• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Structural Engineering and Mechanics
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• v.75 no.3
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• pp.311-325
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• 2020

In applying the spectral stochastic finite element methods to the frequency response analysis, the conventional methods are known to give unstable and inaccurate results near the natural frequencies. To address this issue, a new sensitivity based stabilized formulation for stochastic frequency response analysis is proposed in this paper. The main difference over the conventional spectral methods is that the polynomials of random variables are applied to both numerator and denominator in approximating the harmonic response solution. In order to reflect the resonance behavior of the structure, the denominator polynomials is constructed by utilizing the natural frequency sensitivity and the random mode superposition. The numerator is approximated by applying a polynomial chaos expansion, and its coefficients are obtained through the Galerkin or the spectral projection method. Through various numerical studies, it is seen that the proposed method improves accuracy, especially in the vicinities of structural natural frequencies compared to conventional spectral methods.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

• The Journal of Society for e-Business Studies
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• v.6 no.2
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• pp.159-166
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• 2001

EC(Electronic Commerce) is increasing with high speed based on the expansion of Internet. EC which is done through Internet has strong point like independence from time and space, On the contrary, it also has weak point like security problem because anybody can access easily to the system due to open network attribute of Internet. Therefore, we need the solutions that protect the security problem for safe and useful U activity, One of these solutions is the implementation of strong cipher algorithm. NPC(Non-Polynomial Complete) cipher algorithm proposed in this paper is good for the security and it overcome the limit of current 64bits cipher algorithm using 256bits key for input output and encryption key, Moreover, it is designed for the increase of calculation complexity and probability calculation by adapting more complex design for subkey generation regarded as one of important element effected to encryption.

• Proceedings of the SAREK Conference
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• 2009.06a
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• pp.435-440
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• 2009

For the effective control of a $CO_2$ air-conditioning system, the system high-side pressure algorithm, the indoor temperature algorithm, and the outdoor fan algorithm were developed. The system high-side pressure algorithm was composed of the setpoint algorithm, the reset algorithm, and the electronic expansion valve control algorithm. The indoor temperature algorithm was composed of the compressor control algorithm and the indoor fan control algorithm. These algorithms were tested by using mathematical models developed from the previous study. Results from the setpoint step change test and the disturbance test showed good control performances. Therefore, algorithms developed in this study may practically used for the control of a $CO_2$ air-conditioning system.

• Wind and Structures
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• v.25 no.6
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• pp.589-608
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• 2017

A novel probabilistic approach is presented for estimating the equivalent static wind loads that produce a static response of the structure, which is "equivalent" in a probabilistic sense, to the extreme dynamic responses due to the unsteady pressure random field induced by the wind. This approach has especially been developed for complex structures (such as stadium roofs) for which the unsteady pressure field is measured in a boundary layer wind tunnel with a turbulent incident flow. The proposed method deals with the non-Gaussian nature of the unsteady pressure random field and presents a model that yields a good representation of both the quasi-static part and the dynamical part of the structural responses. The proposed approach is experimentally validated with a relatively simple application and is then applied to a stadium roof structure for which experimental measurements of unsteady pressures have been performed in boundary layer wind tunnel.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.25-26
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• 2006

The method measuring the absolute position of a point diffraction source emitting a spherical wavefront in three-dimension is proposed. Two-dimensional interference of spherical wavefronts is used to overcome ambiguity of phase order. The spherical wavefront is explicated by Taylor series expansion, from which a radius of curvature of a spherical wavefront and its center position in three-dimension are obtainable. The spherical wavefront is reconstructed by a modified lateral shearing interferometer, which uses single-mode fiber as a point diffraction source.

• Computational Structural Engineering
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• v.4 no.4
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• pp.97-106
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• 1991

The frequency window method has been extended to include strong coupling and multiple connections between the primary structure and the secondary structures. The rational polynomial expansion of the eigenvalue problem and the analytical methods for its solution are novel and distinguish this work from other eigenvalue analysis methods. The key results are the identification of parameters which quantify the resonance and coupling characteristics; the derivation of analytical closed-form expressions describing the fundamental modal properties in the frequency windows; and the development of an iterative procedure which yields accurate convergent results for strongly-coupled primary-secondary structures.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.241-243
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• 1998

This paper describes a new method for the faster shape optimization of the electromagnetic devices. In a conventional iterative method of shape design optimization using design sensitivity based on a finite element method, meshes for a new shape of the model are generated and a discretized system equation is solved using the meshes in each iteration. They cause much design time. To save this time, a polynomial approximation of the finite element solution with respect to the geometric design parameters using Taylor expansion is constructed. This approximate state variable expressed explicitly in terms of design parameters is employed in a gradient-based optimization method. The proposed method is applied to the shape design of quadrupole magnet.