• Nuclear Engineering and Technology
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• v.41 no.8
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• pp.1087-1100
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• 2009

A finite element method utilizing the Galerkin form of the weighted residuals procedure was developed to estimate the mechanical behavior for a coated fuel particle (CFP) of a high temperature gas-cooled reactor (HTGR). Through a weak formulation, finite element equations for multiple layers were set up to calculate the displacements and stresses in a CFP. The finite element method was applied to the stress analyses for three coating layers of a tri-isotropic coated fuel particle (TRISO) of a HTGR. The stresses calculated by the finite element method were in good agreement with those from a previously developed computer code and depicted the typical stress behavior of the coating layers very well. The newly developed finite element method performs a stress analysis for multiple bonded layers in a CFP by changing the material properties at any position in the layers during irradiation.

• Journal of computational fluids engineering
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• v.12 no.4
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• pp.14-19
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• 2007

We present a direct numerical simulation technique and some preliminary results of the capillary spreading of a droplet containing particles on the solid substrate. We used the level-set method with the continuous surface stress for description of droplet spreading with interfacial tension and employed the discontinuous Galerkin method for the stabilization of the interface advection equation. The distributed Lagrangian-multipliers method has been combined for the implicit treatment of rigid particles. We investigated the droplet spreading by the capillary force and discussed effects of the presence of particles on the spreading behavior. It has been observed that a particulate drop spreads less than the pure liquid drop. The amount of spread of a particulate drop has been found smaller than that of the liquid with effectively the same viscosity as the particulate drop.

• Steel and Composite Structures
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• v.32 no.3
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.1
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• pp.34-41
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• 2003

A Green's function approach is adopted for analyzing the thermoelastic deformation and stress analysis of a plate made of functionally graded materials (FGMs). The solution to the 3-dimensional steady temperature is obtained by using the laminate theory. The fundamental equations for thermoelastic problems are derived in terms of out-plane deformation and in-plane force, separately. The thermoelastic deformation and the stress distributions due to the bending and in-plane forces are analyzed by using a Green’Às function based on the Galerkin method. The eigenfunctions of the Galerkin Green's function for the thermoelastic deformation and the stress distributions are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the rectangular plate. Numerical examples are carried out and effects of material properties on thermoelastic behaviors are discussed.

• Advances in nano research
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• v.7 no.5
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• pp.311-324
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• 2019

The present study aims to evaluate the nonlinear and post-buckling behaviors of orthotropic graphene sheets exposed to end-shortening strain by implementing a semi-Galerkin technique, as a new approach. The nano-sheets are regarded to be on elastic foundations and different out-of-plane boundary conditions are considered for graphene sheets. In addition, nonlocal elasticity theory is employed to achieve the post-buckling behavior related to the nano-sheets. In the present study, first, out-of-plane deflection function is considered as the only displacement field in the proposed technique, which is hypothesized by an appropriate deflected form. Then, the exact nonlocal stress function is calculated through a complete solution of the von-Karman compatibility equation. In the next step, Galerkin's method is used to solve the unknown parameters considered in the proposed technique. In addition, three different scenarios, which are significantly different with respect to concept, are used to satisfy the natural in-plane boundary conditions and completely attain the stress function. Finally, the post-buckling behavior of thin graphene sheets are evaluated for all three different scenarios, and the impacts of boundary conditions, polymer substrate, and nonlocal parameter are examined in each scenario.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.585-598
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• 2014

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ normed spaces.

• Advances in aircraft and spacecraft science
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• v.4 no.5
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• pp.555-571
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• 2017

The description of transitional flows by means of RANS equations is sometimes based on non-local approaches which require the computation of some boundary layer properties. In this work a non-local Laminar Kinetic Energy model is used to predict transitional and separated flows. Usually the non-local term of this model is evaluated along the grid lines of a structured mesh. An alternative approach, which does not rely on grid lines, is introduced in the present work. This new approach allows the use of fully unstructured meshes. Furthermore, it reduces the grid-dependence of the predicted results. The approach is employed to study the transitional flows in the T106c turbine cascade and around a NACA0021 airfoil by means of a discontinuous Galerkin method. The local nature of the discontinuous Galerkin reconstruction is exploited to implement an adaptive algorithm which automatically refines the mesh in the most significant regions.

• Proceedings of the KIEE Conference
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• 1999.07a
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• pp.76-78
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• 1999

This paper presents Galerkin- and Upwind-finite element analyses solution in the travelling magnetic filed problem. The travelling magnetic field problem is subject to convective- diffusion equation. Therefore, the solution derived from Galerkin-FEM with linear interpolation function may oscillate between the adjacent nodes. A simple model with Derichlet, Noumann and periodic boundary condition respectively, have been analyzed to investigate stabilities of solutions. It is concluded that the solution of Galerkin-FEM may oscillate according to boundary condition and element type, but that of Upwind-FEM is stable regardless boundary condition.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.1996-1998
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• 2001

This paper presents the closed-loop composite control for weakly coupled bilinear systems with a quadratic performance criterion. The Riccati equation for weakly coupled bilinear system is decomposed into three reduced Riccati equations by the weak coupling theory, and we obtain optimal solutions of each reduced Riccati equation using successive Galerkin approximation(SGA). We design the composite control law that consists of optimal solutions of each reduced Riccati equation. The proposed algorithm reduces the disadvantages of SGA method.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.193-213
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• 2017

We investigate an efficient approximation of solution to stochastic Burgers equation driven by an additive space-time noise. We discuss existence and uniqueness of a solution through the Orstein-Uhlenbeck (OU) process. To approximate the OU process, we introduce the Karhunen-$Lo{\grave{e}}ve$ expansion, and sparse grid stochastic collocation method. About spatial discretization of Burgers equation, two separate finite element approximations are presented: the conventional Galerkin method and Galerkin-conservation method. Numerical experiments are provided to demonstrate the efficacy of schemes mentioned above.