• Title/Summary/Keyword: navier method

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Impact of viscoelastic foundation on bending behavior of FG plate subjected to hygro-thermo-mechanical loads

  • Ismail M. Mudhaffar;Abdelbaki Chikh;Abdelouahed Tounsi;Mohammed A. Al-Osta;Mesfer M. Al-Zahrani;Salah U. Al-Dulaijan
    • Structural Engineering and Mechanics
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    • v.86 no.2
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    • pp.167-180
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    • 2023
  • This work applies a four-known quasi-3D shear deformation theory to investigate the bending behavior of a functionally graded plate resting on a viscoelastic foundation and subjected to hygro-thermo-mechanical loading. The theory utilizes a hyperbolic shape function to predict the transverse shear stress, and the transverse stretching effect of the plate is considered. The principle of virtual displacement is applied to obtain the governing differential equations, and the Navier method, which comprises an exponential term, is used to obtain the solution. Novel to the current study, the impact of the viscoelastic foundation model, which includes a time-dependent viscosity parameter in addition to Winkler's and Pasternak parameters, is carefully investigated. Numerical examples are presented to validate the theory. A parametric study is conducted to study the effect of the damping coefficient, the linear and nonlinear loadings, the power-law index, and the plate width-tothickness ratio on the plate bending response. The results show that the presence of the viscoelastic foundation causes an 18% decrease in the plate deflection and about a 10% increase in transverse shear stresses under both linear and nonlinear loading conditions. Additionally, nonlinear loading causes a one-and-a-half times increase in horizontal stresses and a nearly two-times increase in normal transverse stresses compared to linear loading. Based on the article's findings, it can be concluded that the viscosity effect plays a significant role in the bending response of plates in hygrothermal environments. Hence it shall be considered in the design.

Lubrication Analysis of Parallel Slider Bearing with Nanolubricant (나노윤활유를 사용하는 평행 슬라이더 베어링의 윤활해석)

  • TaeJo Park;JeongGuk Kang
    • Tribology and Lubricants
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    • v.39 no.3
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    • pp.87-93
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    • 2023
  • Nanofluids are dispersions of particles smaller than 100 nm (nanoparticles) in base fluids. They exhibit high thermal conductivity and are mainly applied in cooling applications. Nanolubricants use nanoparticles in base oils as lubricant additives, and have recently started gathering increased attention owing to their potential to improve the tribological and thermal performances of various machinery. Nanolubricants reduce friction and wear, mainly by the action of nanoparticles; however, only a few studies have considered the rheological properties of lubricants. In this study, we adopt a parallel slider bearing model that does not generate geometrical wedge effects, and conduct thermohydrodynamic (THD) analyses to evaluate the effect of higher thermal conductivity and viscosity, which are the main rheological properties of nanolubricants, on the lubrication performances. We use a commercial computational fluid dynamics code, FLUENT, to numerically analyze the continuity, Navier-Stokes, energy equations with temperature-viscosity-density relations, and thermal conductivity and viscosity models of the nanolubricant. The results show the temperature and pressure distributions, load-carrying capacity (LCC), and friction force for three film-temperature boundary conditions (FTBCs). The effects of the higher thermal conductivity and viscosity of the nanolubricant on the LCC and friction force differ significantly, according to the FTBC. The thermal conductivity increases with temperature, improving the cooling performance, reducing LCC, and slightly increasing the friction. The increase in viscosity increases both the LCC and friction. The analysis method in this study can be applied to develop nanolubricants that can improve the tribological and cooling performances of various equipment; however, additional research is required on this topic.

Warping and porosity effects on the mechanical response of FG-Beams on non-homogeneous foundations via a Quasi-3D HSDT

  • Mokhtar Nebab;Hassen Ait Atmane;Riadh Bennai;Mouloud Dahmane
    • Structural Engineering and Mechanics
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    • v.90 no.1
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    • pp.83-96
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    • 2024
  • This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

Bending analysis of porous microbeams based on the modified strain gradient theory including stretching effect

  • Lemya Hanifi Hachemi Amar;Abdelhakim Kaci;Aicha Bessaim;Mohammed Sid Ahmed Houari;Abdelouahed Tounsi
    • Structural Engineering and Mechanics
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    • v.89 no.3
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    • pp.225-238
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    • 2024
  • In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

Quantitative Analysis of Quadrupole Noise Sources upon Quick Opening The Throttle (쓰로틀밸브 급개방시 기류소음의 4극음원에 대한 정량적 해석)

