• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.2
• /
• pp.127-134
• /
• 2009

T-splines are recently proposed geometric modeling tools. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. Local refinement can be performed very easily for T-splines while it is limited for B-splines or NURBS. Using T-splines, patches with unmatched boundaries can be combined easily without special technique. In this study, the analysis methodology using T-splines is proposed. In this methodology, T-splines are used both for description of geometries and for approximation of solution spaces. Two-dimensional linear elastic and dynamic problems will be solved by employing the proposed T-spline finite element method, and the effectiveness of the current analysis methodology will be verified.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.16 no.3
• /
• pp.75-80
• /
• 2007

It is necessary to analyze the contact phenomena in order to effectively design the machine components with contact surfaces. In general, the contact action is highly nonlinear and irreversible because we cannot predict the contact regions and conditions. Recently, the finite element method is used to analyze the contact problem. In this paper, the contact element method is applied to avoid the mesh refinement and iterative calculation of general contact algorithms. By use of it, the deformation and stress concentration of turbo compressor rotor are computed. It shown that the contact element is convenient analysis and the results are relatively accurate.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1995.10a
• /
• pp.736-739
• /
• 1995

The meshless adaptive method based on multiple scale analysis is developed to simulate large deformation problems. In the procedure, new particles are simply added to the orginal particle distribution because meshless methods do not require mesh structures in the formulations. The high scale component of the approximated solution detects the localized region where a refinement is needed. The high scale component of the second invariant od Green-Lagrangian strain tensor is suggested as the new high gradient detector for adaptive procedures. The feasibility of the proposed theory is demonstrated by a numerical experiment for the large deformation of hyperelastic materials.

• East Asian mathematical journal
• /
• v.24 no.1
• /
• pp.21-25
• /
• 2008

The semilocal convergence of the secant method under $H{\ddot{o}}lder$ continuous divided differences in a Banach space setting for solving nonlinear equations has been examined by us in [3]. The local convergence was recently examined in [4]. Motivated by optimization considerations and using the same hypotheses but more precise estimates than in [4] we provide a local convergence analysis with the following advantages: larger radius of convergence and finer error estimates on the distances involved. The results can be used for projection methods, to develop the cheapest possible mesh refinement strategies and to solve equations involving autonomous differential equations [1], [4], [7], [8].

• Journal of ILASS-Korea
• /
• v.16 no.4
• /
• pp.186-194
• /
• 2011

This study performed the numerical analysis of the internal nozzle flows including cavitation phenomena by using the automated body-fitted grid generator and the multi-fluid model. The effect of grid refinement and the validation of multifluid model were investigated using four computational meshes under two test conditions. The mesh #3 was chosen as the optimum which can reduce the computational time and have good prediction ability to identify the cavitation region simultaneously. In addition, the computed results using multi-fluid model were compared with the reference experimental observations and numerical simulation results using homogeneous equilibrium model. From the distribution of volume fraction and velocity field, the multi-fluid model predicted the internal nozzle flows well when the liquid quality parameters were selected as $1.0{\times}10^{12}$ for initial number density and 25 ${\mu}m$ for bubble diameter.

• 한국전산유체공학회:학술대회논문집
• /
• 1995.10a
• /
• pp.182-187
• /
• 1995

The present paper explains some advancement made by the authors for the compressible flow computation of the Euler equations based on the unstructured grid and vertex- centered finite volume method. Accurate solutions to the unsteady axisymmetric shock wave propagation problems and three-dimensional airplane flows have been obtained by a high-order upwind TVD and FCT schemes. Unstructured grid adaption is made for the unsteady shock wave problems by the dynamic h-refinement/unrefinement procedure and for the three-dimensional steady flows by the Delaunay point-insertion method to generate three-dimensional tetrahedral mesh enrichment. Some physics of the shock wave diffraction phenomena and three-dimensional airplane flow are discussed.

• Journal of Mechanical Science and Technology
• /
• v.14 no.7
• /
• pp.789-795
• /
• 2000

Free-surface flows with an arbitrary deformation, induced by a submerged hydrofoil, are simulated numerically, considering two-fluid flows of both water and air. The computation is performed by a finite volume method using unstructured meshes and an interface capturing scheme to determine the shape of the free surface. The method uses control volumes with an arbitrary number of faces and allows cell wise local mesh refinement. The integration in space is of second order, based on midpoint rule integration and linear interpolation. The method is fully implicit and uses quadratic interpolation in time through three time levels. The linear equations are solved by conjugate gradient type solvers, and the non-linearity of equations is accounted for through Picard iterations. The solution method is of pressure-correction type and solves sequentially the linearized momentum equations, the continuity equation, the conservation equation of one species, and the equations for two turbulence quantities. Finally, a comparison is quantitatively made at the same speed between the computation and experiment in which the grid sensitivity is numerically checked.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.335-349
• /
• 2003

Almost all business are affected by the weather so that weather derivatives has been traded to hedge weather risk. Since the weather itself is not an asset with a market price, some analysts believe that the Black-Scholes equation could not be used appropriately to price weather derivative options. But some weather derivatives can be considered as an Asian option, we revisit the Black-scholes model. Numerical solution of the Black-Scholes equation has a significant error at the money option or around the money option, it is necessary to adopt adaptive mesh near to the strike value. Here we propose a numerical method with an adaptive grid refinement.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.1-17
• /
• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.24 no.7 s.178
• /
• pp.1833-1840
• /
• 2000

Commercially pure copper is tested to obtain creep curves at 2500C. Constitutive relations adopting continuum damage mechanics concept is found to be appropriate to model the creep defor mation up to the tertiary stage. Microscopic observation by SEM reveals that creep condition induces cavities and microcracks subsequently. The constitutive equations along with evaluated creep parameters are implemented into finite element analysis code. The analysis reproduces creep curves under step loading as well as constant loading with reasonable accuracy. Distribution and evolution of damage under creep loading are numerically simulated for two different types of notched specimen. Predicted creep life agrees quite well with rupture test results. The influence of mesh size at notch tip on rupture time prediction is studied, and a degree of refinement is suggested for the specific notched specimens.