• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.937-948
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• 2011

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

• Journal of Computational Design and Engineering
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• v.3 no.4
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• pp.330-336
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• 2016

The present work is concerned with heat and mass transfer of an electrically conducting second grade MHD fluid past a semi-infinite stretching sheet with convective surface heat flux. The analysis accounts for thermophoresis and thermal radiation. A similarity transformations is used to reduce the governing equations into a dimensionless form. The local similarity equations are derived and solved using Nachtsheim-Swigert shooting iteration technique together with Runge-Kutta sixth order integration scheme. Results for various flow characteristics are presented through graphs and tables delineating the effect of various parameters characterizing the flow. Our analysis explores that the rate of heat transfer enhances with increasing the values of the surface convection parameter. Also the fluid velocity and temperature in the boundary layer region rise significantly for increasing the values of thermal radiation parameter.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.10a
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• pp.43-44
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• 2006

• Journal of the Korean Society for Precision Engineering
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• v.25 no.8
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• pp.80-87
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• 2008

This paper investigated into the impact characteristics of the stainless sheet with thickness of 0.7 mm on the stretching boundary condition through three-dimensional finite element analysis. High speed tensile tests were carried out to obtain strain-stress relationships with the effects of the strain rate. The FE analysis was performed by the ABAQUS explicit code. In order to improve an accuracy of the FE analysis, the hyper-elastic model and the damping factor were introduced. Through the comparison of the results of the FE analyses and those of the impact tests, a proper FE model was obtained. The results of the FE analyses showed that the absorption rate of energy maintains almost 82.5-83.5% irrespective of the impact energy level and the diameter of the impact head. From the results of FE analyses, variations of stress, strain, dissipation energy, strain energy density, and local deformation characteristics in the stainless sheet during the collision and the rebound of the impact head were quantitatively examined. In addition, it was shown that the fracture of the specimen occurs when the plastic strain is 0.42 and the maximum value of the plastic dissipation energy of the specimen is nearly 1.83 J.

• The Journal of the Acoustical Society of Korea
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• v.25 no.3E
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• pp.131-136
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• 2006

The PML developed for the radio wave propagation is a powerful numerical domain truncation technique. We perform an analytic study on the reflection from the PML inserted in the ocean bottom. In the ocean bottom, we show the PML to have the improved performance but simultaneously the degeneration below the critical angle of the fast ocean bottom. The degeneration of the PML can be simply relaxed by stretching the thickness of the PML or putting the attenuation coefficient to the ocean bottom. As a better solution, we propose the improved truncation technique based on the PML and the non-local boundary condition. Finally, we apply the PML to the acoustic wave propagation using split-step Pade PE solver. For the problems of the ocean waveguide, the numerical efficiency of the PML is examined and the usefulness of the PML is confirmed.

• Transactions of Materials Processing
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• v.4 no.4
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• pp.365-374
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• 1995

Numerical simulation of blade forming is carried out as stretch forming by an elasto-plastic finite element method. The method adopts a Lagrangian formulation, which incorporates large deformation and rotation, with a penalty method to treat the contact boundary condition. Numerical integration is done with a directional reduced integration scheme to avoid shear locking. The numerical results demonstrates various final shapes of blades which depend on the variation of the stretching force. The strain distributions in deformed blades are also obtained with the variation of the stretching force.

• Structural Engineering and Mechanics
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• v.33 no.1
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• pp.15-30
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• 2009

In this study, the nonlinear vibrations of stepped beams having different boundary conditions were investigated. The equations of motions were obtained by using Hamilton's principle and made non dimensional. The stretching effect induced non-linear terms to the equations. Natural frequencies are calculated for different boundary conditions, stepped ratios and stepped locations by Newton-Raphson Method. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. At the second part, an alternative method is produced for the analysis. The calculated natural frequencies and nonlinear corrections are used for training an artificial neural network (ANN) program which has a multi-layer, feed-forward, back-propagation algorithm. The results of the algorithm produce errors less than 2.5% for linear case and 10.12% for nonlinear case. The errors are much lower for most cases except clamped-clamped end condition. By employing the ANN algorithm, the natural frequencies and nonlinear corrections are easily calculated by little errors, and the computational time is drastically reduced compared with the conventional numerical techniques.

• Transactions of the Korean Society of Mechanical Engineers
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• v.8 no.5
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• pp.435-441
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• 1984

The matrix method, as an effective FEM formulation for the analysis of rigid-plastic deformation, was applied to the bore expanding of anisotropic sheet metal. The effect of planar anisotropy on sheet metal deformation was studied for bore expanding process under the uniform radial stretching condition, and the results were compared with isotropic and normal anisotropic solutions. Experiments were carried out using a flat punch for cold-rolled sheet metal. The experimental results were compared with computations from the matrix method with the boundary conditions corresponding to actual experiment. Both in theory and experiment, it is found that the maximum thinning which results in necking occurs in the direction of the minimum R-value. The results also suggest that the matrix method is efficient for analyzing planar anisotropic sheet metal. The comparison between theory and experiment suggests that Hill's theory of planar anisotropy is somewhat exaggerated. However, the theoretical predictions are in qualitative agreement with the experimental results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.3
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• pp.968-977
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• 1996

The linear/nonlinear vibration response of the rotating hybrid cylindrical shell with simply supported boundary condition is studied. The Ritz-Galerkin method is applied to obtain the nonlinear frequency equation, which excludes in-plane and rotatory inertia but includes bending stretching coupling terms. The bifurcation phenomena for the linear frequency and the frequency ratio(nonlinear/linear frequency ratio) are presented. The hybrid cylindrical shells are composed of composite(GFRP, CFRP) metal(aluminium, steel) with symmetric and antisymmetric stacking sequence. The effects of the Coriolis and centrifugal force are considered The results also present the effects of length-to- radies ratio, radius-to-thickness ratio, the circumferential wave number, the stacking sequence, the material property, the initial excitation amplitude and the rotating speed. The present linear frequency results are compared with those of the available literature.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2007.11a
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• pp.119-122
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• 2007

The present study employs experimental approach to identify combustion stability characteristics of fuel-rich gas generators. The gas generator of interest, fueled by LOx and Jet A-1, experienced combustion instability coupled to a longitudinal resonant mode of the combustion chamber at about 1200 Hz. The occurrence of instability is strongly associated with acoustic boundary condition at the exit .and axial location of maximum heat release. As a result, stretching heat release zone in the axial direction by increase of the fuel nozzle diameter has dramatically stabilized combustion.