• Journal of Mechanical Science and Technology
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• v.19 no.8
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• pp.1649-1661
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• 2005

We consider. a horizontal static liquid layer on a planar solid boundary. The layer is evaporating when the plate is heated. Vapor recoil and thermo-capillary are discussed along with the effect of mass loss and vapor convection due to evaporating liquid and non-equilibrium thermodynamic effects. These coupled systems of equations are reduced to a single evolution equation for the local thickness of the liquid layer by using a long-wave asymptotics. The partial differential equation is solved numerically.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.53-67
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• 2022

Nonlinear system of initial value problems involving R-L fractional derivative is studied. Monotone iterative technique coupled with lower and upper solutions is developed for the problem. It is successfully applied to study qualitative properties of solutions of nonlinear system of initial value problem when the function on the right hand side is nondecreasing.

• Nuclear Engineering and Technology
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• v.16 no.2
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• pp.47-57
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• 1984

Mathematically-rigorous time-volume averaged conservation equations were simplified to established the differential equations of THERMIT-6S, which is a two-fluid 3-D code. The difference equations of THERMIT-6S were obtained by discretizing the proceeding set of differential equations. The spatial discretization is characterized by a first-order spatial scheme, donor cell method, and staggered mesh layout. For time discretization, a first order semi-implicit scheme treats implictly sonic terms and terms relating to local transport phenomena and explicitly convective terms. The results were linearized by the Newton-Raphson method. In order to construct the reduced pressure equation, the linearized equations were manipulated so that all variables are coupled between mesh cells through only the pressure variable. By simulating numerically the OPERA-15 experiment, it was found that THERMIT-6S is a very powerful code in predicting reactor behavior after sodium boiling including flow coastdown, reversal flow and flow oscillation.

• Steel and Composite Structures
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• v.26 no.4
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• pp.473-484
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• 2018

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Steel and Composite Structures
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• v.45 no.5
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• pp.729-747
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• 2022

The critical buckling loads and buckling modes of bi-directional functionally graded porous unified higher order shear plate with elastic foundation are investigated. A mathematical model based on neutral axis rather than midplane is developed in comprehensive way for the first time in this article. The material constituents form ceramic and metal are graded through thickness and axial direction by the power function distribution. The voids and cavities inside the material are proposed by three different porosity models through the thickness of plate. The constitutive parameters and force resultants are evaluated relative to the neutral axis. Unified higher order shear plate theories are used to satisfy the zero-shear strain/stress at the top and bottom surfaces. The governing equilibrium equations of bi-directional functionally graded porous unified plate (BDFGPUP) are derived by Hamilton's principle. The equilibrium equations in the form of coupled variable coefficients partial differential equations is solved by using numerical differential integral quadrature method (DIQM). The validation of the present model is presented and compared with previous works for bucking. Deviation in buckling loads for both mid-plane and neutral plane are developed and discussed. The numerical results prove that the shear functions, distribution indices, boundary conditions, elastic foundation and porosity type have significant influence on buckling stability of BDFGPUP. The current mathematical model may be used in design and analysis of BDFGPU used in nuclear, mechanical, aerospace, and naval application.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.219-232
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• 2024

In current study, for the first time, Nonlinear Bending of a skew microplate made of a laminated composite strengthened with graphene nanosheets is investigated. A mixture of mechanical and thermal stresses is applied to the plate, and the reaction is analyzed using the First Shear Deformation Theory (FSDT). Since different percentages of graphene sheets are included in the multilayer structure of the composite, the characteristics of the composite are functionally graded throughout its thickness. Halpin-Tsai models are used to characterize mechanical qualities, whereas Schapery models are used to characterize thermal properties. The microplate's non-linear strain is first calculated by calculating the plate shear deformation and using the Green-Lagrange tensor and von Karman assumptions. Then the elements of the Couple and Cauchy stress tensors using the Modified Coupled Stress Theory (MCST) are derived. Next, using the Hamilton Principle, the microplate's governing equations and associated boundary conditions are calculated. The nonlinear differential equations are linearized by utilizing auxiliary variables in the nonlinear solution by applying the Frechet approach. The linearized equations are rectified via an iterative loop to precisely solve the problem. For this, the Differential Quadrature Method (DQM) is utilized, and the outcomes are shown for the basic support boundary condition. To ascertain the maximum values of microplate deflection for a range of circumstances-such as skew angles, volume fractions, configurations, temperatures, and length scales-a parametric analysis is carried out. To shed light on how the microplate behaves in these various circumstances, the resulting results are analyzed.

