• 대한수학회지
• /
• 제59권3호
• /
• pp.519-548
• /
• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Steel and Composite Structures
• /
• 제33권1호
• /
• pp.133-142
• /
• 2019

In the present study, microstructure-dependent static stability analysis of inhomogeneous tapered micro-columns is performed. It is considered that the micro column is made of functionally graded materials and has a variable cross-section. The material and geometrical properties of micro column vary continuously throughout the axial direction. Euler-Bernoulli beam and modified couple stress theories are used to model the nonhomogeneous micro column with variable cross section. Rayleigh-Ritz solution method is implemented to obtain the critical buckling loads for various parameters. A detailed parametric study is performed to examine the influences of taper ratio, material gradation, length scale parameter, and boundary conditions. The validity of the present results is demonstrated by comparing them with some related results available in the literature. It can be emphasized that the size-dependency on the critical buckling loads is more prominent for bigger length scale parameter-to-thickness ratio and changes in the material gradation and taper ratio affect significantly the values of critical buckling loads.

• Structural Engineering and Mechanics
• /
• 제10권5호
• /
• pp.451-462
• /
• 2000

Buckling loads are determined for thin isotropic circular cylindrical shell panels subject to radial pressure using the new differential quadrature method. The Budiansky stability theory serves as the basis of the analysis. For this problem involving four boundary lines a two-dimensional approach is used, and a detailed convergence study is carried out to determine the appropriate analysis parameters for the method. Numerical results are determined for a total of twelve cylindrical shell panel cases for a number of different boundary support conditions. The results are compared with analytical and finite element method results. Conclusions are drawn about the technical significance of the results and the solution process.

• Journal of electromagnetic engineering and science
• /
• 제11권1호
• /
• pp.11-15
• /
• 2011

Preserving high-order accuracy in high-order FDTD solutions across dielectric interfaces is very important for practical time-domain electromagnetic simulations. This paper presents a fourth-order accurate numerical boundary scheme for the planar dielectric interface to be used in the fourth-order FDTD method proposed earlier by the author. The interface scheme for the two-dimensional (2-D) transverse magnetic (TM) polarization case is derived and validated by monitoring the $L_2$ norm errors in the numerical solutions of a partially-filled cavity demonstrating its fourth-order convergence and long-time numerical stability in the presence of the planar dielectric interface.

• Nonlinear Functional Analysis and Applications
• /
• 제26권1호
• /
• pp.197-223
• /
• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

• 한국지진공학회:학술대회논문집
• /
• 한국지진공학회 2005년도 학술발표회 논문집
• /
• pp.74-81
• /
• 2005

The purpose of this study is to suggest a proper analysis model that can evaluate seismic stability for local rock foundation of nuclear power plant. Sliding Analysis, Pseudo-static Analysis and Danamic Analysis methods are used for analysing NPP rock foundation with the conditions like acting directions of input earthquake, boundary conditions, width and depth of analysing model, and modeling methods of weakness fault zones. As the results of study, Pseudo-static Analysis for lateral roller and dynamic analysis for transfer boundary condition showed good results, and analysing ranges of width and depth were 5 times of structure width and over 2 times of structure depth.

• Advances in concrete construction
• /
• 제17권4호
• /
• pp.187-210
• /
• 2024

Cantilever structures demonstrate diverse nonlocal effects, resulting in either stiffness hardening or dynamic softening behaviors, as various studies have indicated. This research delves into the free and forced vibration analysis of rotating nanoscale cylindrical beams and tubes under external dynamic stress, aiming to thoroughly explore the nonlocal impact from both angles. Utilizing Euler-Bernoulli and Reddy beam theories, in conjunction with higher-order tube theory and Hamilton's principle, nonlocal governing equations are derived with precise boundary conditions for both local and nonlocal behaviors. The study specifically examines two-dimensional functionally graded materials (2D-FGM), characterized by axially functionally graded (AFG) and radial porosity distributions. The resulting partial differential equations are solved using the generalized differential quadrature element method (GDQEM) and Newmark-beta procedures to acquire time-dependent results. This investigation underscores the significant influence of boundary conditions when nonlocal forces act on cantilever structures.

• 대한기계학회논문집A
• /
• 제21권2호
• /
• pp.337-345
• /
• 1997

An analysis is presented for the response of a beam constrained by a nonlinear spring to a harmonic excitation. The system is governed by a linear partial differential equation with a nonlinear boundary condition. The method of multiple scales is used to reduce the nonlinear boundary value problem to a system of autonomous ordinary differential equations of the amplitudes and phases. The case of the third-order subharmonic resonance is considered in this study. The autonomous system is used to determine the steady-state responses and their stability.

• 한국환경과학회지
• /
• 제11권3호
• /
• pp.155-160
• /
• 2002

Using measured data at Daegu by tethersonde for the period of 1984∼1987, we have investigated the lower atmospheric boundary layer structure including relationships between inversion layer and meteorological factors(wind and temperature), and the inversion strength and inversion height. The inversion layer was defined from the vertical temperature profile and its strength was analyzed with the wind shear as well as the vertical temperature gradient. From October to January, measured inversion layer isn't destroyed, however, in June, after sun rise, it is destroyed by surface heating and mixed layer is developed from surface. According to Pasquill stability classes, the moderately stable cases dominated. It's the larger vertical temperature gradient the lower SBL height. We have introduced B(bulk turbulence scale) which indicated SBL height. It's larger B, the higher SBL height and vice versa. It was noted that the bulk turbulence scale (B) is appropriate to determine the stable boundary layer height.

• 대한수학회지
• /
• 제42권6호
• /
• pp.1121-1136
• /
• 2005

Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $$U_t\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;U_x,\;U_{xx})\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(u,\;u_x),\;{\alpha}\;=\;0,\;1,\;2$$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.