• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.621-633
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• 2023

The major objective of this paper is to study the receding contact problem between two functional graded layers under a flat indenter. The gravity is assumed negligible, and the shear moduli of both layers are assumed to vary exponentially along the thickness direction. In the absence of body forces, the problem is reduced to a system of Fredholm singular integral equations with the contact pressure and contact size as unknowns via Fourier integral transform, which is transformed into an algebraic one by the Gauss-Chebyshev quadratures and polynomials of both the first and second kinds. Then, an iterative speediest descending algorithm is proposed to numerically solve the system of algebraic equations. Both semi-analytical and finite element method, FEM solutions for the presented problem validate each other. To improve the accuracy of the numerical result of FEM, a graded FEM solution is performed to simulate the FGM mechanical characteristics. The results reveal the potential links between the contact stress/size and the indenter size, the thickness, as well as some other material properties of FGM.

• Bulletin of the Society of Naval Architects of Korea
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• v.23 no.4
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• pp.25-34
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• 1986

A two-dimensional linear method has been developed for the motion and the second-order steady force arising from the hydrodynamic coupling between waves and currents in the presence of a body of arbitrary shape. Interaction between the incident wave and current in the absence of the body lies in the realm beyond our interest. A Fredholm integral equation of the second kind is employed in association with the Haskind's potential for a steadily moving source of pulsating strength located in or below the free surface. The numerical calculations at the preliminary stage showed a significant fluctuation of the hydrodynamic forces on the surface-piercing body. The problem is approximately solved by using the asymptotic Green function for $U^2{\rightarrow}0$. The original Green function, however, is applied for the fully submerged body. Numerical calculations are made for a submerged and for a half-immersed circular cylinder and extensively for the mid-ship section of a Lewis-form. Some of the results are compared with other analytical results without any available experimental data. The current has strong influence on roll motion near resonance. When the current opposes the waves, the roll response are generally negligible in the low frequency region. The current has strong influence on roll motion near resonance. When the current opposes the wave, the roll response decreases. When the current and wave come from the same direction, the roll response increases significantly, as the current speed increases. The mean drift forces and moment on the submerged body are more affected by current than those on the semi-immersed circular cylinder or on the ship-like section in the encounter frequency domain.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.206-213
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• 2013

Transient response of a crack in a functionally graded piezoelectric material (FGPM) interface layer between two dissimilar homogeneous piezoelectric layers under anti-plane shear is analyzed using integral transform approaches. The properties of the FGPM layer vary continuously along the thickness. Laplace and Fourier transforms are used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on electric loading, gradient of the material properties, and thickness of the layers. Computed results yield following conclusions: (a) the DERR increases with the increase of the gradient of the material properties of the FGPM layer; (b) certain direction and magnitude of the electric impact loading impedes crack extension; (c) increase of the thickness of the FGPM layer and the homogeneous piezoelectric layer which has larger material properties than those of the crack plane are beneficial to increase of the resistance of transient fracture of the FGPM layer.

• Geomechanics and Engineering
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• v.31 no.5
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• pp.477-488
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• 2022

Pile composite foundation (PCF) has been commonly applied in practice. Existing research has focused primarily on semi-infinite media having equal pile lengths with little attention given to the effects of inclined bedrock and dissimilar pile lengths. This investigation considers the effects of inclined bedrock on vertical loaded PCF with dissimilar pile lengths. The pile-soil system is decomposed into fictitious piles and extended soil. The Fredholm integral equation about the axial force along fictitious piles is then established based on the compatibility of axial strain between fictitious piles and extended soil. Then, an iterative procedure is induced to calculate the PCF characteristics with a rigid cap. The results agree well with two field load tests of a single pile and numerical simulation case. The settlement and load transfer behaviors of dissimilar 3-pile PCFs and the effects of inclined bedrock are analyzed, which shows that the embedded depth of the inclined bedrock significantly affects the pile-soil load sharing ratios, non-dimensional vertical stiffness N₀/wdE_s, and differential settlement for different length-diameter ratios of the pile l/d and pile-soil stiffness ratio k conditions. The differential settlement and pile-soil load sharing ratios are also influenced by the inclined angle of the bedrock for different k and l/d. The developed model helps better understand the PCF characteristics over inclined bedrock under vertical loading.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.12-18
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• 1991

Three-dimensional nonlinear sloshing effects due to tank motions are simulated by solving boundary value problem using the panel method based on boundary integral technique. While Shinkai used boundary elements on which source strengths vary linearly between nodes, the source of constant strength is distributed on each triangular panel in the present study. The source strength at each time step is determined by solving the Fredholm integral equation of the second kind obtained from Green's theorem. To avoid cumulative numerical errors as time elapses, Adam-Bashforth-Moulton method is employed. Numerical examples for the case of partially filled spherical tank on board oscillating in harmonic sway mode or pitch mode are solved. The elevation of the free surface is compared with the result by Shinkai and confirmed in good agreement during early time. The input and the output energy are comparatively evaluated to check the overall accuracy of the present numerical scheme. Although some leakage of energy are found as time marches, it is plausible when we take into account nonlinearities of the problem and the number of panels of the model.