• Korean Journal of Mathematics
• /
• 제31권3호
• /
• pp.269-294
• /
• 2023

The purpose of this paper is to introduce a new three-step iterative process and show that our iteration scheme is faster than other existing iteration schemes in the literature. We provide a numerical example supported by graphs and tables to validate our proofs. We also prove convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some weak and strong convergence theorems for nonexpansive mappings.

• Journal of Mechanical Science and Technology
• /
• 제15권9호
• /
• pp.1257-1267
• /
• 2001

For efficient mechanical system optimization, a new two-point approximation method is presented. Unlike the conventional two-point approximation methods such as TPEA, TANA, TANA-1, TANA-2 and TANA-3, this introduces the shifting level into each exponential intervening variable to avoid the lack of definition of the conventional exponential intervening variables due to zero-or negative-valued design variables. Then a new quadratic approximation whose Hessian matrix has only diagonal elements of different values is proposed in terms of these shifted exponential intervening variables. These diagonal elements are determined in a closed form that corrects the typical error in the approximate gradient of the TANA series due to the lack of definition of exponential type intervening variables and their incomplete second-order terms. Also, a correction coefficient is multiplied to the pre-determined quadratic term to match the value of approximate function with that of the previous point. Finally, in order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve six typical design problems. These optimization results are compared with those of TANA-3. These comparisons show that the proposed method gives more efficient and reliable results than TANA-3.

• Journal of Mechanical Science and Technology
• /
• 제16권10호
• /
• pp.1264-1275
• /
• 2002

This paper is concerned with the investigation on the stability and convergence characteristics of the Crank-Nicolson-Galerkin scheme that is widely being employed for the numerical approximation of parabolic-type partial differential equations. Here, we present the theoretical analysis on its consistency and convergence, and we carry out the numerical experiments to examine the effect of the time-step size △t on the h- and P-convergence rates for various mesh sizes h and approximation orders P. We observed that the optimal convergence rates are achieved only when △t, h and P are chosen such that the total error is not affected by the oscillation behavior. In such case, △t is in linear relation with DOF, and furthermore its size depends on the singularity intensity of problems.

• 유체기계공업학회:학술대회논문집
• /
• 유체기계공업학회 2001년도 유체기계 연구개발 발표회 논문집
• /
• pp.454-459
• /
• 2001

The present study is concerned with the flow patterns induced by other impellers in a rectangular tank Impellers are FBT(Flat blade turbine), PBT(Pitched blade turbine), Shroud turbine, Rushton Turbine, and Helical ribbon turbine. The solution of flows in moving reference frames requires the use of 'moving' cell zone. The moving zone approaches are MRF(Multiple reference frame), which is a steady-state approximation and Sliding method, which is a unsteady-state approximation. Numerical results using two moving zone approaches are compared with experiments by Ranade & Joshi, which have done extensive LDA measurements of the flow generated by a standard six-bladed Rushton turbine in a cylindrical baffled vessel. In this paper we simulated the flow patterns with above mentioned moving zone approaches and impellers. Turbulence model is RNG k-$\epsilon$ model.

• Ocean Systems Engineering
• /
• 제7권1호
• /
• pp.53-74
• /
• 2017

Ship shaped FPSO (Floating Production, Storage and Offloading) units are the most commonly used floating production units to extract hydrocarbons from reservoirs under the seabed. These structures are usually much larger than general cargo ships and have their natural frequency outside the wave frequency range. This results in the response to first order wave forces acting on the hull to be negligible. However, second order difference frequency forces start to significantly impact the motions of the structure. When the difference frequency between wave components matches the roll natural frequency, the structure experiences a significant roll motion which is also termed as second order roll. This paper describes the theory and numerical implementation behind the calculation of second order forces and motions of any general floating structure subjected to waves. The numerical implementation is validated in zero speed case against the commercial code OrcaFlex. The paper also describes in detail the popular approximations used to simplify the computation of second order forces and provides a discussion on the limitations of each approximation.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
• /
• pp.201-208
• /
• 2003

Since the real steel box girder bridges have a large number of design variables and show complex structural behavior, it would be impractical to directly use the algorithm for its optimum design. Thus, in this study, for optimum design of real steel box girder bridge, approximated reanalysis using an higher-order Improved self-adjusted Convex Approximation (ISACA) which was newly proposed on a previous study by the author is applied for the numerical efficiency. To demonstrate the efficiency, robustness, and convergence of the approximated reanalysis technique using the ISACA, a real bridge having two continuous spans is used as an illustrative example. From the results of the numerical investigation, it may be positively stated that the efficiency, robustness, and convergence of the approximated reanalysis using an ISACA is superior compared with the previous approximated reanalysis techniques.

• 대한산업공학회지
• /
• 제7권1호
• /
• pp.5-11
• /
• 1981

In the case of numerical implementation, the exact solution method for the M/M/s system where customers demand multiple server use [2] reveals limitations, if a system has large number of servers or types of customers. This is due to the huge matrices involved in the course of the calculations. This paper offers an approximation scheme for such cases. Capitalizing the characteristics of the service rate curve of the system, this method approximates the service rate as a piecewise linear function. With the service rates obtained from the linear function for each number of customers n (n=0. 1. 2,$\cdots$), ${\mu}(n)$, steady-state probabilities and measures of performance are found treating this system as an ordinary M/M/s system. This scheme performs well when the traffic intensity of a system is below about 0.8. Some numerical examples are presented.

• Interaction and multiscale mechanics
• /
• 제6권2호
• /
• pp.107-125
• /
• 2013

A strain smoothing meshfree formulation with stabilized conforming nodal integration is presented for modeling the consolidation process in saturated porous media. In the present method, nodal strain smoothing is consistently introduced into the meshfree approximation of strain and pore pressure gradient variables associated with the saturated porous media. Meanwhile, in order to achieve a consistent numerical implementation, a smoothing approximation of the meshfree shape function within a nodal representative domain is also proposed in the stiffness construction. The resulting discrete system of equations is all expressed in smoothed nodal measures that are very efficient for numerical evaluation. Subsequently the space-time fully discrete equations are further established by the generalized trapezoidal rule for time integration. The effectiveness of the proposed meshfree consolidation analysis method is systematically illustrated by several benchmark problems.

• Structural Engineering and Mechanics
• /
• 제4권1호
• /
• pp.61-72
• /
• 1996

The time-stepping boundary element method has been so far applied by the authors to transient heat conduction in isotropic solids as well as in orthotropic solids. In this paper, attempt is made to extend the method to 2-D transient heat conduction in arbitrarily anisotropic solids. The resulting boundary integral equation is discretized by means of the boundary element with quadratic interpolation. The final system of equations thus obtained is solved by advancing the time step from the given initial state to the final state. Through numerical compuation of a few examples the potential usefulness of the proposed method is demonstrated.

• Structural Engineering and Mechanics
• /
• 제46권4호
• /
• pp.549-569
• /
• 2013

A passive control using flaps will be an alternative solution for flutter stability and buffeting response of a long suspension bridge. This method not only enables a lightweight economic stiffening girder without an additional stiffness for aerodynamic stability but also avoid the problems from the malfunctions of control systems and energy supply system of an active control by winglets and flaps. A time domain approach for predicting the coupled flutter and buffeting response of bridge deck with flaps is investigated. First, the flutter derivatives of bridge deck and flaps are found by experiment. Next, the derivation of time domain model of self-excited forces and control forces of sectional model is reported by using the rational function approximation. Finally, the effectiveness of passive flap control is investigated by the numerical simulation. The results show that the passive control by using flaps can increase the flutter speed and decrease the buffeting response. The experiment results are matched with numerical ones.