• Steel and Composite Structures
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• v.11 no.3
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• pp.183-205
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• 2011

This paper presents the results of an investigation into the post-buckling behaviour and ultimate strength of imperfect corroded steel plates used in ship and other marine-related structures. A series of elastic-plastic large deflection finite element analyses is performed on randomly corroded steel plates. The effects of general corrosion on both sides of the plates are introduced into the finite element models using a random thickness surface model. The effects on plate compressive strength as a result of parametric variation of the corroded surface geometry are evaluated. A proposal on the effective thickness is concluded in order to estimate the ultimate strength and explore the post-buckling behaviour of randomly corroded steel plates under uniaxial compression.

• Coupled systems mechanics
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• v.3 no.4
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• pp.385-403
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• 2014

In this paper, the forced vibration problem of an Euler-Bernoulli beam that is joined with a semi-infinite field of a compressible fluid is considered as a boundary value problem (BVP). This BVP includes two partial differential equations (PDE) and some boundary conditions (BC), which are introduced comprehensively. After that, the closed-form solution of this fluid-structure interaction problem is obtained in the frequency domain. Some mathematical techniques are utilized, and two unknown functions of the BVP, including the beam displacement at each section and the fluid dynamic pressure at all points, are attained. These functions are expressed as an infinite series and evaluated quantitatively for a real example in the results section. In addition, finite element analysis is carried out for comparison.

• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.3
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• pp.159-173
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• 2011

The two different numerical approaches for solving the nonlinear ship wave problem are discussed in the present paper. One is based on a panel method, which neglects the viscous effects. The other is based on a finite volume method, which take into account the viscous effects by solving RANS equations. Focus is laid upon on the advantages and disadvantages of two methods. The developed methods are applied to calculating the flow around Series 60 hull to validate the performance of the present nonlinear methods. Although the two methods employ quite different numerical approaches, the calculated wave patterns from both methods show good agreements with the experiments. However the potential method simu-lates the global wave pattern accurately, while the viscous method shows better performance for the local wave prediction near a ship.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.1
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• pp.39-59
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• 2014

Nowadays aluminum stiffened plates are one of the major constituents of the marine structures, especially high-speed vessels. On one hand, these structures are subject to various forms of loading in the harsh sea environment, like hydrostatic lateral pressures and in-plane compression. On the other hand, fusion welding is often used to assemble those panels. The common marine aluminum alloys in the both 5,000 and 6,000 series, however, lose a remarkable portion of their load carrying capacity due to welding. This paper presents the results of sophisticated finite-element investigations considering both geometrical and mechanical imperfections. The tested models were those proposed by the ultimate strength committee of $15^{th}$ ISSC. The presented data illuminates the effects of welding on the strength of aluminum plates under above-mentioned load conditions.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.623-641
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• 2021

In this paper, numerical treatment of singularly perturbed parabolic delay differential equations is considered. The considered problem have small delay on the spatial variable of the reaction term. To treat the delay term, Taylor series approximation is applied. The resulting singularly perturbed parabolic PDEs is solved using Crank Nicolson method in temporal direction with non-standard finite difference method in spatial direction. A detail stability and convergence analysis of the scheme is given. We proved the uniform convergence of the scheme with order of convergence O(N^-1 + (∆t)²), where N is the number of mesh points in spatial discretization and ∆t is mesh length in temporal discretization. Two test examples are used to validate the theoretical results of the scheme.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.3
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• pp.117-131
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• 2021

The problem of generalized thermoelasticity of two-temperature for finite piezoelectric rod will be modified by applying three different types of heating applications namely, thermal shock, ramp-type heating and harmonically vary heating. The solutions will be derived with direct approach by the application of Laplace transform and the Caputo-Fabrizio fractional order derivative. The inverse Laplace transforms are numerically evaluated with the help of a method formulated on Fourier series expansion. The results obtained for the conductive temperature, the dynamical temperature, the displacement, the stress and the strain distributions have represented graphically using MATLAB.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.523-532
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• 2019

Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi et al. [2, 3]. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized k-Bessel functions. Also, we consider some integral formulas of the (p, q)-extended Bessel functions $J_{{\nu},p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of (p, q)-extended generalized hypergeometric functions, and the generalized Wright hypergeometric functions, respectively.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.10a
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• pp.183-186
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• 2003

A finite element-based, integrated process model is presented for a three dimensional, coupled analysis of the thermal and mechanical behavior of type 304 stainless slab during hot charge rolling (HCR) and cold charge rolling (CCR) processes. The validity of the proposed model is examined through comparison with measurements. The susceptibility on micro-crack initiation or propagation due to the thermal stress in these two different process conditions was examined. The model's capability of revealing the effect of diverse process parameters is demonstrated through a series of process simulation.

• International Journal of Korean Welding Society
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• v.2 no.1
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• pp.62-66
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• 2002

The Friction Stir Welding (FSW) is a new joining method that was developed at The Welding Institute (TWI) in England in 1991. It applied heating by the rotational friction and material plastic flow. It was developed as a new joining method to solve the problems of epochally in the welding of Al alloys. In the study, 6000series of Alloy composed of Al-Mg-Si, one of the Al alloys that are utilized for shipbuilding and construction, is selected as a specimen and the numerical is executed against the welded zone of FSW. The material used in this study had the unique properties of strength and anti-corrosion, but since the welded joint of this material is easily softened by the welding heat, FSW is executed and the numerical analysis is carried out around the joint. To examine the mechanical behaviors and properties, F.E.M analysis is executed and the developed thermal-elastic-plastic finite analysis are used.