• 대한수학회보
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• 제31권2호
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• pp.309-318
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• 1994

The approach presented in this paper is based on the transformation of the Stefan problem in one space dimension to an initial-boundary value problem for the heat equation in a fixed domain. Of course, the problem is non-linear. The finite element approximation adopted here is the standared continuous Galerkin method in time. In this paper, only the regular case is discussed. This means the error analysis is based on the assumption that the solution is sufficiently smooth. The aim of this paper is the existence of the solution in a finite Galerkin system of ordinary equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권1호
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• pp.13-23
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• 2008

In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in $H^2$ is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and Poisson equations with the mixed boundary condition. In this paper, we give NSF method for the Helmholtz equations ${\Delta}u+Ku=f$ with homogeneous Dirichlet boundary condition. Examples with a singular point are given with numerical results.

• 동력기계공학회지
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• 제14권5호
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• pp.48-55
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• 2010

When a large ship is advancing in waves, ship undergoes the hydroelastic response, which has influences on structural stability and the fatigue destruction etc. of the ship. Therefore, to predict accurate hydroelastic response, it is necessary to analyze hydroelastic response including fluid-structure interaction. In this research, a ship is divided into many hull elements to calculate the fluid forces and wave exciting forces on each elements using three-dimensional source distribution method. The calculated fluid forces and wave exciting forces are assigned to nodes of hull elements. The neighbor nodes are connected with elastic beam elements. We analyzed hydroelastic responses, and those are formulated by using finite element method. Particularly, to estimate the influence of forward speed on the hydroelastic responses, we use two different methods : Full Hull Rotation Method(FHRM) and Sectional Hull Rotation Method(SHRM).

• East Asian mathematical journal
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• 제36권5호
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• pp.583-591
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• 2020

In [8, 9] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 가을 학술발표회 논문집
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• pp.112-119
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• 2002

In this paper, an Extended Finite Element Method is proposed by adding discontinuity and singularity enrichment functions to the standard FEM approximation. In this method, the singularity and the discontinuity of the crack are efficiently modeled by using initial regular mesh without refining mesh near the crack tip, so that it enables express the asymptotic stress field near crack tip and crack surface successfully. The developed method was verified by evaluating crack tip stress profile and stress intensity factor of mode Ⅰ/mode Ⅱ fracture problems and the results showed the effectiveness and robustness for fracture problem.

• Structural Engineering and Mechanics
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• 제67권5호
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• pp.457-464
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• 2018

This paper presents a method for detecting damage in irregular 2D and 3D continuum structures based on combination of wavelet transform (WT) with fuzzy inference system (FIS) and particle swarm optimization (PSO). Many damage detection methods study regular structures. This method studies irregular structures and doesn't need response of healthy structures. First the damaged structure is analyzed with finite element methods, and damage response is obtained at the finite element points that have irregular distance, secondly the FIS, which is optimized by PSO is used to obtain responses at points, having equal distance by response at those points that previously obtained by the finite element methods. Then a 2D (for 2D continuum structures) or a 3D (for 3D continuum structures) matrix is performed by equal distance point response. Thirdly, by applying 2D or 3D wavelet transform on 2D or 3D matrix that previously obtained by FIS detail matrix coefficient of WT is obtained. It is shown that detail matrix coefficient can determine the damage zone of the structure by perturbation in the damaged area. In order to illustrate the capability of proposed method some examples are considered.

• Journal of Advanced Research in Ocean Engineering
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• 제4권4호
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• pp.195-203
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• 2018

The wave impact on ships could cause local damage to the ship's hull, which has been a concerning issue during the ship design process. In recent years, local structural damages of ships caused by slamming loads have been reported by accident; therefore, it is necessary to study the local slamming pressure loads and structural response assessment. In the present study, slamming loads around the ship's bow region in the presence of regular wave have been simulated by RANS equations discretized with a cell-centered finite volume method (FVM) in conjunction with the $k-{\Box}$ turbulence model. The dynamic structural response has been calculated using an explicit FE method. By adding the slamming pressure load of each time step to the finite element model, establishing the reasonable boundary conditions, and considering the material strain-rate effects, the dynamic response prediction of the bow flare structure has been achieved. The results and insights of this study will be helpful to design a container ship that is resistant enough to withstand bow flare slamming loads.

• 한국해양공학회지
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• 제18권6호
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• pp.29-36
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• 2004

Floating breakwaters have been recently studied to reduce the transmission ratio of wave energy. The numerical study shows how wave pressure and stress act on the rectangular floating breakwater under various regular wave conditions. In order to evaluate hydrodynamic pressure on the floating breakwater, the infinite element is applied to the linear wave diffraction and radiation problems. SAP2000, a structural analysis program, is used to evaluate stress on the floating breakwater.

• Structural Engineering and Mechanics
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• 제14권5호
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• pp.595-610
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• 2002

This paper presents an efficiency of various non-conforming (NC) modes in development of a series of new finite elements with the special emphasis on 4-node quadrilateral elements. The NC modes have been used as a key scheme to improve the behaviors of various types of new finite elements, i.e., Mindlin plate bending elements, membrane elements with drilling degrees of freedom, flat shell elements. The NC modes are classified into three groups according to the 'correction constants' of 'Direct Modification Method'. The first group is 'basic NC modes', which have been widely used by a number of researchers in the finite element communities. The basic NC modes are effective to improve the behaviors of regular shaped elements. The second group is 'hierarchical NC modes' which improve the behaviors of distorted elements effectively. The last group is 'higher order NC modes' which improve the behaviors of plate-bending elements. When the basic NC modes are combined with hierarchical or higher order NC modes, the elements become insensitive to mesh distortions. When the membrane component of a flat shell has 'hierarchical NC modes', the membrane locking can be suppressed. A number of numerical tests are carried out to show the positive effect of aforementioned various NC modes incorporated into various types of finite elements.

• 한국해양공학회지
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• 제20권4호
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• pp.64-69
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• 2006

A numerical analysis is made to investigate the wave absorption efficiency of a OWC-type wave power generator. Energy absorption by an OWC(Oscillating Water Column) air-chamber is computed in regular waves, taking account of the oscillating surface-pressure, due to pressure drop, across the duct of the air chamber. The problem is formulated in the scope of potential theory and solved by the Localized Finite Element Method(LFEM), based on the classical variational principle. The efficiency of energy absorption is investigated by. changing wave conditions, sea-bottom slope and pressure drop coefficient.