• 한국공간구조학회논문집
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• 제22권2호
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• pp.57-64
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• 2022

In this paper, the physical model and governing equations of a shallow arch with a moving boundary were studied. A model with a moving boundary can be easily found in a long span retractable roof, and it corresponds to a problem of a non-cylindrical domain in which the boundary moves with time. In particular, a motion equation of a shallow arch having a moving boundary is expressed in the form of an integral-differential equation. This is expressed by the time-varying integration interval of the integral coefficient term in the arch equation with an un-movable boundary. Also, the change in internal force due to the moving boundary is also considered. Therefore, in this study, the governing equation was derived by transforming the equation of the non-cylindrical domain into the cylindrical domain to solve this problem. A governing equation for vertical vibration was derived from the transformed equation, where a sinusoidal function was used as the orthonormal basis. Terms that consider the effect of the moving boundary over time in the original equation were added in the equation of the transformed cylindrical problem. In addition, a solution was obtained using a numerical analysis technique in a symmetric mode arch system, and the result effectively reflected the effect of the moving boundary.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.49-64
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• 2024

When setting up a structure with an embedded shallow arch, there is a phenomenon where the end of the arch moves. To study the so-called moving domain problem, one try to transform a considered noncylindrical domain into the cylindrical domain using the transform operator, as well as utilizing the method of penalty and other approaches. However, challenges arise when calculating time derivatives of solutions in a domain depending on time, or when extending the initial conditions from the non-cylindrical domain to the cylindrical domain. In this paper, we employ the transform operator to prove the existence and uniqueness of weak solutions of the shallow arch equation on the moving domain as clarifying the time derivatives of solutions in the moving domain.

• Structural Engineering and Mechanics
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• 제67권6호
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• pp.659-669
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• 2018

The Dynamic equations in the polar coordinates are drawn out using the MLPG method for the non-symmetric FG cylindrical shell. To simulate the mechanical properties of FGM, the nonlinear volume fractions for radial direction are used. The shape function applied in this paper is a form of the radial basis functions, by using this function all the requirements for an effective and suitable shape function are established. Hence in this study, the multiquadrics (MQ) radial basis functions are exploited as the shape function governing the problem. The MLPG method is combined with the the Newmark time approximation scheme to solve dynamic equations in the time domain. The obtained results by the MLPG method to be verified are compared with the analytical solution and the FEM. The obtained results through the MLPG method show a good agreement in comparison to other results and the MLPG method has high accuracy for dynamic analysis of the non-symmetric FG cylindrical shell. To demonstrate the capability of the present method to dynamic analysis of the non-symmetric FG cylindrical shell, it is analyzed dynamically with different volume fraction exponents under harmonic and rectangular shock loading. The present method shows high accuracy, efficiency and capability to dynamic analysis of the non-symmetric FG cylindrical shell with nonlinear grading patterns.

• Tribology and Lubricants
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• 제24권1호
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• pp.34-43
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• 2008

In this paper, an actively controlled aerostatic bearing is studied to overcome the defects of air bearing such as low stiffness and damping coefficients. The actively controlled aerostatic bearing is composed of aerostatic bearings, non-contact type of displacement sensors, piezoelectric actuators and controllers. The cylindrical capacitance sensor (CCS) is used as the displacement sensor. The reason for using CCS instead of the commercial gap sensor is that it can give us the pure error motion of the spindle because it removes the roundness error or the geometric errors in the spindle. The controller is designed by the state space equation and quadratic optimal control theory. The characteristic data of the actively controlled aerostatic bearing system in the frequency domain are presented and the stiffness and damping coefficients of the bearing are mentioned. This paper shows the possibility to reduce the motion error up to 6000 rpm.

• International Journal of Ocean System Engineering
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• 제3권2호
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• pp.68-76
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• 2013

In this study, a 3D numerical model was used to predict nonlinear wave forces on a cylindrical pile installed in a shallow water region. The model was based on solving the viscous and incompressible Navier-Stokes equations for a two-phase flow (water and air) model and the volume of fluid method for treating the free surface of water. A new application was developed based on the cut-cell method to allow easy installation of complicated obstacles (e.g., bottom geometry and cylindrical pile) in a computational domain. Free-surface elevation, water particle velocities, and inline wave forces were calculated, and the results show good agreement with experimental data obtained by the Danish Hydraulic Institute. The simulation results revealed that the proposed model can, without the use of empirical formulas (i.e., Morison equation) and additional wave analysis models, reliably predict non-linear wave forces on an offshore wind turbine foundation installed in a shallow water region.

