• Bulletin of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.697-710
• /
• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.4 no.2
• /
• pp.67-75
• /
• 2000

Sufficient conditions for boundary controllability of time varying delay integrodifferential systems in Banach spaces are established. The results are obtained by using the strongly continuous semigroup theory and the Banach contraction principle.

• Kyungpook Mathematical Journal
• /
• v.47 no.4
• /
• pp.569-578
• /
• 2007

Sufficient conditions for the existence of at least one solution of boundary value problems for higher order nonlinear difference equations are established. We allow $f$ to be at most linear, superlinear or sublinear in obtained results.

• Journal of computational fluids engineering
• /
• v.14 no.4
• /
• pp.23-30
• /
• 2009

The existing code which solves two-dimensional RANS(Reynolds Averaged Navier-Stokes) equations and 2-equation turbulence model equations was modified to enable numerical simulation of various supersonic flows. For this, various boundary conditions have been implemented to the code. Bleed boundary condition was incorporated into the code for calculating wall mean flow quantities. Furthermore, boundary conditions for the turbulence quantities along rough surfaces as well as porous walls were applied to the code. The code was verified and validated by comparing the computational results against the experimental data for the supersonic flows over bleed region on a flat plate. Furthermore, numerical simulations for supersonic shock boundary layer interaction with a bleed region were performed and their results were compared with the existing computational results.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.30 no.4
• /
• pp.335-341
• /
• 2017

In this paper, beam finite elements with higher-order derivatives' continuity are formulated and evaluated for various boundary conditions. All the beam elements are based on Euler-Bernoulli beam theory. These higher-order beam elements are often required to analyze structures by using newly developed higher-order beam theories and/or non-classical beam theories based on nonlocal elasticity. It is however rare to assess the performance of such elements in terms of boundary and loading conditions. To this end, two higher-order beam elements are formulated, in which $C^2$ and $C^3$ continuities of the deflection are enforced, respectively. Three different boundary conditions are then applied to solve beam structures, such as cantilever, simply-support and clamped-hinge conditions. In addition to conventional Euler-Bernoulli beam boundary conditions, the effect of higher-order boundary conditions is investigated. Depending on the boundary conditions, the oscillatory behavior of deflections is observed. Especially the geometric boundary conditions are problematic, which trigger unstable solutions when higher-order deflections are prescribed. It is expected that the results obtained herein serve as a guideline for higher-order derivatives' continuous finite elements.

• Fire Science and Engineering
• /
• v.29 no.4
• /
• pp.33-38
• /
• 2015

Loads applied on the floor are transferred through beams to columns. The beams can be designed as both end fixed or simple beams. The load bearing capacity of a beam depends on each boundary condition. However, when the load bearing capacity of a beam is evaluated in fire tests, all kinds of beams are tested using simple beam conditions. In this study, an analytical method performed using heat transfer theory and heat stress analysis based on the mechanical and thermal properties of SS-400 steel at high temperature. This method was used to clarify the differences between the two types of boundary conditions at normal and high temperature. The results show that the load bearing capacity of a both-end fixed beam at high temperature is superior to that of a simple beam. Therefore, the application of simple beam conditions in fire tests for evaluation of load bearing capacity is conservatively safe compared to fixed boundary conditions.

• Interaction and multiscale mechanics
• /
• v.2 no.4
• /
• pp.333-352
• /
• 2009

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

• Coupled systems mechanics
• /
• v.12 no.4
• /
• pp.365-389
• /
• 2023

Dynamic analysis of a typical concrete gravity dam-reservoir system is formulated by FE-(FE-TE) approach (i.e., Finite Element-(Finite Element-Truncation Element)). In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the H-W (i.e., Hagstrom-Warburton) high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model. The formulation is initially reviewed which was originally proposed in a previous study. Thereafter, the response of Pine Flat dam-reservoir system is studied due to horizontal and vertical ground motions for two types of reservoir bottom conditions of full reflective and absorptive. It should be emphasized that study is carried out under high order of H-W condition applied on the truncation boundary. The initial part of study is focused on the time harmonic analysis. In this part, it is possible to compare the transfer functions against corresponding responses obtained by FE-(FE-HE) approach (referred to as exact method). Subsequently, the transient analysis is carried out. In that part, it is only possible to compare the results for low and high normalized reservoir length cases. Therefore, the sensitivity of results is controlled due to normalized reservoir length values.

• Korean Journal of Mathematics
• /
• v.4 no.2
• /
• pp.179-193
• /
• 1996

This paper is concerned with the penalized stationary incompressible Navier-Stokes system with the inhomogeneous Dirichlet boundary condition on the part of the boundary. By taking a generalized velocity space on which the homogeneous essential boundary condition is imposed and corresponding trace space on the boundary, we pose the system to the weak form which the stress force is involved. We show the existence and convergence of the penalized system in the regular branch by extending the div-stability condition.

• Journal of the korean society of oceanography
• /
• v.33 no.4
• /
• pp.212-218
• /
• 1998

Three different outflow boundary conditions are considered in modeling the East Sea circulation. The first one is that of the conventional constant volume transport (CT). The second one is the Orlanski radiation boundary condition (OR). The third one is that of the constant sea level just outside the outflow boundary (SL). In the third condition, the outflow current is set to be driven by the sea level differences across the outflow open-boundary lines, based on the recent knowledge that the Tsushima Current is driven by the sea level differences across the inflow and outflow boundaries. In case of OR it takes too much time to reach the steady state, resulting in a large increase of Tsushima Current Water in the basin and low level of kinetic energy. Both CT and SL reach the steady state in a relatively short time. However, SL is more recommendable, because it is based on physical background and generates less numerical noises than CT.