• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.3
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• pp.491-499
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• 2002

A p-version finite element model based on degenerate shell element is proposed tot the analysis of orthotropic laminated plates. In the nonlinear formulation of the model, the total Lagrangian formulation is adopted with large deflection and moderate rotation being accounted tot in the sense of yon Karman hypothesis. The material model is based on the Huber-Mises yield criterion and Prandtl-Reuss flow rule in accordance with the theory of strain hardening yield function, which is generalized lot anisotropic materials by introducing the parameters of anisotropy. The model is also based on extension of equivalent-single layer laminate theory(ESL theory) with shear deformation, leading to continuous shear strain at the interface of two layers. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. Gauss-Lobatto numerical quadrature is used to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed P-version finite element model is demonstrated through several comparative points of iew in terms of ultimate load, convergence characteristics, nonlinear effect, and shape of plastic tone.

• Journal of Korean Ophthalmic Optics Society
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• v.14 no.3
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• pp.17-27
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• 2009

Purpose: This review article was written to determine the effects of parameters characterizing a hard contact lens (RGP included), such as BCs, diameters, edge angles, on the time interval for tight fitted lens to return to the equilibrium when it was decentered from blinking. Methods: A mathematical formulation was established to relate or calculate the restoring forces and thickness of lacrimal layer beneath the cornea with the various lens parameters when the tight fitted lens was decentered from blinking. Based on this formulation the differential equations and their numerical solution program were set up to describe the time dependence of the lens on the position and to estimate the time for the lens's return to the equilibrium after blink. Results: It is found that the time interval for the tight fitted lens to return to the equilibrium decreases as either the BC decreases or the diameter increases because both the reduction in BC and increase in diameter result in the increase in the lacrimal layer thickness between the lens and cornea increase which yielded the lowering of the viscous friction in the lens motion. As the edge angle of tight fitted lens increases the time for recentering decreases due to the increase in restoring force without change in lacrimal thickness beneath the lens. In the case of flat fitted hard lens (RGP included), the lacrimal layer thickness under the lens increases as either BC or diameter increases which results in reduction in viscous friction so that the time for the lens's return to the equilibrium were to decrease. The edge angle of flat fitted lens does not affect the lens motion. Conclusions: The effect of BCs on the lens motion (time to approach the equilibrium) was concluded to be significant with both tight and flat fitted lens where its results are contrary with each other. The edge angle of lens only affects the motion in tight fitted lenses.

• Geophysics and Geophysical Exploration
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• v.27 no.3
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• pp.181-195
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• 2024

This tutorial explains that the static effect in the magnetotelluric (MT) survey is a physical phenomenon caused by charges accumulated on the boundaries of subsurface inhomogeneities. To facilitate understanding of the physical phenomenon, differences between static induction and charge accumulation on the boundary are explained and analyzed with help of schematic illustrations. Subsequently, from the electromagnetic (EM) integral equation formulation, it is clearly shown that the secondary electric field due to charges accumulated on the interface in the presence of the primary field appears as the static effect. Therefore, except in the cases of the layered earth or a two-dimensional earth with transverse magnetic (TM) mode excitation, the static effect always exists in MT responses and further, it is not 'static' but rather frequency dependent. Despite the fact that the static effect is a secondary electric field due to inhomogeneity, inevitable under-sampling in the frequency and spatial domains prevent the effect from being handled properly in numerical inversion. Therefore, considering the practical aspects of the MT survey, which cannot be a continuous measurement covering the entire survey area over a wide frequency band, a three-dimensional (3-D) inversion incorporating the static shift as a constraint with the Gaussian distribution is introduced. To enhance understanding of the integral equation EM modeling, the formulation of the 3-D integral equation and mathematical analyses of the Green tensor and scattering current are described in detail in the Appendix.

• Journal of Ship and Ocean Technology
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• v.11 no.2
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• pp.10-25
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• 2007

With the sharp increase of the oil price, the issue of the energy saving requires even higher propulsive efficiency of the propellers. Traditionally the propellers have been designed with the criteria such as that of Lerbs optimum based on the lifting line theory and the empirical formulae of Lerbs and van Manen giving relations of the wake pitch with the wake non-uniformity. With the aid of the high speed computer, it is now possible to apply the time-consuming iterative approaches for the solution of the lifting surface problems. In this paper we formulate the variational problem to optimize the efficiency of the propeller operating in the given ship wake using the lifting surface method. The variational formulation relating the spanwise circulation distribution with the propulsive efficiency to be maximized is however non-linear in circulation distribution functions, thus the iterative method is applied to the quasi-linearized equations. The blade shape design also requires the iterative procedures, because the shape of the blade which is represented by the lifting surface is unknown a priori. The numerical code was validated with the DTNSRDC propeller 4119 which is well-known to be optimum in uniform inflow condition. In addition existing (well-designed) commercial propellers were selected and compared with the results of the open water tests and the self-propulsion tests.