• 대한조선학회논문집
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• 제57권5호
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• pp.271-277
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• 2020

Recoverability and vulnerability of navy ships under underwater explosion are critical verification factors in the acquisition phase of navy ships. This paper aims to establish numerical analysis techniques for the underwater explosion of navy ships. Doubly Asymptotic Approach (DAA) Equation of Motion (EOM) of primary shock wave and secondary bubble pulse proposed by Geers-Hunter was introduced. Assuming a non-compressive fluid, reference solution of the DAA EOM of Geers-Hunter using Runge-Kutta method was derived for the secondary bubble pulse phase with an assumed charge conditions. Convergence analyses to determine fluid element size were performed, suggesting that the minimum fluid element size for underwater explosion analysis was 0.1 m. The spherical and cylindrical fluid domains were found to be appropriate for the underwater explosion analyses from the fluid domain shape study. Because the element size of 0.1 m was too small to be applied to the actual navy ships, a very slender beam with the square solid section was selected for the study of fluid domain existence effect. The two underwater explosion models with/without fluid domain provided very similar results in terms of the displacement and stress processes.

• Steel and Composite Structures
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• 제21권3호
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• pp.605-628
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• 2016

The energy absorption characteristics of diamond core sandwich cylindrical columns under axial crushing process depend greatly on the amount of material which participates in the plastic deformation. Both the single-objective and multi-objective optimizations are performed for columns under axial crushing load with core thickness and helix pitch of the honeycomb core as design variables. Models are optimized by multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). Results show that optimization improves the energy absorption characteristics with constrained and unconstrained peak crashing load. Also, it is concluded that the aluminum tube has a better energy absorption capability rather than steel tube at a certain peak crushing force. The results justify that the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. A ranking technique for order preference (TOPSIS) is then used to sort the non-dominated solutions by the preference of decision makers. That is, a multi-criteria decision which consists of MOPSO and TOPSIS is presented to find out a compromise solution for decision makers. Furthermore, local and global sensitivity analyses are performed to assess the effect of design variable values on the SEA and PCF functions in design domain. Based on the sensitivity analysis results, it is concluded that for both models, the helix pitch of the honeycomb core has greater effect on the sensitivity of SEA, while, the core thickness has greater effect on the sensitivity of PCF.

• Advances in aircraft and spacecraft science
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• 제8권4호
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.

• 생태와환경
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• 제42권1호
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• pp.85-94
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• 2009

용담댐 저수지에 설치된 대류식 순환장치에 대한 현장 조사 결과에 의하면 수평방향의 직접영향권은 성층 강도에 큰 영향 없이 반지름 $7{\sim}10m$에 이르는 것으로 조사 되었으며 수직방향으로는 성층강도에 따라 또는 가동기간에 따라 조금씩 달라지는 것으로 나타났다. 즉 가동시간이 길어짐에 따라 하층에서 올라온 수온이 낮은 수체는 보다 깊게 먼 곳까지 이동하는 것으로 나타났으나 성층을 깨지는 못하는 것으로 나타났다. 2008년 현장에서 실측 조사한 결과와 CFD모사 결과에 의하면 이런 조건에서 한 달을 가동하면 하층에서 올라온 수체가 대류식 장치 주변으로 수심 8 m, 지름 120 m의 수층을 이루게 되며 50일을 가동하면 수심 10 m, 지름 130m의 수층을 이루는 것으로 평가되었다. 대류식 순환장치가 설치된 지역에 대한 CFD모사를 하기 전에 이 지역의 흐름특성을 평가하였다. 대상 지역의 흐름은 연중 크게 3가지로 구분되었으며 각각의 경우 유량은 다르지만 저수지 수체의 흐름 속도는 모두 $0.05{\sim}1.5cm\;sec^{-1}$로 나타나 CFD모사시에 저수지 흐름을 고려하지 않아도 될 것으로 평가되었다. CFD를 이용한 수체거동 모사결과 순환장치로부터 3m지점에서의 유속은 $0.25m\;sec^{-1}$를 나타냈고, 5m지점에서는 $0.2m\;sec^{-1}$를 나타냈다. 현장 실측 결과와 비교시 유속은 모사 결과가 조금 크게 산정되는 것으로 나타났으나 향후 보다 많은 자료를 확보하여 비교해 보아야 할 것으로 판단되었다. 반면 영향범위는 반경방향으로 10 m지점까지는 직접영향을 받고, 그 보다 먼 지점은 간접영향권임을 나타내고 있어 이는 모사결과와 실측치 간에 일치하는 것으로 나타났다. 수면에서의 온도분포는 순환장치로부터 분출된 저온의 물이 반지름 약 10 m지점까지는 수온변화에 영향을 미치는 직접영향권인 것을 알 수 있다. 이상과 같이 모사 결과는 현장에서 실측한 것과 유사한 결과를 나타내므로 결과의 신뢰성이 높은 것으로 판단되었다.