• Steel and Composite Structures
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• 제17권1호
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• pp.123-131
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• 2014

In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.

• 한국해양공학회지
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• 제17권5호
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• pp.11-18
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• 2003

In two-dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure (HIP) has been implemented on a SUPG finite element formulation. By using the SUPG formulation, one can escape from the LBB constraint hence, achieving an equal order formulation. In this paper, we increased the order of interpolation up to cubic. The conjugate gradient squared (CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements have been used to achieve a higher order accuracy in fluid flow analyses, but a proper and efficient iterative procedure for higher order finite element formulation has not been available, thus far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient, and useful in flow analyses, in conjunction with hierarchical elements.

• 대한기계학회논문집
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• 제7권4호
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• pp.361-371
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• 1983

The turbulent structures of the free plane jet and two dimensional impinging jet are investigated experimentally. In order to get the two dimensional jet, the contour of the cubic equation suggested by Morel is used for a contracting nozzle. A linearized constant-temperature hot-wire anemometer is used for measurement. Mean velocities and turbulent intensities are measured along the centerline of the jet. Jet halp width spatial double velocity correlation coefficients and integral length scales are obtained. It is established that the free plane jet is truly self-preserving about 40 slot widths downstream of the nozzle. The experiments for the impinging jet are carried out at four different impingement wall locations within the self-preserving region of the free plane jet, and comparing the results with that of free plane jet, the mean velocity is changed in the region of 0.25H and turbulent intensities are affected in the region of 0.2H from the wall, respectively, where H means the distance between the nozzle exit and the wall.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2004년도 춘계 학술대회논문집
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• pp.91-98
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• 2004

In two dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure(HIP) has been implemented on a stabilized finite element formulation. The stabilization has been peformed by a modified residual method proposed by Illinca et. al.[3]. The stabilization which is necessary to escape from the LBB constraint renders an equal order formulation. In this paper, we increased the order of interpolation whithin an element up to cubic. The conjugate gradient squared(CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements has been used to achieve a higher order accuracy in fluid flow analyses, but a proper efficient iterative procedure for higher order finite element formulation has not been available so far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient and useful in flow analyses in conjunction with hierarchical elements.

• KSTLE International Journal
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• 제6권1호
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• pp.1-7
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• 2005

Wear model for predicting the vehaviour of a depth is considered in this paper. It is deduced from the energy and volume based wear models such as the Archard equation and the workrate model. A new parameter of the equivalent depth ($D_e$= wear volume /worn area) is considered for the wear model of a depth prediction. A concenpt of a dissipated shear energy density is accommodated for in the suggested models. It is found that $D_e$ can distinguish the worn area shape. A cubic of $D_e$($D_e^3$) gives a better linear regression with the volume than that of the maximmum depth $D_{max}e$($D_{max}^3$) does. Both $D_{max}$ and $D_e$ are used for the presently suggested depth-based wear model. As a result, a wear depth profile can be simulated by a model using $D_{max}$. Wear resistance from the concern of an overall depth can be identified by the wear coefficient of the model using $D_e$.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제49권1호
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• pp.52-58
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• 2000

Signal propagation in nonlinear optical fiber is analyzed numerically by using SS-FEM (Split-Step Finite Element Method). By adopting cubic element function in FEM, soliton equation of which exact solution was well known, has been solved. Also, accuracy of numerical results and computing times are compared with those of Fourier method, and we have found that solution obtained from using FEM was very relatively accurate. Especially, to reduce CPU time in matrix computation in each step, the matrix imposed by the boundary condition is approximated as a sparse matrix. As a result, computation time was shortened even with the same or better accuracy when compared to those of the conventional FEM and Fourier method.

• 유체기계공업학회:학술대회논문집
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• 유체기계공업학회 2000년도 유체기계 연구개발 발표회 논문집
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• pp.169-175
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• 2000

A design method for transonic turbine blades is developed based on Navier-Stokes equations. The present computing process is done on the four separate steps, 1.e., determination of the blade profile, generation of the computational grids, cascade flow simulation and analysis of the computed results in the sense of the aerodynamic performance. The blade shapes are designed using the cubic polynomials under the control of the design parameters. Numerical methods for the flow equations are based on Van-Leer's FVS with an upwind TVD scheme on the finite volume. Applications are made to the VKI transonic rotor blades. Computed results are analyzed with respect to the aerodynamic performance and are compared with the experimental data.

• Journal of applied mathematics & informatics
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• 제5권2호
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• pp.507-516
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• 1998

In this study we are concerned with the problem of ap-proximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4] [5] [8] These results were not given in affine invariant form and made use of a real quadratic majorizing polynomial. Here we provide our re-sults in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.

• Structural Engineering and Mechanics
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• 제54권2호
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• pp.239-256
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• 2015

An adaptive-scale damage detection strategy based on a wavelet finite element model (WFEM) for thin plate structures is established in this study. Equations of motion and corresponding lifting schemes for thin plate structures are derived with the tensor products of cubic Hermite multi-wavelets as the elemental interpolation functions. Sub-element damages are localized by using of the change ratio of modal strain energy. Subsequently, such damages are adaptively quantified by a damage quantification equation deduced from differential equations of plate structure motion. WFEM scales vary spatially and change dynamically according to actual needs. Numerical examples clearly demonstrate that the proposed strategy can progressively locate and quantify plate damages. The strategy can operate efficiently in terms of the degrees-of-freedom in WFEM and sensors in the vibration test.

• Smart Structures and Systems
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• 제19권4호
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• pp.403-413
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• 2017

The present article encompasses a nonlinear finite element (FE) and genetic algorithm (GA) based optimal vibration energy harvesting from nonprismatic piezo-laminated cantilever beams. Three cases of cross section profiles (such as linear, parabolic and cubic) are modelled to analyse the geometric nonlinear effects on the output responses such as displacement, voltage, and power. The simultaneous effects of taper ratios (such as breadth and height taper) on the output power are also studied. The FE based nonlinear dynamic equation of motion has been solved by an implicit integration method (i.e., Newmark method in conjunction with the Newton-Raphson method). Besides this, a real coded GA based constrained optimization scheme has also been proposed to determine the best set of design variables for optimal harvesting of power within the safe limits of beam stress and PZT breakdown voltage.