• Journal of the Korean Society for Advanced Composite Structures
• /
• v.6 no.3
• /
• pp.77-85
• /
• 2015

In this paper, we present the result of investigations pertaining to the elastic buckling of simply supported columns with various cross-sectional dimensions but the same length and volume. In the investigations the accuracy of the analysis methods is studied and it was found that the result obtained by the successive approximations technique is the most accurate. In addition, the elastic buckling loads of columns with variable cross-section dimensions are obtained by the theoretical and numerical methods. From the results, it was found that the buckling loads obtained by the numerical methods are close to the buckling loads obtained by the successive approximations technique for the practical standpoints. Moreover, the buckling load of column with convexity in its middle is the highest while the buckling load of the tapered column is the lowest as expected.

• Journal of applied mathematics & informatics
• /
• v.4 no.2
• /
• pp.447-456
• /
• 1997

In this paper an accurate algorithm for the method of successive approximations for near-parabolic orbits is established symbolically. Numerical applications are given for motion predictions at fifteen epochs between the years 66 to 1835 for Halley's comet. and at fifteen epochs between the years 1417 to 1782 for Encke's comet. Comparisons with the standard Gauss method [4] show that the present algorithm is very accurate and efficient for motion pred-ications of near-parabolic orbits.

• Kyungpook Mathematical Journal
• /
• v.28 no.2
• /
• pp.177-183
• /
• 1988

In this work, two numerical schemes arc proposed for solving a general form of Cauchy problem. Here, the problem, to be defined, consists of a system of Volterra integro-differential equations. Picard's and Seiddl'a methods of successive approximations are ued to obtain the approximate solution. The convergence of these approximations is established and the rate of convergence is estimated in every case.

• Proceedings of the KIEE Conference
• /
• 1999.11c
• /
• pp.591-593
• /
• 1999

The finite time optimum regulation problem of a discrete time bilinear system with a quadratic performance criterion is obtained in terms of a sequence discrete algebraic Lyapunov equations. Our new method is based on the successive approximations. This algorithm saves the computation time to solve the optimal problem, and the design procedure is illustrated for an example.

• The Pure and Applied Mathematics
• /
• v.14 no.4
• /
• pp.283-287
• /
• 2007

An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.

• Journal of the Korean Society for Advanced Composite Structures
• /
• v.6 no.1
• /
• pp.6-13
• /
• 2015

In this paper we present the result of investigations pertaining to the buckling strength of Zelkova Serrata (Elm-like) tree column with entasis at the Muryangsujeon in Buseoksa-Temple, Korea. Wooden columns with entasis had been used in the construction of ancient architectural buildings in Korea. It was not known why did they design columns with entasis of the buildings. It is just presumed that the reason may be the compensation of optical illusion, aesthetics, and/or structural safety. The question is not answered even today and it may not be possible to answer clearly and easily. In the paper, the buckling analyses are conducted on both of the wooden column with entasis and the prismatic wooden column by the successive approximations technique and the finite element methods, respectively. The results of analyses are compared and discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1993.04a
• /
• pp.19-26
• /
• 1993

The p-version crack model based on integrals of Legendre polynomial and virtual crack extension method is proposed with its potential for application to stress intensity factor computations in linear elastic fracture mechanics. The main advantage of this model is that the data preparation effort is minimal because only a small number of elements are used and the high accuracy and the rapid rate of convergence can be achieved in the vicinity of crack tip. There are two important findings from this study. Firstly, the limit value, the strain energy of the exact solution can be estimated with successive three p-version approximations by ascertaining the approximations is entered the asymptotic range. Secondly, the rate of convergence of p-version model is almost twice that of h-version model on the basis of uniform or quasiuniform mesh refinement for the cracked panel problem subjected tension.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 2004.04a
• /
• pp.166-171
• /
• 2004

In this study, shape optimization of micro-static mixer with a cantilever beam was accomplished for mixing the mixing efficiency by using successive response surface approximations. Variables were chosen as the length of cantilever beam and the angle between horizontal and the cantilever beam. Sequential approximate optimization method was used to deal with both highly nonlinear and non-smooth characteristics of flow field in a micro-static mixer. Shape optimization problem of a micro-static mixer can be divided into a series of simple subproblems. Approximation to solve the subproblems was performed by response surface approximation, which does not require the sensitivity analysis. To verify the reliability of approximated objective function and the accuracy of it, ANOVA analysis and variables selection method were implemented, respectively. It was verified that successive response surface approximation worked very well and the mixing efficiency was improved very much comparing with the initial shape of a micro-static mixer.

• Kyungpook Mathematical Journal
• /
• v.60 no.3
• /
• pp.647-671
• /
• 2020

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.

• Journal of the Korean Society of Safety
• /
• v.16 no.4
• /
• pp.208-212
• /
• 2001

DQM(differential quadrature method) is applied to computation of two dimensional elasticity problems in helical spring. Elastic shear stresses in an axially loaded helical spring having rectangular and square cross sections are calculated. The results are compared with those obtained using the method of successive approximations. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.