• 토지주택연구
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• 제1권1호
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• pp.59-65
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• 2010

The paper presents a comparison between a semi-implicit time integration linear finite element implementation and fully-implicit nonlinear Newton-Raphson finite element implementation of a triphasic small strain mixture formulation of an elastic partially saturated porous medium. The pore air phase pressure pa is assumed atmospheric, i.e., $p_a$ = 0, although the formulation and implementation are general to handle increase in pore air pressure as a result of loading, if needed. The solid skeleton phase is assumed linear isotropic elastic and partially saturated 'consolidation' in the presence of surface infiltration and traction is simulated. The verification of the implementation against an analytical solution for partially saturated pore water flow (no deformation) and comparison between the two implementations is presented and the important of the porosity-dependent nature of the partially saturated permeability is assessed on comparison with a commercial code for the partially saturated flow with deformation. As a result, the response of partially saturated permeability subjected to the porosity influences on the saturation of a soil, and the different behaviors of the partially saturated soil between staggered and monolithic coupled programs is worth of attention because the negative pore water pressure in the partially saturated soil depends on the difference.

• Structural Engineering and Mechanics
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• 제87권5호
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• pp.461-473
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• 2023

This study aims to solve for nonlinear cylindrical shell systems with a semi-analytical and numerical approach implementing the P-T method. The procedures and conditions for such a study are presented in practically solving and analyzing the cylindrical shell systems. An analytical model for a nonlinear thick cylindrical shell (TCS) is established on the basis of the stress function and Reddy's higher-order shear deformation theory (HSDT). According to Reddy's HSDT, Hooke's law in three dimensions, and the von-Kármán equation, the stress-strain relations are developed for the thick cylindrical shell systems, and the three coupled nonlinear governing equations are thus established and discretized as per the Galerkin method, for implementing the P-T method. The solution generated with the approach is continuous everywhere in the entire time domain considered. The approach proposed can also be used to numerically solve and analyze the nonlinear shell systems. The procedures and recurrence relations for numerical solutions of shell systems are presented. To demonstrate the application of the approach in numerically solving for nonlinear cylindrical shell systems, a specific nonlinear cylindrical shell system subjected to an external excitation is solved numerically. In numerically solving for the system, the present approach shows higher efficiency, accuracy, and reliability in comparison with that of the Runge-Kutta method. The approach with the P-T method presented is practically sound especially when continuous and high-quality numerical solutions for the shell systems are considered.

• Structural Engineering and Mechanics
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• 제31권4호
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• pp.407-421
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• 2009

The present paper addresses the optimal design of composite laminates with the aim of minimizing free-edge delamination stresses. A technique involving the application of particle swarm optimization (PSO) integrated with FEM was developed for the optimization. Optimization was also conducted with the zero-order method (ZOM) included in ANSYS. The semi-analytical method, which provides an approximation of the interlaminar normal stress of laminates under in-plane load, was used to partially validate the optimization results. It was found that optimal results based on ZOM are sensitive to the starting design points, and an unsuitable initial design set will lead to a result far from global solution. By contrast, the proposed method can find the global optimal solution regardless of initial designs, and the solutions were better than those obtained by ZOM in all the cases investigated.

• International Journal of Naval Architecture and Ocean Engineering
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• 제6권1호
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• pp.132-150
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• 2014

In this study, the inertial properties of fully filled liquid in a tank were studied based on the potential theory. The analytic solution was obtained for the rectangular tank, and the numerical solutions using Green's 2nd identity were obtained for other shapes. The inertia of liquid behaves like solid in recti-linear acceleration. But under rotational acceleration, the moment of inertia of liquid becomes small compared to that of solid. The shapes of tank investigated in this study were ellipse, rectangle, hexagon, and octagon with various aspect ratios. The numerical solutions were compared with analytic solution, and an ad hoc semi-analytical approximate formula is proposed herein and this formula gives very good predictions for the moment of inertia of the liquid in a tank of several different geometrical shapes. The results of this study will be useful in analyzing of the motion of LNG/LPG tanker, liquid cargo ship, and damaged ship.

• Geomechanics and Engineering
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• 제25권4호
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• pp.283-294
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• 2021

This paper presents a rigorous solution for spherical cavity expansion in unsaturated soils under constant suction condition. The hydraulic behavior that describes the saturation-suction relationship is modeled by a void ratio-dependent soil-water characteristic curve, which allows the hydraulic behavior to fully couple with the mechanical behavior that is described by an extended critical state soil model for unsaturated soil through the specific volume. Considering the boundary condition and introducing an auxiliary coordinate, the problem is formulated to a system of first-order differential equations with three principal stress components and suction as basic unknowns, which is solved as an initial value problem. Parameter analyses are conducted to investigate the effects of suction and the overconsolidation ratio on the overall expansion responses, including the pressure-expansion response, the distribution of the stress components around the cavity, and the stress path of the soil during cavity expansion. The results reveal that the expansion pressures and the distribution of the stress components in unsaturated soils are generally higher than those in saturated soils due to the existence of suction.

• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.947-961
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• 2023

This paper summarizes some research findings that show how the differential transform method (DTM) is used to resolve the Holling-Tanner model. To confirm the application, effectiveness, and correctness of the approach, a comparison between the differential transform method (DTM) and the Adomian decomposition method (ADM) is carried out, and an accurate solution representation in truncated series is discovered. The approximate solution obtain using both techniques and comparison demonstrates same outcome which remains a preferred numerical method for resolving a system of nonlinear differential equations.

• Steel and Composite Structures
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• 제51권2호
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• pp.139-151
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• 2024

In this research, a semi-analytical solution is presented for computing mechanical displacements and thermal stresses in rotating thick cylindrical pressure vessels made of functionally graded material (FGM). The modulus of elasticity, linear thermal expansion coefficient, and density of the cylinder are assumed to change along the axial direction as a power-law function. It is also assumed that Poisson's ratio and thermal conductivity are constant. This cylinder was subjected to non-uniform internal pressure and thermal loading. Thermal loading varies in two directions. The governing equations are derived by the first-order shear deformation theory (FSDT). Using the multilayer method, a functionally graded (FG) cylinder with variable thickness is divided into n homogenous disks, and n sets of differential equations are obtained. Applying the boundary conditions and continuity conditions between the layers, the solution of this set of equations is obtained. To the best of the researchers' knowledge, in the literature, there is no study carried out bi-directional thermoelastic analysis of clamped-clamped rotating FGM thick-walled cylindrical pressure vessels under variable pressure in the longitudinal direction.

• 한국해안·해양공학회논문집
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• 제32권4호
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• pp.203-210
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• 2020

반무한방파제 전면 및 후면에서 회절파 진폭의 공간적인 변화에 대해 Penney and Price(1952)의 해석해를 활용하여 분석하였다. 방파제 전면에 회절파의 영향으로 입사파와 반사파를 합친 중복파의 파력보다 더 큰 파력이 발생한다. 좀 자세히 알아보면, 회절파는 방파제의 선단 (x, y) = (0, 0)을 기존으로 동심원 형태로 위상 변화가 발생하는 반면 입사파와 반사파는 평면 형태로 위상 변화가 발생한다. 따라서, 입사파(또는 반사파)와 회절파가 중첩에 의한 파의 진폭은 에너지 불연속선에서부터 떨어진 곳에서는 항상 요동치게 된다. 방파제 전면 및 후면 (x, y) = (0, y) 지점은 회절파 파봉선을 따라 에너지 불연속선 지점에서부터 y(π/2 - β) 만큼 떨어져 있다. 회절파 에너지의 감쇠의 정도는 회절파 파봉선을 따라 에너지 불연속선 지점에서 떨어진 거리에 비례한다. 따라서, 방파제 전면 및 후면(x, y) = (0, y) 지점에서의 회절파의 진폭은 y(π/2 - β)의 제곱근에 반비례한다.

• 분석과학
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• 제25권1호
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• pp.60-68
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• 2012

지표수 중에 GC-MS에 의한 25개 준휘발성유기물질을 동시에 분석하는 방법을 개발하였다. 1.0 L의 물 시료를 분액깔대기 안에 넣고 NaCl로 포화시킨 다음 40 mL methylene chloride로 두 번 추출하였다. 이 방법은 0.01-800 ng/L 범위의 직선성을 보였고 15% 이내의 정밀도를 보였다. 확립한 방법을 사용하여 금강물 16개 시료를 분석한 결과 준휘발성유기화합물이 0.02-96.8 ng/L의 농도범위로 검출되었으며 측정값은 US EPA 또는 독일에서 확립한 준거치 이하의 값을 보였다. 이 측정방법은 지표수에서 SVOCs 대한 국가모니터링사업에 사용할 때 효율적인 것으로 판단된다.

• 한국소음진동공학회논문집
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• 제22권9호
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• pp.879-888
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• 2012

This study aims to apply multistage homotopy perturbation method(MHPM) to space truss composed of discrete members to obtain a semi-analytical solution. For the purpose of this research, a nonlinear governing equation of the structures is formulated in consideration of geometrical nonlinearity, and homotopy equation is derived. The result of carrying out dynamic analysis on a simple model is compared to a numerical method of 4th order Runge-Kutta method(RK4), and the dynamic response by MHPM concurs with the numerical result. Besides, the displacement response and attractor in the phase space is able to delineate dynamic snapping properties under step excitations and the responses of damped system are reflected well the reduction effect of the displacement.