• Journal of the Earthquake Engineering Society of Korea
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• v.19 no.1
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• pp.37-43
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• 2015

This paper presents a detailed procedure for a nonlinear soil-structure interaction of a seismically isolated NPP(Nuclear Power Plant) structure using the boundary reaction method (BRM). The BRM offers a two-step method as follows: (1) the calculation of boundary reaction forces in the frequency domain on an interface of linear and nonlinear regions, (2) solving the wave radiation problem subjected to the boundary reaction forces in the time domain. For the purpose of calculating the boundary reaction forces at the base of the isolator, the KIESSI-3D program is employed in this study to solve soil-foundation interaction problem subjected to vertically incident seismic waves. Wave radiation analysis is also employed, in which the nonlinear structure and the linear soil region are modeled by finite elements and energy absorbing elements on the outer model boundary using a general purpose nonlinear FE program. In this study, the MIDAS/Civil program is employed for modeling the wave radiation problem. In order to absorb the outgoing elastic waves to the unbounded soil region, spring and viscous-damper elements are used at the outer FE boundary. The BRM technique utilizing KIESSI-3D and MIDAS/Civil programs is verified using a linear soil-structure analysis problem. Finally the method is applied to nonlinear seismic analysis of a base-isolated NPP structure. The results show that BRM can effectively be applied to nonlinear soil-structure interaction problems.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.25-45
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• 2022

In this study, the non-standard finite difference method for the numerical solution of singularly perturbed parabolic reaction-diffusion subject to Robin boundary conditions has presented. To discretize temporal and spatial variables, we use the implicit Euler and non-standard finite difference method on a uniform mesh, respectively. We proved that the proposed scheme shows uniform convergence in time with first-order and in space with second-order irrespective of the perturbation parameter. We compute three numerical examples to confirm the theoretical findings.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.3
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• pp.7-20
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• 2007

We examined the steady state solution for a strongly exothermic mixtures in some class A geometries subjected to different boundary conditions under Arrhenius, Bimolecular and Sensitised reactions. The solution of the governing nonlinear reaction diffusion equation was obtained using the variational method formulation executed in Mathematica package. The paper elucidates the influence of geometry, boundary conditions and types of reaction on the thermal ignition of the reactive mixture. Apart from validating known results in literature, the solution gave further insight into the influence of material properties and conditions on the occurrence of thermal ignition.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.499-512
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• 2016

The boundary reaction method(BRM) is a substructure time domain method, it removes global iterations between frequency and time domain analyses commonly required in the hybrid approaches, so that it operates as a two-step uncoupled method. The BRM offers a two-step method as follows: (1) the calculation of boundary reaction forces in the frequency domain on an interface of linear and nonlinear regions, (2) solving the wave radiation problem subjected to the boundary reaction forces in the time domain. In the time domain analysis, the near-field soil is modeled to simulate the wave radiation problem. This paper evaluates the performance of the BRM according to modeling extent of near-field soil for the nonlinear SSI analysis of base-isolated NPP structure. For this purpose, parametric studies are performed using equivalent linear SSI problems. The accuracy of the BRM solution is evaluated by comparing the BRM solution with that of conventional SSI seismic technique. The numerical results show that the soil condition affects the modeling range of near-field soil for the BRM analysis as well as the size of the basemat. Finally, the BRM is applied for the nonlinear SSI analysis of a base-isolated NPP structure to demonstrate the accuracy and effectiveness of the method.

• Journal of the Korean Ceramic Society
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• v.21 no.1
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• pp.60-66
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• 1984

During the metallization in the manufacturing of the ceramic capacitor at the boundary layer between Pd or Pt electrode and $BaTiO_3$-dielectric reactions were analysed. For the study of the reaction Electron Spin Resonance (ESR) Method was used. With the aid of ESR an increased of the concentration of the paramagnetic $Ti^{3+}$-Centers on the metallizing process could be seen. It meaned a reduction effect although the metallization was accomplished under oxidation atmosphere. Therefore it could be regarded as a reaction at the boundary layer. In order to investigate the reaction ad double octahedral model was compared and the increase of the $Ti^{3+}$-concentration was studied.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.2
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• pp.95-102
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• 2014

In this paper, a coupling scheme for applying finite element analysis(FEA) programs, such as, LS-DYNA and MIDAS/Civil, to a nonlinear soil structure interaction analysis by the boundary reaction method(BRM) is presented. With the FEA programs, the structure and soil media are discretized by linear or nonlinear finite elements. To absorb the outgoing elastic waves to unbounded soil region as much as possible, the PML elements and viscous-spring elements are used at the outer FE boundary, in the LS-DYNA model and in MIDAS/Civil model, respectively. It is also assumed that all the nonlinear elements in the problem are limited to structural region. In this study, the boundary reaction forces for the use in the BRM are calculated using the KIESSI-3D program by solving soil-foundation interaction problem subjected to incident seismic waves. The effectiveness of the proposed approach is demonstrated with a linear SSI seismic analysis problem by comparing the BRM solution with the conventional SSI solution. Numerical comparison indicates that the BRM can effectively be applied to a nonlinear soil-structure analysis if motions at the foundation obtained by the BRM for a linear SSI problem excluding the nonlinear structure is conservative.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.05a
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• pp.97-100
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• 2002

In this research, the impact behavior of the boundary between MMC-reinforced SiC whisker and Al alloy were studied. It is known that the resultant of the interfacial reaction between SiC whisker and Al alloy has brittle and low toughness property. In this paper, impact behavior of graded MMC & Al alloy shows the interfacial opening at the boundary. Generally this phenomenon is generated by thermal residual stress, brittle interfacial reaction resultant and difference of the deflection. So, these results may be interpreted as a macroscopic method of measuring the interfacial strength between matrix and reinforcement