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

• Geomechanics and Engineering
• /
• v.37 no.4
• /
• pp.371-382
• /
• 2024

Measurement or prediction of compression index (C_c) of soils is essential for assessment of total and differential settlement of structures. It is a well-known fact that this parameter is controlled by several index identifiers of soil including initial void ratio, Atterberg limits, overconsolidation ratio, specific gravity, etc. Many studies in the past proposed relationships for prediction of C_c based on different index properties. Therefore, this study aims to present a comparison of previously proposed equations for estimation of C_c. Data from literature was compiled, and a total of 90 and 623 test results on remolded and undisturbed specimens were used to question the validity of previously proposed equations. Nevertheless, the modeling ability of 7 and 12 equations for estimation of C_c of remolded and undisturbed soils were questioned by use of compiled data. Moreover, new empirical relationships based on initial void ratio and toughness limit for prediction of C_c was proposed by use of nonlinear multivariable regression and evolutionary based regression analyses. The results are promising-the performances of models established are quite acceptable, which are verified by statistical analyses.

• Korean Journal of Mathematics
• /
• v.32 no.1
• /
• pp.137-162
• /
• 2024

This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on [0, L], where 0 < L < ∞. The fractional integral is described here in the sense of the Katugampola fractional integral of order λ > 0 and with the parameter β > 0. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.

• Computational Structural Engineering : An International Journal
• /
• v.1 no.2
• /
• pp.117-130
• /
• 2001

Investigations of low-rice unbounded reinforced concrete shear walls with or without openings are performed with comparison of analytical and experimental results. Theoretical analysis is based on nonlinear finite element algorithm, which incorporates concrete failure criterion and nonlinear constitutive relationships. Studios focus on the effects of height-to-length ratio of shear walls, opening ratio, horizontal and vertical reinforcement radios, and diagonal reinforcement. Analytical solutions conform well with experimental results. Equations for cracking, yielding and ultimate loads with corresponding lateral displacements are derived by regression using analytical results and experimental data. Also, failure modes of low-rise unbounded shear walls are theoretically investigated. An explanation of change in failure mode is ascertained by comparing analytical results and ACI code equations. Shear-flexural failure can be obtained with additional flexural reinforcement to increase a wall's capacity. This concept leads to a design method of reducing flexural reinforcement in low-rise bounded solid shear wall's. Avoidance of shear failure as well as less reinforcement congestion leer these walls is expected.

• Korean Journal of Computational Design and Engineering
• /
• v.21 no.1
• /
• pp.90-98
• /
• 2016

When ships and offshore plants are flooded or the floating crane is equipped with a heavy object, these floating structures are excessively inclined. In this case, immersion, heel, and trim affecting the hydrostatic restoration performance are very large and are coupled each other. In this paper, in order to calculate a static equilibrium position of floating structures with excessive inclination, the nonlinear governing equations were constructed by sequential linearization. In the governing equation, the immersion, heel, and trim are fully coupled, and the equations are represented using a plane area, a primary moment, and a moment of inertia of the water plane area. Therefore, it is possible to calculate the additional factor related the water plane area for estimating stability. Position and orientation of the floating structure are obtained by iterative calculation. The calculated results are compared with the previous studies in the aspect to the performance and the accuracy.

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

• Wind and Structures
• /
• v.26 no.6
• /
• pp.355-367
• /
• 2018

This paper studies the aerodynamic stability of a tensioned, geometrically nonlinear orthotropic membrane structure with hyperbolic paraboloid in sag direction. Considering flow separation, the wind field around membrane structure is simulated as the superposition of a uniform flow and a continuous vortex layer. By the potential flow theory in fluid mechanics and the thin airfoil theory in aerodynamics, aerodynamic pressure acting on membrane surface can be determined. And based on the large amplitude theory of membrane and D'Alembert's principle, interaction governing equations of wind-structure are established. Then, under the circumstance of single-mode response, the Bubnov-Galerkin approximate method is applied to transform the complicated interaction governing equations into a system of second-order nonlinear differential equation with constant coefficients. Through judging the frequency characteristic of the system characteristic equation, the critical velocity of divergence instability is determined. Different parameter analysis shows that the orthotropy, geometrical nonlinearity and scantling of structure is significant for preventing destructive aerodynamic instability in membrane structures. Compared to the model without considering flow separation, it's basically consistent about the divergence instability regularities in the flow separation model.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11a
• /
• pp.297-303
• /
• 2001

This research presents an analytical model to characterize the ball bearing vibration due to the waviness in a rigid rotor supported by multi-row ball bearings considering centrifugal force and gyroscopic moment of ball. The effects of centrifugal force and gyroscopic moment are introduced to the kinematic constraints and force equilibrium equations. The waviness of ball and races is modeled by the superposition of sinusoidal function and it is introduced to position vectors of race curvature center to use the Hertzian contact theory in order to calculate the elastic deflection and nonlinear contact force resulting from the waviness while the rotor has translational and angular motion. They can be determined by solving the nonlinear equations of motion with five degrees of freedom by using the Runge-Kutta-Fehlberg algorithm. The accuracy of this research is validated by comparing with the results of the prior researches. It characterizes the vibration frequencies resulting from the various kinds of waviness in rolling elements, the harmonic frequencies resulting from the nonlinear load-deflection characteristics of ball bearing resulting from the waviness interaction.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.2
• /
• pp.160-168
• /
• 2008

This paper presents the study on the stability of nonlinear oscillations of a thin cantilever beam subject to harmonic base excitation in vertical direction. Two partial differential governing equations under combined parametric and external excitations were derived and converted into two-degree-of-freedom ordinary differential Mathieu equations by using the Galerkin method. We used the method of multiple scales in order to analyze one-to-one combination resonance. From these, we could obtain the eigenvalue problem and analyze the stability of the system. From the thin cantilever experiment using foamax, we could observe the nonlinear modes of bending, twisting, sway, and snap-through buckling. In addition to qualitative information, the experiment using aluminum gave also the quantitative information for the stability of combination resonance of a thin cantilever beam under parametric excitation.

• Journal of the Institute of Convergence Signal Processing
• /
• v.8 no.3
• /
• pp.217-221
• /
• 2007

This paper deals with the robust nonlinear controller design using output feedback for a Chua circuit which is one of the well-known nonlinear models. First, an exosystem for reference signal tracking is defined, and error dynamic equations are derived from the differentiation of the output tracking error equation. The normal sliding surface is modified using the integral type servo compensator. The parameters in the equations of the modified sliding surface and servo compensator are determined by using the Hurwitz condition of stability. Especially the error signals can't be obtained directly from the output because all parameters are assumed unknown. So instead, a high gain observer is designed. From this estimated error signals, a stabilizing controller is designed. Simulation is done for demonstrating the effectiveness of the suggested algorithm.