• Structural Engineering and Mechanics
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• v.35 no.2
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• pp.141-173
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• 2010

In this paper a boundary element method is developed for the general flexural-torsional buckling analysis of Timoshenko beams of arbitrarily shaped cross section. The beam is subjected to a compressive centrally applied concentrated axial load together with arbitrarily axial, transverse and torsional distributed loading, while its edges are restrained by the most general linear boundary conditions. The resulting boundary value problem, described by three coupled ordinary differential equations, is solved employing a boundary integral equation approach. All basic equations are formulated with respect to the principal shear axes coordinate system, which does not coincide with the principal bending one in a nonsymmetric cross section. To account for shear deformations, the concept of shear deformation coefficients is used. Six coupled boundary value problems are formulated with respect to the transverse displacements, to the angle of twist, to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Several beams are analysed to illustrate the method and demonstrate its efficiency and wherever possible its accuracy. The range of applicability of the thin-walled theory and the significant influence of the boundary conditions and the shear deformation effect on the buckling load are investigated through examples with great practical interest.

• Korean Journal of Optics and Photonics
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• v.4 no.4
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• pp.464-473
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• 1993

The dynamics of phase grating formation with visible light in an optical fiber is investigated. Adopting a simple two-photon local bleaching model, it is shown that the grating self-organize into an ideal grating, where the writing frequency is always in the center of the local band gap, as it evolves. The evolution at each point in the fiber is described in terms of a universal parameter that reduces the coupled partial differential equations describing the system to ordinary differential equatior~s. These equations are used to prove that there exists a fixed point of the grating growth process that corresponds to a perfectly phase-mached grating.

• Journal of Biomedical Engineering Research
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• v.13 no.3
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• pp.181-188
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• 1992

This paper provides an overview of system analysis of immunology. The theoretical research in this area is aimed at an understanding of the precise manner by which the immune system controls Infec pious diseases, cancer, and AIDS. This can provide a systematic plan for immunological experimentation by means of an integrated program of immune system analysis, mathematical modeling and computer simulation. Biochemical reactions and cellular fission are naturally modeled as nonlinear dynamical processes to synthesize the human immune system! as well as the complete organism it is intended to protect. A foundation for the control of tumors is presented, based upon the formulation of a realistic, knowledge based mathematical model of the interaction between tumor cells and the immune system. Ordinary bilinear differential equations which are coupled by such nonlinear term as saturation are derived from the basic physical phenomena of cellular and molecular conservation. The parametric control variables relevant to the latest experimental data are also considered. The model consists of 12 states, each composed of first-order, nonlinear differential equations based on cellular kinetics and each of which can be modeled bilinearly. Finally, tumor control as an application of immunotherapy is analyzed from the basis established.

• Journal of the Korean Geotechnical Society
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• v.30 no.9
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• pp.67-75
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• 2014

Methane gas hydrate which is considered energy source for the next generation has an urgent need to develop reliable numerical simulator for coupled THM phenomena in the porous media, to minimize problems arising during the production and optimize production procedures. International collaborations to improve previous numerical codes are in progress, but they still have mismatch in the predicted value and unstable convergence. In this paper, FEM code for fully coupled THM phenomena is developed to analyze methane hydrate dissociation in the porous media. Coupled partial differential equations are derived from four mass balance equations (methane hydrate, soil, water, and hydrate gas), energy balance equation, and force equilibrium equation. Five main variables (displacement, gas saturation, fluid pressure, temperature, and hydrate saturation) are chosen to give higher numerical convergence through trial combinations of variables, and they can analyze the whole region of a phase change in hydrate bearing porous media. The kinetic model is used to predict dissociation of methane hydrate. Developed THM FEM code is applied to the comparative study on a Masuda's laboratory experiment for the hydrate production, and verified for the stability and convergence.