• Journal of Ship and Ocean Technology
• /
• v.10 no.1
• /
• pp.10-26
• /
• 2006

The radiation problem for oscillating bodies on the free surface has been formulated by the over-determined Green integral equation, where the boundary condition on the free surface is satisfied by adopting the Kelvin-type Green function and the irregular frequencies are removed by placing additional control points on the free surface surrounded by the body. The B-Spline based higher order panel method is then applied to solve the problem numerically. Because both the body geometry and the potential on the body surface are represented by the B-Splines, that is in polynomials of space parameters, the unknown potential can be determined accurately to the order desired above the constant value. In addition, the potential expressed in B-Spline can be differentiated analytically to get the velocity on the surface without introducing any numerical error. Sample computations are performed for a semispherical body and a rectangular box floating on the free surface for six-degrees of freedom motions. The added mass and damping coefficients are compared with those by the already-validated constant panel method of the same formulation showing strikingly good agreements.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.22 no.3
• /
• pp.9-18
• /
• 1985

The numerical calculation for solving boundary-value problem related to potential flows with a free surface is carried out by application of the localized finite element method. Only forced motion of 2-D body in infinitely deep fluid is considered, although this schemes is equally applicable to any first order time-harmonic problems of similar nature. The infinite domain of the fluid is separated into the inner flow field and the outer flow field with common inter-surface boundary. The finite element method is applied to obtain the solution in the inner flow field and the Green functions are utilized to represent the solution in the outer flow field. At the inter-surface boundary, the continuity of the value of potential and the normal derivative of the potential(i.e. matching condition) is conserved. The present method has better computational efficiency than the previous LFEM and the integral equation method of Frank. This enhanced computational efficiency is presumably due to the fact that the present method gives a symmetric coefficient matrix and requires less computational time in calculating the influence coefficient matrix of Green function than the integral equation method. And the irregular frequency desen't exist because the uniqueness of the solution is assured by the such that the exact free surface condition is satisfied on the boundary of the localized finite element region(i.e. inner region). As an example of the above method, the hydrodynamic forces for the circular cylinder and the rectangular cylinders are calculated. In the computed results, the small number of singularity distribution segments($3{\sim}6$) give good result relative to Ursell's and Vugts'.

• Communications of the Korean Mathematical Society
• /
• v.16 no.1
• /
• pp.137-152
• /
• 2001

Steady two-dimensional flows due to an applied pressure distribution in water of finite depth are considered. Gravity is included in the dynamic boundary condition. Gravity is included in the dynamic boundary condition. The problem is solved numerically by using the boundary integral equation technique. It is shown that, for both supercritical and subcritical flows, solutions depend on three parameters: (i) the Froude number, (ii) the magnitude of applied pressure distribution, and (iii) the span length of pressure distribution. For supercritical flows, there exist up to two solutions corresponding to the same value of Froude number for positive pressures and a unique solution for negative pressures. For subcritical flows, there are solutions with waves behind the applied pressure distribution. As the Froude number decreases, these waves when the Froude numbers approach the critical values.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.16 no.5
• /
• pp.838-848
• /
• 1992

The objective of the study is to provide a theoretical tools for analyzing the fracture of leyered composites with a center crack. It is assumed that the composite is composed of successive accumulation of the fiber layer and resin layer with the fiber layer being perfectly bonded to the resin layer except the region of a center crack. In-plane shear loading (Mode II) and the anti-plane shear loading (Mode III) are considered separately. Boundary value problems are formulated by using a plane theory of elasticity and governing equations are reduced to a Fredholm integral equation of a second kind. The equation is solved numerically and the stress intensity factors are obtained. The normalized Mode II and Mode III stress intensity factors are evaluated for various combinations of material properties and for various geometrical parametes.

• Structural Engineering and Mechanics
• /
• v.52 no.1
• /
• pp.1-17
• /
• 2014

An interfacial penny-shaped crack between piezoelectric layer and elastic half-space subjected to mechanical and electric loads is investigated. Using Hankel transform technique, the mixed boundary value problem is reduced to a system of singular integral equations. The integral equations are further reduced to a system of algebraic equations with the aid of Jacobi polynomials. The stress intensity factor and energy release rate are determined. Numerical results reveal the effects of electric loadings and material parameters of composite on crack propagation and growth. The results seem useful for design of the piezoelectric composite structures and devices of high performance.

