• International Journal of Naval Architecture and Ocean Engineering
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• v.5 no.4
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• pp.546-558
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• 2013

The research performed in this paper was carried out to investigate the numerical analysis of the sheet cavitation on marine propeller. The method is boundary element method (BEM). Using the Green's theorem, the velocity potential is expressed as an integral equation on the surface of the propeller by hyperboloid-shaped elements. Employing the boundary conditions, the potential is determined via solving the resulting system of equations. For the case study, a DTMB4119 propeller is analyzed with and without cavitating conditions. The pressure distribution and hydrodynamic performance curves of the propellers as well as cavity thickness obtained by numerical method are calculated and compared by the experimental results. Specifically in this article cavitation changes are investigate in both the radial and chord direction. Thus, cross flow variation has been studied in the formation and growth of sheet cavitation. According to the data obtained it can be seen that there is a better agreement and less error between the numerical results gained from the present method and Fluent results than Hong Sun method. This confirms the accurate estimation of the detachment point and the cavity change in radial direction.

• Computational Structural Engineering
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• v.8 no.4
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• pp.129-136
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• 1995

This paper presents a boundary element method for obtaining approximate solutions of 2-dimensional consolidation problems based on the Biot's linear theory. Laplace transform is applied to differential equation system in order to eliminate the time dependency. The boundary integral equations in transformed space are formulated and the fundamental solutions are shown in a closed form. In order to convert the transformed solutions to the ones in real space, the Hosono's numerical Laplace transform inversion method is applied. As a numerical example, a half-space consolidation problem subjected to a strip local load is selected and the applicability of the method is demonstrated through the comparison with the exact solutions.

• Geophysics and Geophysical Exploration
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• v.2 no.2
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• pp.86-95
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• 1999

This paper presents an efficient three-dimensional (3-D) modeling algorithm using the extended approximation to an electric field integral equation. Numerical evaluations of Green's tensor integral are performed in the spatial wavenumber domain. This approach makes it possible to reduce computing time, to handle smoothly varying conductivity model and to remove singularity problems encountered in the integration of Green's tensor at a source point. The responses obtained by 3-D modeling algorithm developed in this study are compared with those by the full integral equation for a thin-sheet EM scattering. The extensive analyses on the performance of modeling algorithm are made with the conductivity contrasts and source frequencies. These results show that the modeling algorithm are accurate up to the conductivity contrast of 1:16 and the frequency range of 100 Hz-100 kHz. The extended Born approximation, however, may produce inaccurate results for some source and model configurations in which the electric field is discontinuous across the conductivity boundary. We performed the modeling of a composite model of which conductivity varies continuously and this shows the modeling algorithm developed in this study is efficient for 3-D EM modeling. For a cross-hole source-receiver configuration a composite model of which conductivity varies continuously can be successfully simulated using this algorithm.

• Steel and Composite Structures
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• v.45 no.4
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• pp.547-554
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• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.4
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• pp.1-10
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• 1998

This paper presents a vorticity-based numerical method for analyzing an incompressible Newtonian viscous flow around an impulsively started cylinder. The Navier-Stockes equations have a natural Helmholtz decomposition. The vorticity transport equation and the pressure equation are derived from this decoupled form. The associated boundary conditions are dynamic for the vorticity and pressure variables representing the coupling relation between them and the force balance on the wall. The various numerical treatments for solving the governing equations are introduced. According to Wu et al.(1994), the boundary conditions are decoupled, keeping the dynamic relation between vorticity and pressure. The vorticity transport equation is formulated by FVM and TVD(Total Variation Diminishing) scheme is used for the convection term. An integral approach similar to the panel method is used to obtain the velocity field for a given vorticity field and the pressure field, instead of the conventional differential approaches. In the numerical process, the structured grid is generated. The results are compared to existing numerical and analytic results for the validity of the present method.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.607-622
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• 2015

This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.

• Structural Engineering and Mechanics
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• v.76 no.3
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• pp.325-336
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• 2020

In this study, the continuous and discontinuous contact problems of functionally graded (FG) layer resting on a rigid foundation were considered. The top of the FG layer was loaded by a distributed load. It was assumed that the shear modulus and the density of the layer varied according to exponential functions along the depth whereas the the Poisson ratio remained constant. The problem first was solved analytically and the results were verified with the ones obtained from finite element (FE) solution. In analytical solution, the stress and displacement components for FG layer were obtained by the help of Fourier integral transform. Critical load expression and integral equation for continuous and discontinuous contact, respectively, using corresponding boundary conditions in each case. The finite element solution of the problem was carried out using ANSYS software program. In continuous contact case, initial separation distance and contact stresses along the contact surface between the FG layer and the rigid foundation were examined. Separation distances and contact stresses were obtained in case of discontinuous contact. The effect of material properties and loading were investigated using both analytical and FE solutions. It was shown that obtained results were compatible with each other.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.4
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• pp.82-98
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• 1994

A mathematical model for the hydrodynamic forces acting on the ship manoeuvring in waves is formulated and a numerical method for the problem is developed. The motion of a ship, which manoeuvres in waves, may be thought to have two components; one is a high frequency component due to encounter waves, and the other is a low frequency component due to manoeuvring motion. So the method of two time scale expansion is used to divide linear boundary value problem. For the effects of waves on the manoeuvring motion of a ship, only the second order drift forces are considered. The integral equation for the velocity potential is solved by 3 dimensional panel method and hydrodynamic forces are calculated by direct integral method.

• Economic and Environmental Geology
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• v.27 no.2
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• pp.191-199
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• 1994

We have developed an algorithm based on the method of integral equations to simulate the magnetotelluric (MT) responses of three-dimensional (3-D) bodies in a layered half-space. The inhomogeneities are divided into a number of cells and are replaced by an equivalent current distribution which is approximated by pulse basis functions. A matrix equation is constructed using the electric Green's tensor function appropriate to a layered earth, and is solved for the vector current in each cell. Subsequently, scattered fields are found by integrating electric and magnetic Green's tensor functions over the scattering current About a 3-D conductive body near the earth's surface, interpretation using 2-D transverse electric modeling schemes can imply highly erratic low resistivities at depth. This is why these routines do not account for the effect of boundary charges. However, centrally located profiles across elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic algorithm, which implicitly includes boundary charges in its formulation. Multifrequency calculations show that apparent resistivity and impedance phase are really two complementary parameters. Hence, they should be treated simultaneously in broadband MT interpretation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.12 no.6
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• pp.931-939
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• 2001

The slot coupling characteristics was analysed in a radial-line slot antenna for its design. The previously proposed waveguide model with a periodic boundary condition on its narrow walls and periodically arranged slots on its wide wall was used. The magnetic field integral equation and two dyadic Green\`s functions for respective regions was derived and the method of moments was used. To maximize the efficiency of numerical analysis and to extract singularities, two different kinds of basis functions, the entire domain basis function and the sub-domain one, are used. In addition, the Ewald sum technique for the rectangular waveguide and the Shanks transform for the half space were used to accelerate the computation of the slowly convergent potential Green\`s functions. Simulation results expressed the effects of the various design parameters on the slot coupling.