• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.513-521
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• 2014

Via extension of the classical double-Newton method, we propose high-order family of two-point methods in this paper. Theoretical and computational properties of the proposed methods are fully investigated along with a main theorem describing methodology and convergence analysis. Typical numerical examples are thoroughly treated to verify the underlying theory.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.3
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• pp.237-244
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• 2016

This paper presents a nonlinear Moving Least Squares(MLS) difference method for material nonlinearity problem. The MLS difference method, which employs strong formulation involving the fast derivative approximation, discretizes governing partial differential equation based on a node model. However, the conventional MLS difference method cannot explicitly handle constitutive equation since it solves solid mechanics problems by using the Navier's equation that unifies unknowns into one variable, displacement. In this study, a double derivative approximation is devised to treat the constitutive equation of inelastic material in the framework of strong formulation; in fact, it manipulates the first order derivative approximation two times. The equilibrium equation described by the divergence of stress tensor is directly discretized and is linearized by the Newton method; as a result, an iterative procedure is developed to find convergent solution. Stresses and internal variables are calculated and updated by the return mapping algorithm. Effectiveness and stability of the iterative procedure is improved by using algorithmic tangent modulus. The consistency of the double derivative approximation was shown by the reproducing property test. Also, accuracy and stability of the procedure were verified by analyzing inelastic beam under incremental tensile loading.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.1-14
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• 2016

In this paper, an alternative analytical method is presented to evaluate the nonlinear vibration behavior of single and double tapered cantilever beams. The admissible lateral displacement function satisfying the geometric boundary conditions of a single or double tapered cantilever beam is derived by using Rayleigh-Ritz method. Based on the Lagrange method and the Newton Harmonic Balance (NHB) method, analytical approximate solutions in closed and explicit form are obtained. These approximate solutions show excellent agreement with those of numeric method for small as well as large amplitude. Moreover, due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large amplitude vibration response of tapered beams.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.491-497
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• 2015

In this paper, we have suggested an extended double Newton's method with sixth-order convergence by considering a control parameter ${\gamma}$ and a weight function H(s, u). We have determined forms of ${\gamma}$ and H(s, u) in order to induce the greatest order of convergence and established the main theorem utilizing related properties. The developed theory is ensured by numerical experiments with high-precision computation for a number of test functions.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.1
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• pp.49-55
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• 1996

In this paper, the characteristics of a double-sided linear pulse motor (DLPM) with permanent magnet are analysed using the method which combined the coenergy method and the equivalent magnetic circuit method. In the process of computation, the magnetic material nonlinealities of the permanent magnet, the primary and the secondary core are interpolated by the cubic spline method. Then, the equivalent magnetic circuit modelled by the permeance method including airgap reluctance, which is a function of displacement, is obtained. The static thrust which is the derivative of coenergy is computed by Newton Raphson method at each dispacement. And, in order to investigate the characteristics of the DLPM, the thrust shows as a function of displacement, input current and air gap. The simulation resuls are compared with experimental ones obtained from the DLPM with 2 phase and 4 poles.

• Steel and Composite Structures
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• v.31 no.4
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• pp.397-408
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• 2019

In this paper, a geometrically nonlinear meshfree analysis of 3D various forms of shell structures using the double director shell theory with finite rotations is proposed. This theory is introduced in the present method to remove the shear correction factor and to improve the accuracy of transverse shear stresses with the consideration of rotational degrees of freedom.The present meshfree method is based on the radial point interpolation method (RPIM) which is employed for the construction of shape functions for a set of nodes distributed in a problem domain. Discrete system of geometrically nonlinear equilibrium equations solved with the Newton-Raphson method is obtained by incorporating these interpolations into the weak form. The accuracy of the proposed method is examined by comparing the present results with the accurate ones available in the literature and good agreements are found.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.16 no.3
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• pp.152-161
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• 2004

Double-peak normal distribution function was suggested as the probability density function of the tidal elevation data in Korean coastal zone. Frequency distribution analysis was carried out using hourly tidal elevation data of the ten tidal gauging stations, i.e., Incheon, Kunsan, Mokpo, Cheju, Yeosu, Masan, Gadeokdo, Pusan, Pohang, and Sokcho which were served through the Internet Homepage by the National Ocean Research Institute. Based on the RMS error and $R^2$ value comparison analysis, it was found that this suggested function as the probability density function of the tidal elevation data was found to be more appropriate than the normal distribution function. The parameters of the double-peak function were estimated optimally using Levenberg-Marquardt method which was modified from the Newton method. The estimated parameters were highly correlated with the non-tidal constants of the tidal gauging stations.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.219-224
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• 1992

A numerical method using the truncated Fourier series is presented to predict the wave potential and water surface profile for two dimensional nonlinear standing waves. The unknown coefficients of the series are to be determined through the Newton solution of nonlinear simultaneous equations given by the governing equation and boundary conditions of the problem. In order to prove the effectiveness of the present method. an existing Stokes-like perturbation method is considered together, and a hydraulic experiment for measuring water surface profile and wave pressure is performed as well. The results are such that the present method can generally give exact solutions even for relatively big wave stiffness regardless of the water depth condition. It also demonstrates its validity by showing double humps in the crest of temporal wave pressure profile which normally appear in strongly nonlinear standing waves.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.43 no.5
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• pp.753-760
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• 1994

This paper proposes a new method to compute the static thrust of a hybrid-type LPM by the coenergy method, which can be applied to a nonlinear programming of the optimization techniques for the optimal design. In the process of the computation, the magnetic nonlinearities of the permanent magnet, the primary and the secondary core are interpolated by the cubic spline method. And then, the equivalent magnetic circuit including the airgap reluctance which is a function of the displacement is modelled by the permeance method. The static thrust which is a derivative of the coenergy is computed by the Newton Raphson method at each displacement. To verify this proposed method, the results of the compjutation are compaction with those of the experiment obtained from the DLPM with 2 phase and 4 poles.

• Tribology and Lubricants
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• v.34 no.4
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• pp.125-131
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• 2018

A precision tribometer consisting of a cantilever was designed to measure frictional forces in the micro-Newton range. As frictional forces are measured based on the bending of the cantilever, vibration of the cantilever is the most significant factor affecting the quality of the friction measurement. Therefore, improved design of the tribometer with double cantilevers and a connecting plate that united the two cantilevers mechanically was suggested. For the verification of the modified design of the tribometer, numerical analysis and experiments were conducted. Examination using the finite element method revealed that the tribometer with a double cantilever and a connecting plate exhibited faster damping characteristics than the tribometer with a single cantilever. In the experiment, effectiveness of the double cantilever and connecting plate for vibration reduction was also confirmed. Vibration of the tribometer with double cantilever decreased eight times faster than that of the tribometer with a single cantilever. The faster damping of the double cantilever design is attributed to the mechanical interaction at the contacting surfaces between the cantilever and the connecting plate. Tribotesting using the tribometer with a single cantilever resulted in random fluctuation of frictional forces due to the stick-slip behavior. However, using the tribometer with a double cantilever and connecting plate for the tribotest gave relatively uniform and steady measurement of frictional forces. Increased stiffness owing to using a double cantilever and mechanical damping of the connecting plate were responsible for the stable friction signal.