• Wind and Structures
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• v.22 no.3
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• pp.329-348
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• 2016

This work presents a simple hyperbolic shear deformation theory for analysis of functionally graded plates resting on elastic foundation. The proposed model contains fewer number of unknowns and equations of motion than the first-order shear deformation model, but the transverse shear stresses account for a hyperbolic variation and respect the tangential stress-free boundary conditions on the plate boundary surface without introducing shear correction factors. Equations of motion are obtained from Hamilton's principle. The Navier-type analytical solutions for simply-supported plates are compared with the existing solutions to demonstrate the accuracy of the proposed theory.

• Structural Engineering and Mechanics
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• v.67 no.3
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• pp.291-300
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• 2018

In this work, a new trigonometry theory of shear deformation is developed for the static analysis of thick isotropic beams. The number of variables used in this theory is identical to that required in the theory of Euler-Bernoulli, sine function is used in the displacement field in terms of the coordinates of the thickness to represent the effects of shear deformation. The advantage of this theory is that shear stresses can be obtained directly from the relationships constitute, while respecting the boundary conditions at the free surface level of the beam. Therefore, this theory avoids the use of shear correction coefficients. The differential equilibrium equations are obtained using the principle of virtual works. A thick isotropic beam is considered, whose numerical study to show the effectiveness of this theory.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2002.03a
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• pp.145-153
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• 2002

A coastwise chemical tanker sailing at full speed has capsized in calm water and whole turing. In the precious paper, we investigated reasons of the accident by demonstrating the proper correction for the free surface effect of the liquid cargo and the bow-sinkage effect. In this paper, we also carry out model experiments of a transverse pressure under the seawater and an outward heel moment according to the heel angle and rudder angle, on the basis of radius of turning circle, ship's speed and drift angle of model ship occurring in turning. It is also shown that the flooding of seawater onto the deck occurring in turning generated a significant outward heel moment and the vertical distance between the center of gravity of the ship and the renter of lateral water drag.

• Steel and Composite Structures
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• v.18 no.3
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• pp.793-809
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• 2015

In this scientific work, constructing of a novel shear deformation beam model including the stretching effect is of concern for flexural and free vibration responses of functionally graded beams. The particularity of this model is that, in addition to considering the transverse shear deformation and the stretching effect, the zero transverse shear stress condition on the beam surface is assured without introducing the shear correction parameter. By employing the Hamilton's principle together with the concept of the neutral axe's position for such beams, the equations of motion are obtained. Some examples are performed to demonstrate the effects of changing gradients, thickness stretching, and thickness to length ratios on the bending and vibration of functionally graded beams.

• Smart Structures and Systems
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• v.19 no.2
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• pp.115-126
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• 2017

In this paper, size dependent bending and free flexural vibration behaviors of functionally graded (FG) nanobeams are investigated using a nonlocal quasi-3D theory in which both shear deformation and thickness stretching effects are introduced. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present theory incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a hyperbolic variation of all displacements through the thickness without using shear correction factor. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The neutral surface position for such FG nanobeams is determined and the present theory based on exact neutral surface position is employed here. The governing equations are derived using the principal of minimum total potential energy. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and dynamic responses of the FG nanobeam are discussed in detail. A detailed numerical study is carried out to examine the effect of material gradient index, the nonlocal parameter, the beam aspect ratio on the global response of the FG nanobeam. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.23 no.5
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• pp.335-344
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• 2011

A curvilinear non-hydrostatic free surface model is developed to investigate nonlinear wave interactions in a circular channel. The proposed model solves the unsteady Navier-Stokes equations in a three-dimensional domain with a pressure correction method, which is one of fractional step methods. A hybrid staggered-grid layout in the vertical direction is implemented, which renders relatively simple resulting pressure equation as well as free surface closure. Numerical accuracy with respect to wave nonlinearity is tested against the fifth-order Stokes solution in a two-dimensional numerical wave tank. Numerical applications center on the evolution of nonlinear waves including diffraction and reflection affected by the curvature of side wall in a circular channel comparing with linear waves. Except for a highly nonlinear bichrmatic wave, the model's results are in good agreement with superimposed analytical solution that neglects nonlinear effects. Through the numerical simulation of the highly nonlinear bichramatic wave, the model shows its capability to investigate the evolution of nonlinear wave groups in a circular channel.

• Steel and Composite Structures
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• v.18 no.1
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• pp.187-212
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• 2015

In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

• Journal of Ship and Ocean Technology
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• v.10 no.4
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• pp.1-11
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• 2006

The finite volume based multi-block RANS code, WAVIS developed at MOERI is applied to the numerical self-propulsion test. WAVIS uses the cell-centered finite volume method for discretization of the governing equations. The realizable $k-{\epsilon}$ turbulence model with a wall function is employed for the turbulence closure. The free surface is captured with the two-phase level set method and body forces are used to model the effects of a propeller without resolving the detail blade flow. The propeller forces are obtained using an unsteady lifting surface method based on potential flow theory. The numerical procedure followed the self-propulsion model experiment based on the 1978 ITTC performance prediction method. The self-propulsion point is obtained iteratively through balancing the propeller thrust, the ship hull resistance and towing force that is correction for Reynolds number difference between the model and full scale. The unsteady lifting surface code is also iterated until the propeller induced velocity is converged in order to obtain the propeller force. The self-propulsion characteristics such as thrust deduction, wake fraction, propeller efficiency, and hull efficiency are compared with the experimental data of the practical container ship. The present paper shows that hybrid RANS and potential flow based numerical method is promising to predict the self-propulsion parameters of practical ships as a useful tool for the hull form and propeller design.

• Journal of Korea Water Resources Association
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• v.43 no.10
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• pp.911-920
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• 2010

The closed water bodies, such as reservoirs and lakes, could be contaminated by an inflow of pollutants in the upstream as well as a stratification caused by seasonal natural phenomena. The vertical circulation particularly plays an important role in reduction of environmental pollutants. The factors of the vertical circulation are the temperature, wind, thermal diffusivity and sunlight. The wind is probably the most significant factor among them. Thus, it is necessary to describe the validation and application of a three-dimensional numerical model of wind-induced circulation in a thermally stratified flow. In this paper, a three-dimensional numerical model for the thermally stratified flows is presented. The model is conducted in three steps to calculate the velocity components from the momentum equations in x- and y- axis directions, the elevations from the free surface equation and the temperature from the scalar transport equation. Numerical predictions are compared with available analytical solutions for the sloshing free surface movement in a rectangular basin. The numerical results generally show a reasonable agreement with analytical solutions. And the model is applied to the circulation for the wind induced flow in a thermally stratification. Consequently, the developed model is validated by two verifications and phenomena of the internal flow.

• Coupled systems mechanics
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• v.5 no.3
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.