• Journal of the Korean Geotechnical Society
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• v.27 no.3
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• pp.75-83
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• 2011

Emerging issues related with fully coupled Thermo-Hydro-Mechanical (THM) behavior of unsaturated soil demand the development of a numerical tool in diverse geo-mechanical and geo-environmental areas. This paper presents general governing equations for coupled THM processes in unsaturated porous media. Coupled partial differential equations are derived from three mass balances equations (solid, water, and air), energy balance equation, and force equilibrium equation. With Galerkin formulation and time integration of these governing equations, finite element code is developed to find nonlinear solution of four main variables (displacement-u, gas pressure-$P_g$), liquid pressure-$P_1$), and temperature-T) using Newton's iterative scheme. Three cases of numerical simulations are conducted and discussed: one-dimensional drainage experiments (u-$P_g-P_1$), thermal consolidation (u-$P_1$-T), and effect of pile on surrounding soil due to surface temperature variation (u-$P_1$-T).

• Proceedings of the Membrane Society of Korea Conference
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• 1999.07a
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• pp.48-51
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• 1999

To investigate numerically the removal behavior of carbon dioxide in a hollow fiber membrane contactor, the system controlling equations were developed including the nonlinear reversible reaction terms. The reversible chemical reactions were incorporated in the system controlling equations, resulting in the coupled nonlinear partial differential equations which could describe either the absorption of the desorption of carbon dioxide. The computer program was coded using the Fortran language and run with a personal computer to find out the effects of the system variables: the pressures of absorbed and desorbed gases, the absorbent flow rate, the concentration of potassium carbonate, the fiber diameter and the length.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.3
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• pp.243-259
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• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• Coupled systems mechanics
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• v.10 no.1
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• pp.39-60
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• 2021

The present paper is concerned with the study of nonlinear ultrasonic waves in a magneto thermo (MT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. The analytical formulation is developed based on Eringen's nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Parametric work is carried out to scrutinize the influence of the non local scaling, magneto-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter, and tube geometrical parameters have significant effects on dimensionless frequency of nano tubes. The results presented in this study can provide mechanism for the study and design of the nano devices like component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro- magneto-mechanical systems (NEMMS) that make use of the wave propagation properties of armchair single-walled carbon nanotubes embedded on polymer matrix.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.689-703
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• 2011

A new perturbation method is introduced to study the undamped free vibration of a non-prismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• Advances in nano research
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• v.8 no.3
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• pp.245-254
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• 2020

This work examines the fundamental vibrational characteristics of a spinning CNT-based nano-rotor assuming a nonlocal elasticity Euler-Bernoulli beam theory. The rotary inertia, gyroscopic, and rotor mass unbalance effects are all taken into consideration in the beam model. Assuming a nonlocal theory, two coupled 6th-order partial differential equations governing the vibration of the rotating SWCNT are first derived. In order to acquire the natural frequencies and dynamic response of the nano-rotor system, the nonlinear equations of motion are numerically solved. The nano-rotor system frequency spectrum is shown to exhibit two distinct frequencies: one positive and one negative. The positive frequency is known as to represent the forward whirling mode, whereas the negative characterizes the backward mode. First, the results obtained within the framework of this numerical study are compared with few existing data (i.e., molecular dynamics) and showed an overall acceptable agreement. Then, a thorough and detailed parametric study is carried out to study the effect of several parameters on the nano-rotor frequencies such as: the nanotube radius, the input angular velocity and the small scale parameters. It is shown that the vibration characteristics of a spinning SWCNT are significantly influenced when these parameters are changed.

• Journal of the Korean Geotechnical Society
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• v.19 no.4
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• pp.55-64
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• 2003

Desiccation of a soil is basically the removal of water by evaporation, which is controlled by evaporativity and evaporability. Surface evaporation improves the trafficability which is essential for the access of construction equipment in the area reclaimed with soft clay. The existing traditional methods for evaluating evaporation can not account for the deformation of reclaimed soft soils during evaporation. Therefore, a theoretical model for predicting the rate of evaporation from the surface of a deformable material is proposed. The model is based on a system of equations for coupled heat and mass transfer in unsaturated soils. The modified pressure plate extractor test and glass desiccator test were carried out to obtain the soil-water characteristic curve for a deformable soil. The column drying test was conducted to investigate one dimensional water flow, heat flow and evaporation in the surface. A finite difference program was developed to solve the coupled nonlinear partial differential equations, which permit the study of water, vapor and heat flows in the deformable soil. Comparison between measured and simulated values shows a reasonably good matching between the two.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.32 no.1
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• pp.16-24
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• 2022

A computational study of combined thermal and solutal convection (double diffusive convection) in a sealed crystal growth reactor is presented, based on a two-dimensional numerical analysis of the nonlinear and strongly coupled partial differential equations and their associated boundary conditions. The average Nusselt numbers for the source regions are greater than those at the crystal regions for 9.73 × 10³ ≤ Gr_t ≤ 6.22 × 10⁵. The average Nusselt numbers for the source regions varies linearly and increases directly with the thermal Grashof number form 9.73 × 10³ ≤ Gr_t ≤ 6.22 × 10⁵ for aspect ratio, Ar (transport length-to-width) = 1 and 2. Additionally, the average Nusselt numbers for the crystal regions at Ar = 1 are much greater than those at Ar = 2. Also, the occurrence of one unicellular flow structure is caused by both the thermal and solutal convection, which is inherent during the physical vapor transport of Hg₂Br₂. When the aspect ratio of the enclosure increases, the fluid movement is hindered and results in the decrease of thermal buoyancy force.

• Geomechanics and Engineering
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• v.8 no.4
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• pp.559-594
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• 2015

A nonlinear creep function incorporated into the elastic visco-plastic model may describe the long-term soil deformation more accurately. However, by applying the conventional procedure, there are challenges to determine the model parameters due to limitation of suitable data points. This paper presents a numerical solution to obtain several parameters simultaneously for a nonlinear elastic visco-plastic (EVP) model using the available consolidation data. The finite difference scheme using the Crank-Nicolson procedure is applied to solve a set of coupled partial differential equations of the time dependent strain and pore water pressure dissipation. The model parameters are determined by applying the algorithm of trust-region reflective optimisation in conjunction with the finite difference solution. The proposed method utilises all available consolidation data during dissipation of the excess pore water pressure to determine the required model parameters. Moreover, the reference time in the elastic visco-plastic model can readily be adopted as a unit of time; denoting creep is included in the numerical predictions explicitly from the very first time steps. In this paper, the settlement predictions of thick soft clay layers are presented and discussed to evaluate and compare the accuracy and reliability of the proposed method against the graphical procedure to obtain the model parameters. In addition, comparison of the available experimental results to the numerical predictions confirms the accuracy of the numerical procedure.