• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.605-615
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• 2009

In this paper, we develop a reliable algorithm which is called the variation of parameters method for solving sixth-order boundary value problems. The proposed technique is quite efficient and is practically well suited for use in these problems. The suggested iterative scheme finds the solution without any perturbation, discritization, linearization or restrictive assumptions. Moreover, the method is free from the identification of Lagrange multipliers. The fact that the proposed technique solves nonlinear problems without using the Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method. Several examples are given to verify the reliability and efficiency of the proposed method. Comparisons are made to reconfirm the efficiency and accuracy of the suggested technique.

• Journal of Electrical Engineering and Technology
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• v.10 no.2
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• pp.676-687
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• 2015

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.4 no.2
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• pp.182-186
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• 2004

This paper describes an advanced compensation for non-linear functions designed to remove steering aberrations from phased array antennas. This system alters the steering command applied to the antenna in a way that the appropriate angle commands are given to the array steering software for the antenna to point to the desired position instead of squinting. Artificial neural networks are used to develop the inverse function necessary to correct the aberration. Also a straightforward antenna steering function is implemented with neural networks for the 9-term polynomials of forward steering function. In all cases the aberration is removed resulting in small RMS angular errors across the operational angle space when the actual antenna position is compared with the desired position. The use of neural network model provides a method of producing a non-linear system that can correct antenna performance and demonstrates the feasibility of generating an inverse steering algorithm.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.151-167
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• 2006

A p-version of the finite element method in conjunction with the modeling dynamic method using the arc-length stretch deformation is considered to determine the bending natural frequencies of a cantilever flexible plate mounted on the periphery of a rotating hub. The plate Fourier p-element is used to set up the linear equations of motion. The transverse displacements are formulated in terms of cubic polynomials functions used generally in FEM plus a variable number of trigonometric shapes functions representing the internals DOF for the plate element. Trigonometric enriched stiffness, mass and centrifugal stiffness matrices are derived using symbolic computation. The convergence properties of the rotating plate Fourier p-element proposed and the results are in good agreement with the work of other investigators. From the results of the computation, the influences of rotating speed, aspect ratio, Poisson's ratio and the hub radius on the natural frequencies are investigated.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.2
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• pp.206-222
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• 2015

This work uses different finite element approaches to the free vibration analysis of reinforced shell structures, and a simplified model of a typical launcher with two boosters is used as an example. The results obtained using a refined one-dimensional (1D) beam model are compared to those obtained with commercial finite element software. The 1D models that are used in the present work are based on the Carrera Unified Formulation (CUF), which assumes a variable kinematic displacement field over the cross-sections of the beam. Two different sets of polynomials that correspond to Taylor (TE) or Lagrange (LE) expansions were used. The analyses focused on three reinforced structures: a stiffened panel, a reinforced cylinder and the complete structure of the launcher. The frequencies and natural modes obtained using one-dimensional models are compared to those obtained from classical finite element analysis. The classical FE models were built using a beam-shell or solid elements, and the results indicate that the refined beam models can in fact be used to investigate the behavior of very complex reinforced structures. These models can predict the shell-like modes that are typical of thin-walled structures that cannot be detected using classical beam models. The refined 1D models used in the present work provide results that are as accurate as those from solid FE models, but the 1D models have a much lower computational cost.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.3
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• pp.207-215
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• 2015

This paper deals with a theoretical method to calculate natural frequencies of a fixed-free rectangular tank partially in contact with an outer water gap. Orthogonal polynomials satisfying the boundary conditions of the tank are used as admissible functions in the Rayleigh-Ritz method. A quarter model of the liquid-coupled system is constructed and it is simplified to a line supported flat plate in contact with the liquid. The liquid displacement potential functions satisfying the Laplace equation and water boundary conditions are derived, and the finite Fourier transform is accomplished in conjunction with the compatibility requirement along the contacting interfaces between the tank and water. An eigenvalue problem is derived so that the natural frequencies of the wet rectangular tank can be extracted. The predictions from the proposed analytical method show good agreement with the finite element analysis results.

• Journal of Korean Society of Steel Construction
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• v.10 no.1 s.34
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• pp.47-61
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• 1998

The behavior of horizontally curved I-girder bridges is complex because the flexural and torsional behavior of curved girders are coupled due to their initial curvature. Also, the behavior is affected by cross beams. To investigate the behavior of horizontally curved I-girder bridges, it is necessary to consider curved girders with cross beams. In order to perform free vibration analyses of horizontally curved I-girder bridges, a finite element formulation is presented here and a finite element analysis program is developed. The formulation that is presented here consists of curved and straight beam elements, including the warping degree of freedom. Based on the theory of thin-walled curved beams, the shape functions of the curved beam elements are derived from homogeneous solutions of the static equilibrium equations. Third-order hermits polynomials are used to form the shape functions of the straight beam elements. In the finite element analysis program, global stiffness and mass matrix are composed, based on the Cartesian coordinate system. The Gupta method is used to efficiently solve the eigenvalue problem. Comparing the results of several examples here with those of previous studies, the formulation presented is verified. The validity of the program developed is shown by comparing results with those analyzed by the shell element.

• Journal of Korea Water Resources Association
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• v.32 no.3
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• pp.237-246
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• 1999

A finite element model is studied to simulate unsteady free surface flow based on dynamic wave equation and collocation method. The collocation method is used in conjunction with Hermite polynomials, and resulting matrix equations are solved by skyline method. The model is verified by applying to hydraulic jump, nonlinear disturbance propagation and dam-break flow in a horizontal frictionless channel. The computed results are compared with those by Bubnov-Galerkin and Petrov-Galerkin methods. It is also applied to the North Han River to simulate the floodwave propagation. The computed results have good agreements with those of DWOPER model in terms of discharge hydrographs. The suggested model has proven to be one of the promising scheme for simulating the gradually and rapidly varied unsteady flow in open channels.