• Structural Engineering and Mechanics
• /
• v.23 no.2
• /
• pp.163-175
• /
• 2006

In this paper, the dynamic response of a piezoelectric layer with a penny-shaped crack is investigated. The piezoelectric layer is subjected to an axisymmetrical action of both mechanical and electrical impacts. Two kinds of crack surface conditions, i.e., electrically impermeable and electrically permeable, are adopted. Based upon integral transform technique, the crack boundary value problem is reduced to a system of Fredholm integral equations in the Laplace transform domain. By making use of numerical Laplace inversion the time-dependent dynamic stress and electric displacement intensity factors are obtained, and the dynamic energy release rate is further derived. Numerical results are plotted to show the effects of both the piezoelectric layer thickness and the electrical impact loadings on the dynamic fracture behaviors of the crack tips.

• Journal of the Society of Naval Architects of Korea
• /
• v.32 no.3
• /
• pp.62-71
• /
• 1995

In the numerical analysis of incompressible unsteady Navier-stokes equation, large time is required for solving the pressure Poisson equation of the elliptic type at each time step. In this paper, a numerical analysis by the direct method is carried out to solve the pressure Poisson equation and the computing time is analyzed as mesh size increases. The pressure Poisson equation can be transformed to the boundary value problem by the Green theorem. The computing time for the convolution type of the domain integral can be reduced by using F.F.T. and the computing time in the direct method depends entirely on obtaining the solution of the boundary value problem. The numerical analysis on the known solutions is carried out and compared for the verification of the direct method. And the numerical analysis on the body boundary and domain decomposition problem are carried out with the computing time less than O($n^{3}$) in the (n.n) mesh.

• Journal of the Korean Society for Marine Environment & Energy
• /
• v.13 no.2
• /
• pp.83-90
• /
• 2010

The hydrodynamic interaction of two floating bodies in waves freely floating or connected by a rigid link is studied by using a boundary element method in the frequency-domain. The exact two-body hydrodynamic coefficients of added mass, wave damping and exciting force are calculated from the radiation-diffraction potential solution of the improved Green integral equation associated with the free surface Green function. The irregular frequencies in the conventional Green integral equation make it difficult to predict the physical resonance of the fluid in the gap between two bodies floating side by side. However, the improved Green integral equation employed in this study is free of irregular frequencies and always yields the exact solution of the multi-body radiation-diffraction potential boundary value problem. The 6 degree-of-freedom motions of two bodies freely floating side by side or connected parallel by a rigid link have been calculated for the incident wave frequencies ranging from 0.1 to 5 radians per second in head, left and right bow quartering seas. The 6-component load of the rigid link have also been presented.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 1997.04a
• /
• pp.128-135
• /
• 1997

The indirect boundary integral equation is formulated to analyze the behavior of a cavity in a multilayered half-plane subjected to earthquake waves. This formulation uses the fundamental solutions that are numerically calculated by the generalized transmission and reflection coefficient method. The free surface of the cavity without external excitation influences the behavior of the half-plane. Consequently this analysis adds the consideration of scattering-field into the analysis and the total motion field of the cavity is decomposed into the free-field and scattering-field motions. The free-field motion is obtained from the modification of the transmission and reflection coefficient method. The scattering-field motion is calculated is calculated by the indirect boundary value problem which has the ficticious boundaries and sources. In this study, P wave, SV wave, SH wave, and Rayleigh wave are analyzed respectively.

• Journal of the Society of Naval Architects of Korea
• /
• v.28 no.1
• /
• pp.27-37
• /
• 1991

In this paper the nonlinear free surface flows for an axisymmetric submerged body oscillating beneath the free surface are solved and the forces acting on the body are calculated. A boundary integral method is applied to solve the axisymmetric boundary value problem and the Runge-Kutta 4-th order method is used for the time stepping of the free surface location. The nonlinear forces acting on the axisymmetric body are computed and compared with published results.