• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.329-337
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• 2008

This paper presents the derivation of the generalized governing equations in theory of elasticity, their weak forms and the some applications in the numerical analysis of structural mechanics. Unlike the differential equations in classical elasticity theory, the generalized equations of the equilibrium and compatibility equations presented here take the form of integral equations, and the generalized equilibrium equations contain the classical differential equations and the boundary conditions in a single equation. By using appropriate test functions, the weak forms of these generalized governing equations can be established. It can be shown that various variational principles in structural analysis are merely the special cases of these weak forms of generalized governing equations in elasticity. The present weak forms of elasticity equations extend greatly the choices of the trial functions for approximate solutions in the numerical analysis of various engineering problems. Therefore, the weak forms of generalized governing equations in elasticity provide a powerful modeling tool in the computational structural mechanics.

• Journal of Korean Association for Spatial Structures
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• v.2 no.3 s.5
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• pp.115-122
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• 2002

It is often hard to obtain analytical solutions of boundary value problems of shells. Introducing some approximations into the governing equations may allow us to get analytical solutions of boundary value problems. Instead of an analytical procedure, we can apply a numerical method to the governing equations. Since the governing equations of shells of revolution under symmetric load are expressed by ordinary differential equations, a numerical solution of ordinary differential equations is applicable to solve the equations. In this paper, the governing equations of orthotropic spherical shells under symmetric load are derived from the classical theory based on differential geometry, and the analysis is numerically carried out by computer program of Runge-Kutta methods. The numerical results are compared to the solutions of a commercial analysis program, SAP2000, and show good agreement.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.5
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• pp.621-626
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• 1985

Unsteady groundwater flow in a three-layer unconfined aquifer has been studied theoretically and experimentally. Two different methods have been used in solving the governing equations of the flow, the nonlinear partial differential equations; (1) The governing equations are linearized for each layer and approximate solutions are obtained. (2) The governing equations are transformed to nonlinear ordinary differential equations, which are solved numerically by Runge-Kutta procedure. Fine, middle sized and coarse sands are used in the experiments. It is found that the solutions from the method(2) ( the reduction of partial differential equations to ordinary differential equations) give better agreement with the experimental results than the solution from the method(1).

• Structural Engineering and Mechanics
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• v.5 no.2
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• pp.209-220
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• 1997

The dynamic equations for an arbitrary cluster comprising rigid spheres or assemblies of spheres (subclusters) encountered in granular-type systems are considered. The system is treated within the framework of multibody dynamics. It is shown that for an arbitrary cluster topology the governing equations can be given in an explicit scalar from. The derivation is based on the D'Alembert principle, on inertial coordinate system for each body and direct utilization of the path matrix describing the topology. The scalar form of the equations is important in computer simulations of flow of granular-type materials. An illustrative example of a three-body system is given.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.383-405
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• 2004

We study the incomprssible Navier Stokes equations for the flow inside contraction geometry. The governing equations are expressed in the vorticity-stream function formulations. A rectangular computational domain is arised by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of acurvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over relaxation iteration. The time dependent of the vorticity equation solved by using explicit marching procedure. We will apply the technique on several irregular-shapes.

• Water Engineering Research
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• v.4 no.4
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• pp.175-185
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• 2003

A numerical model to analyze dam break flows has been developed based on approximate Riemann solver. The governing equations of the model are the nonlinear shallow-water equations. The governing equations are discretized explicitly by using finite volume method and the numerical flux are reconstructed with weighted averaged flux (WAF) method. The developed model is verified. The first verification problem is about idealized dam break flow on wet and dry beds. The second problem is about experimental data of dam break flow. From the results of the verifications, very good agreements have been observed

• Computers and Concrete
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• v.11 no.3
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• pp.201-222
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• 2013

A comprehensive simulation model for the transport process of fully coupled moisture and multi-species in non-saturated concrete structures is proposed. The governing equations of moisture and ion diffusion are formulated based on Fick's law and the Nernst-Planck equation, respectively. The governing equations are modified by explicitly including the coupling terms corresponding to the coupled mechanisms. The ionic interaction-induced electrostatic potential is described by electroneutrality condition. The model takes into account the two-way coupled effect of moisture diffusion and ion transport in concrete. The coupling parameters are evaluated based on the available experimental data and incorporated in the governing equations. Differing from previous researches, the material parameters related to moisture diffusion and ion transport in concrete are considered not to be constant numbers and characterized by the material models that account for the concrete mix design parameters and age of concrete. Then, the material models are included in the numerical analysis and the governing equations are solved by using finite element method. The numerical results obtained from the present model agree very well with available test data. Thus, the model can predict satisfactorily the ingress of deicing salts into non-saturated concrete.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.10
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• pp.2011-2015
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• 2009

In an insulating dielectric liquid such as transformer oil, space charge injection and propagation were analyzed under the Fowler-Nordheim and Richardson-Dushman's thermal emission charge injection conditions for blade-plane electrodes stressed by a step voltage. The governing equations were composed of all five equations such as the Poisson's equation for electric fields, three continuity equations for electrons, negative, and positive ions, and energy balanced equation for temperature distributions. The governing equations for each carrier, the continuity equations, belong to the hyperbolic-type PDE of which the solution has a step change at the space charge front resulting in numerical instabilities. To decrease these instabilities, the governing equations were solved simultaneously by the Finite Element Method (FEM) employing the artificial diffusion scheme as a stabilization technique. Additionally, the terminal current was calculated by using the generalized energy method which is based on the Poynting's theorem, and represents more reliable and stable approach for evaluating discharge current. To verify the proposed method, the discharge phenomena were successfully applied to the blade~plane electrodes, where the radius of blade cap was $50{\mu}m$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.820-833
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• 1995

An analysis is performed to examine the equilibrium state and the stability of modeled Reynolds stress equations for homogeneous turbulent shear flows. The system of the governing equations consists of four coupled ordinary differential equations. The equilibrium states are found by the steady state solution of the governing equations. In order to investigate the stability of the system about its state in equilibrium, and eigenvalue problem is constructed. As a result, constraints for the coeffieients in the model equations are obtained by the stability condition of the equilibrium state as well as by their physically realizable bounds. It is observed that the models with pressure-strain rate correlation that are linear in the anisotropy tensor are stable and produce reasonable equilibrium tensor do not behave properly. Stability considerations about three most commonly used models are given in detail in the final section.

• Transactions of the Korean hydrogen and new energy society
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• v.21 no.6
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• pp.513-518
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• 2010

In the present work the second-order perturbation solutions of the simple physical model for liquid pool spreading is obtained for the case of instantaneous spill. To generalize the solution governing equations are non-dimensionalized, and two dimensionless parameters, dimensionless evaporation rate and aspect ratio of the initial pool, are identified to control the governing equations. The dimensional governing equations have three parameters. The second-order solution improves fairly the first-order solution for the pool volume.