• Geomechanics and Engineering
• /
• v.16 no.4
• /
• pp.355-361
• /
• 2018

In this paper, nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation is studied. It has been tried to prepare a semi-analytical solution for whole domain of vibration. Only one iteration lead us to high accurate solution. The effects of linear elastic foundation on the response of the beam vibration are considered and studied. The effects of important parameters on the ratio of nonlinear to linear frequency of the system are studied. The results are compared with numerical solution using Runge-Kutta $4^{th}$ technique. It has been shown that the Max-Min approach can be easily extended in nonlinear partial differential equations.

• Proceedings of the KSME Conference
• /
• 2001.06d
• /
• pp.371-376
• /
• 2001

Radiative transfer by nongray gas mixtures with nonuniform concentration and temperature profiles were studied by using the statistical narrow-band model and ray-tracing method with the sufficiently accurate $T_{60}$ quadrature set. Transmittances through the nonhomogeneous gas mixtures were calculated by using the Curtis-Godson approximation. Three different cases with different temperature and concentration profiles were considered to obtain benchmark solutions for nongray gas mixtures with nonuniform concentration and temperature profiles. The solutions obtained from this study were verified and found to be very well matched with the previous solutions for uniform gas mixtures. The results presented in this paper can be used in developing various solution methods for radiative transfer by nongray gas mixtures.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.347-350
• /
• 2004

In this paper, the acceleration is studied for the rigid-plastic FEM of metal forming simulation. In the FEM, the direct iteration and Newton-Raphson iteration are applied to obtain the initial solution and accurate solution respectively. In general, the acceleration scheme for the direct iteration is not used. In this paper, an Aitken accelerator is applied to the direct iteration. In the modified Newton-Raphson iteration, the step length or the deceleration coefficient is used for the fast and robust convergence. The step length can be determined by using the accelerator. The numerical experiments have been performed for the comparisons. The faster convergence is obtained with the acceleration in the direct and Newton-Raphson iterations.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.899-911
• /
• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• Structural Engineering and Mechanics
• /
• v.47 no.3
• /
• pp.345-359
• /
• 2013

For the purpose of investigating the free vibration response of the spatial curved beams, the governing equations are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius' scheme and the dynamic stiffness method are then applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. As a special case, the dynamic stiffness and further the natural frequencies of a cylindrical helical spring under fixed-fixed boundary condition are carried out. Comparison of the present results with the FEM results using body elements in I-DEAS shows good accuracy in computation and validity of the model. Further, the present model is used for reciprocal spiral rods with different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the resultant provide a relatively accurate solution.

• Structural Engineering and Mechanics
• /
• v.62 no.6
• /
• pp.675-693
• /
• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.701-721
• /
• 2007

Recently, a new singular function(NSF) method was posed to get accurate numerical solution on quasi-uniform grids for two-dimensional Poisson and interface problems with domain singularities by the first author and his coworkers. Using the singular function representation of the solution, dual singular functions, and an extraction formula for stress intensity factors, the method poses a weak problem whose solution is in $H^2({\Omega})$ or $H^2({\Omega}_i)$. In this paper, we show that the singular functions, which are not in $H^2({\Omega})$, also satisfy the integration by parts and note that this fact suggests the possibility of different choice of the weak formulations. We show that the original choice of weak formulation of NSF method is critical.

• Journal of Ocean Engineering and Technology
• /
• v.22 no.4
• /
• pp.1-7
• /
• 2008

The primary aim of the paper is to solve an unstable axisymmetric initial value problem of wave propagation when given initial data that is deteriorated by noise such as measurement error. To overcome the instability of the problem, Tikhonov's regularization, known as a non-iterative numerical regularization method, is introduced to solve the problem. The L-curvecriterion is introduced to find the optimal regularization parameter for the solution. It is confirmed that fairly stable solutions are realized and that they are accurate when compared to the exact solution.

• 한국전산유체공학회:학술대회논문집
• /
• 2011.05a
• /
• pp.86-87
• /
• 2011

In this paper, a conjugate heat transfer around cylinder with heat generation was investigated. Both forced convection and conduction was considered in the present finite element simulation. A finite element formulation based on SIMPLE type algorithm was adopted for the solution of the incompressible Navier-Stokes equations. We compared the finite element solution with that of Ansys fluent 12.0, in which finite volume method was employed for spatial discretization. It was found that the finite element method gave more accurate solution than Ansys fluent 12.0. Further, it was found that the maximum temperature inside cylinder is positioned at the rear side due to the flow separation.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.16 no.4
• /
• pp.225-234
• /
• 2012

We present two high-order potential flow models for the evolution of the interface in the Rayleigh-Taylor instability in two dimensions. One is the source-flow model and the other is the Layzer-type model which is based on an analytic potential. The late-time asymptotic solution of the source-flow model for arbitrary density jump is obtained. The asymptotic bubble curvature is found to be independent to the density jump of the fluids. We also give the time-evolution solutions of the two models by integrating equations numerically. We show that the two high-order models give more accurate solutions for the bubble evolution than their low-order models, but the solution of the source-flow model agrees much better with the numerical solution than the Layzer model.