• 한국해양공학회지
• /
• 제22권5호
• /
• pp.39-43
• /
• 2008

For a partially filled and deeply submersed membrane container, an analytic solution for similarity shape was studied. The static shape of a membrane container can be expressed as a set of nonlinear ordinary differential equations. These equations are combined into an integrable equation. The solution of the equation is derived in terms of elliptic integrals, the arguments of which contain an unknown at the point of inflection. The point of inflection is determined by using the boundary condition at a separating point. Some characteristic values of the similarity shape were evaluated and the shapes are illustrated.

• 한국해양공학회지
• /
• 제21권1호
• /
• pp.45-50
• /
• 2007

For a long partially-filled membrane container on an incline, the analytic solution of the similarity shape is studied. The nonlinear equation is solved and its solution is expressed as elliptic integrals, which include an unknown at the point of inflection. The point of inflection is determined by using the boundary condition at the upper separating point. Some characteristic values of the universal shape are evaluated, as the functions of inclination angle and shapes are illustrated for some cases.

• 한국해양공학회지
• /
• 제23권4호
• /
• pp.32-37
• /
• 2009

An analytic similarity shape solution was studied for a two-dimensional floating and fluid-filled membrane structure. The static shape of a membrane structure can be expressed as a set of nonlinear ordinary differential equations. The integration of curvature leads to an analytic solution for the shape, which contains unknown boundary values. Matching the upper and lower shapes at the free surface incorporated with their buoyancy allowed the unknowns to be determined. Some characteristic values of similarity shapes were evaluated and shapes are illustrated for various density ratios and volume efficiency ratios.

• Journal of Welding and Joining
• /
• 제8권2호
• /
• pp.53-57
• /
• 1990

Analytic solutions of heat conduction during welding which were first found by Resenthal have some restrictions. One of these is that models to which analytic solutions can be applied must have simple geometric shape, and another is that quasi-stationary state must be created. On the other hand, computational methods developed recently with the aid of the computer can overcome these shortcomings, but the methods raise problems from economic point of view when they are applied to 3 dimensional problems. Taking account of these problems, a new method combinig the analytic method with the computational one is proposed. This method can be ued in weldments with complicated geometric shape in non-stationary state, but with the aid of the analytic method can reduce the computing time.

• 한국지구물리탐사학회:학술대회논문집
• /
• 한국지구물리탐사학회 2003년도 Proceedings of the international symposium on the fusion technology
• /
• pp.238-243
• /
• 2003

As there are many advantages on underground caverns, such as safety and operation, they can also be used for gas storage purpose. When liquefied gas is stored underground, the cryogenic temperature of the gas will affect the stability of the storage cavern. In order to store the liquefied gas successfully, it is essential to estimate the exact temperature distribution of the rock mass around the cavern. In this study, an analytic solution and a conceptual model that can estimate three-dimensional temperature distribution around the storage cavern are suggested. When calculating the heat transfer within a solid, it is likely to consider the solid as the intersection of two or more infinite or semi-infinite geometries. Therefore heat transfer solution for the solid is expressed by the product of the dimensionless temperatures of the geometries, which are used to form the combined solid. Based on the multi-dimensional transient heat transfer theory, the analytic solution is successfully derived by assuming the cavern shape to be of simplified geometry. Also, a conceptual model is developed by using the analytic solution of this study. By performing numerical experiments of this multi-dimensional model, the temperature distribution of the analytic solution is compared with that of numerical analysis and theoretical solutions.

• 대한기계학회논문집A
• /
• 제20권5호
• /
• pp.1458-1467
• /
• 1996

A direct differentiationmethod is presented for the shape design sensitivity analysis of axisymmeetric elastic solids. Based on the exisymmetric boundary integralequaiton formulation, a new boundary ntegral equatio for sensitivity analysis is derived by taking meterial derivative to the same integral identity that was used in the adjoint variable melthod. Numerical implementation is performed to show the applicaiton of the theoretical formulation. For a simple example with analytic solution, the sensitivities by present method are compared with analytic sensitivities. As an application to the shape optimization, an optimal shape of a gas turbine disc toinimize the weight under stress constraints is found by incorporating the sensitivity analysis algorithm in an optimizatio program.

• 한국해양공학회지
• /
• 제28권3호
• /
• pp.193-198
• /
• 2014

An elastic cable with piecewise constant properties under the action of concentrated static loads is studied analytically. Analytic solutions for catenary cables are combined at the discontinuous points caused by the discontinuous elastic properties or concentrated loads. The application of the boundary conditions at both ends of the multi-component cable results in three algebraic non-linear equations for three unknown parameters, which are determined numerically. The solutions for the shape, tension, elongation, and cross-sectional contraction of the cable are expressed in closed forms. Some examples are given for cases of two- and three-dimensional loads.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제17권3호
• /
• pp.181-195
• /
• 2013

This study considers an air and liquid-filled geomembrane tube section resting on a horizontal foundation. All quantities are normalized to obtain geometrically similar solutions in the static equilibrium condition. Analytic solutions are expressed in closed form. The solution for the air or liquid-filled tube section is derived systematically as an extreme case of the air and liquid-filled tube section. The validity of these solutions is confirmed by comparing to previous study, and some results are shown for the characteristic parameters and shapes of air and/or liquid-filled cases. Using the result of present study, one can estimate the shape and characteristic parameters of a tube section without numerical integrations or iterations.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1998년도 봄 학술발표회 논문집
• /
• pp.465-472
• /
• 1998

In this study, analytic solution and finite element formulation for the free vibration analysis of thin-walled circular arch, based on linearized virtual work and Vlasov's assumption, including restrained warping effect and second order terms of finite semitangential rotations, is presented. The total potential energy is derived by applying the Hellinger-Reissner principle. In this formulation, all displacement parameters of deformation are defined at the centroid axis. For the finite element formulation, the two node cubic Hermitian polynomials are utilized as shape functions. In special case, potential energy functional of thin-walled curved beam with monosymmetric cross section is derived. From this methodology, analytic solution for the free vibration of monosymmetric circular arch with simply supported is derived. In order to illustrate the accuracy of this study, various parameter studies for free vibration of circular arches are presented and compared with numerical solution analyzed by the FEM using straight beam element.

• 대한조선학회논문집
• /
• 제54권6호
• /
• pp.461-469
• /
• 2017

A segment of the wave board has been expressed as a submerged line segment in the two dimensional wave flume. The lower end of the line segment could be extended to the bottom of the wave flume and the other opposite upper end of the board could be extended to the free surface. It is assumed that the motion of the wave board could be defined by the sinusoidal motion in horizontal direction on either end of the wave board. When the amplitude of sinusoidal motion of the wave board on lower and upper end are equal, the wave board motion could express the horizontally oscillating submerged segment of piston type wave generator. The submerged segment of flap type wave generator also could be expressed by taking the motion amplitude differently for the either end of the board. The pivot point of the segment motion could play a role of hinge point of the flap type wave generator. Simplified analytic solution of oscillating submerged wave board segment in water of finite depth has been derived through the first order perturbation method at two dimensional domain. The case study of the analytic solution has been carried out and it is found out that the solution could be utilized for the design of wave generator with arbitrary shape by linear superposition.