• Journal of Korean Society of Steel Construction
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• v.10 no.3 s.36
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• pp.509-523
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• 1998

A consistent finite element formulation and analytic solutions are presented for stability of thin-walled circular arch. The total potential energy is derived by applying the principle of linearized virtual work and including second order terms of finite semitangential rotations. As a result, the energy functional corresponding to the semitangential moment is newly derived. Analytic solutions for the out-of-plane buckling of symmetric thin-walled curved beam subjected to pure bending or uniform compression with simply supported boundary conditions are obtained. For finite element analysis, the cubic Hermitian polynomials are utilized as shape functions and $16{\times}16$ stiffness matrix for curved beam elements and $14{\times}14$ stiffness matrix for straight beam elements are evaluated, respectively. In order to illustrate the accuracy of this study, analytical and numerical results for lateral buckling problems of circular arch are presented and compared with available analytical solutions.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.4
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• pp.274-286
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• 1996

Two-dimensional flexible body analysis (hydroelasticity theory) is adopted to a very large floating structure that may be multimodule and extend in the longitudinal direction. The boundary-element method (BEM) and Green function method(GFM) are used to obtain the hydrodynamic coefficients. The structure is considered to be a flexible beam responding to waves in the vertical direction and a consistent formulation for the hydrostatic stiffness is derived. The resulting coupled equations of motion are solved directly. Two designs of the module connectors are considered: a rotationally-flexible hinge connector, and a rotationally-rigid connector Numerical examples are presented to an integrated system of semi-submersibles. The analysis provides basic motions and section forces, which are useful to develop an understanding of the fundamental modes of displacement and force amplitudes for which multi-module VLFSs must be designed. The results show that while the hinge connectors result in greater motion, the rigid connectors increase substantially the sectional moments.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.2
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• pp.91-107
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• 1992

A numerical formulation is developed to solve the linear three-dimensional hydrodynamic equations which describes wind induced flows in a homogeneous shelf sea. The hydmdynamic equations are at the outset separated into two systems. namely, an equation containing the gradient of sea surface elevation and the mean flow (external mode) and an equation describing the deviation from the mean flow (internal mode). The Galerkin method is then applied to the internal mode equation. The eigenvalues are determined from the eigenvalue problem involving the vertical eddy viscosity subject to a homogeneous boundary condition at the surface and a sheared boundary condition at the sea bed. The model is tested in a one-dimensional channel with uniform depth under a steady, uniform wind. The analytical velocity profile by Cooper and Pearce (1977) using a constant vertical eddy viscosity in channels of infinite and finite length is chosen as a benchmark solution. The model is also tested in a homogeneous, rectangular basin with constant depth under a steady, uniform wind field (the Heaps' Basin of the North Sea scale).

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.17 no.3
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• pp.158-165
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• 2005

In order to analyze incompressible two-phase flow, Level Set method was applied on pseudo-compressibility formulation. Level Set function is defined as a signed distance function from the phase interface, and gives the information of the each phase location and the geometric data to the flow. In this study, Level Set function transport equation was coupled with flow conservation equations, and owing to pseudo-compressibility technique we could solve the resultant vector equation iteratively. Two-phase flow analysis code was developed on general curvilinear coordinate, and numerical tests of bubble dynamics and surging wave problems demonstrate its capability successfully.

• Structural Engineering and Mechanics
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• v.48 no.4
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• pp.547-567
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• 2013

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.2
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• pp.317-324
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• 1994

The circulation of Lake Paldang is analysed numerically as an ultimate goal to develop a vehicle predicting the dispersion and concentration of pollutants and sediment flowed into the lake. In finite difference formulation of 2-D depth averaged governing equations. Abbott's 3-time level scheme is employed and for nonlinear terms time centering iteration technique in time and space is used. Model parameters for shear stresses and eddy diffusivities are determined through measured data in and near the lake. Predicted velocities for steady flow are shown to be close to the measured velocities and further improved by taking into account of wind effect. This indicates that the wind effect is needed for proper circulation analysis and it calls for the inclusion of the wind effect. Simulated results of unsteady flow caused by flood inflows and release through Paldang dam are found to characterize the flow features quite well as expected. This implies that the developed model can be used as a tool to analysing the circulation in the lake.