear frame structures with plastic hinges or local defect.

• Steel and Composite Structures
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• 제42권2호
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• pp.243-256
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• 2022

A coupled finite element method (FEM)-boundary element method (BEM) for analyzing the hydroelastic response of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) floating plates under moving loads is firstly introduced in this article. For that aim, the plate displacement field is described utilizing a generalized shear deformation theory (GSDT)-based FEM, meanwhile the linear water-wave theory (LWWT)-relied BEM is employed for the fluid hydrodynamic modeling. Both computational domains of the plate and fluid are coincidentally discretized into 4-node Hermite elements. Accordingly, the C1-continuous plate element model can be simply captured owing to the inherent feature of third-order Hermite polynomials. In addition, this model is also completely free from shear correction factors, although the shear deformation effects are still taken into account. While the fluid BEM can easily handle the free surface with a lower computational effort due to its boundary integral performance. Material properties through the plate thickness follow four specific CNT distributions. Outcomes gained by the present FEM-BEM are compared with those of previously released papers including analytical solutions and experimental data to validate its reliability. In addition, the influences of CNT volume fraction, different CNT configurations, water depth, and load speed on the hydroelastic behavior of FG-CNTRC plates are also examined.

• 한국농공학회논문집
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• 제55권3호
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• pp.75-84
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• 2013

The seepage quantity analysis of reservoir embankment is very important for assessment of embankment safety. However, the conventional analysis does not consider uncertainty of soil properties. Permeability is known that the coefficient of variation is larger than other soil properties and seepage quantity is highly dependent on the permeability of embankment. Therefore, probabilistic analysis should be carried out for seepage analysis. To designers, however, the probabilistic analysis is not an easy task. In this paper, the method that can be performed probabilistic analysis easily and efficiently through the numerical analysis based commercial program is proposed. Stochastic response surface method is used for approximate the limit state function and when estimating the coefficients, the moving least squares method is applied in order to reduce local error. The probabilistic analysis is performed by LHC-MCS through the response surface. This method was applied to two type (homogeneous, core zone) earth dams and permeability of embankment body and core are considered as random variables. As a result, seepage quantity was predicted effectively by response surface and probabilistic analysis could be successfully implemented.