  • Kim Jaeheon;Cheong Cheolung;Kim SungTae;Lee Soogab
    • Proceedings of the Acoustical Society of Korea Conference
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    • spring
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    • pp.469-474
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    • 2002
  • In recent years, modularization of engine parts has increased the application of plastic products in air intake systems. Plastic intake manifolds provide many advantages including reduced weight, contracted cost, and lower intake air temperatures. These manifolds, however, have some weakness when compared with customary aluminium intake manifolds, in that they have low sound transmission loss because of their lower material density. This low transmission loss of plastic intake manifolds causes several problems related to flow noise, especially when the throttle is opened quickly. The physical processes, responsible for this flow noise, include turbulent fluid motion and relative motion of the throttle to the airflow. The former is generated by high-speed airflow in the splits between the throttle valve and the inner-surface of the throttle body and surge-tank, which can be categorized into the quadrupole source. The latter induces the unsteady force on the flow, which can be classified into the dipole source. In this paper, the mechanism of noise generation from the turbulence is only investigated as a preliminary study. Stochastic noise source synthesis method is adopted for the analysis of turbulence-induced, i.e. quadrupole noise by throttle at quick opening state. The method consists of three procedures. The first step corresponds to the preliminary time-averaged Navier-Stokes computation with a $k-\varepsilon$ turbulence model providing mean flow field characteristics. The second step is the synthesis of time-dependent turbulent velocity field associated with quadrupole noise sources. The final step is devoted to the determination of acoustic source terms associated with turbulent velocity. For the first step, we used market available analysis tools such as STAR-CD, the trade names of fluid analysis tools available on the market. The steady state flows at three open angle of throttle valve, i.e. 20, 35 and 60 degree, are numerically analyzed. Then, time-dependent turbulent velocity fields are produced by using the stochastic model and the flow analysis results. Using this turbulent velocity field, the turbulence-originated noise sources, i.e. the self-noise and shear-noise sources are synthesized. Based on these numerical results, it is found that the origin of the turbulent flow and noise might be attributed to the process of formulation and the interaction of two vortex lines formed in the downstream of the throttle valve. These vortex lines are produced by the non-uniform splits between the throttle valve and inner cylinder surface. Based on the analysis, we present the low-noise design of the inner geometry of throttle body.

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Effect of Wind Speed Profile on Wind Loads of a Fishing Boat (풍속 분포곡선이 어선의 풍하중에 미치는 영향에 관한 연구)

  • Lee, Sang-Eui
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.26 no.7
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    • pp.922-930
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    • 2020
  • Marine accidents involving fishing boats, caused by a loss of stability, have been increasing over the last decade. One of the main reasons for these accidents is a sudden wind attacks. In this regard, the wind loads acting on the ship hull need to be estimated accurately for safety assessments of the motion and maneuverability of the ship. Therefore, this study aims to develop a computational model for the inlet boundary condition and to numerically estimate the wind load acting on a fishing boat. In particular, wind loads acting on a fishing boat at the wind speed profile boundary condition were compared with the numerical results obtained under uniform wind speed. The wind loads were estimated at intervals of 15° over the range of 0° to 180°, and i.e., a total of 13 cases. Furthermore, a numerical mesh model was developed based on the results of the mesh dependency test. The numerical analysis was performed using the RANS-based commercial solver STAR-CCM+ (ver. 13.06) with the k-ω turbulent model in the steady state. The wind loads for surge, sway, and heave motions were reduced by 39.5 %, 41.6 %, and 46.1 % and roll, pitch, and yaw motions were 48.2 %, 50.6 %, and 36.5 %, respectively, as compared with the values under uniform wind speed. It was confirmed that the developed inlet boundary condition describing the wind speed gradient with respect to height features higher accuracy than the boundary condition of uniform wind speed. The insights obtained in this study can be useful for the development of a numerical computation method for ships.

A Study of Dynamic Instability for Sigmoid Functionally Graded Material Plates on Elastic Foundation (탄성지반위에 놓인 S형상 점진기능재료(FGM)판의 동적 불안정성에 관한 연구)

  • Lee, Won-Hong;Han, Sung-Cheon;Park, Weon-Tae
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.28 no.1
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    • pp.85-92
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    • 2015
  • This article presents the dynamic instability response of sigmoid functionally graded material plates on elastic foundation using the higher-order shear deformation theory. The higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The governing equations are then written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. The results of dynamic instability analysis of sigmoid functionally graded material plate are presented using the Navier's procedure to illustrate the effect of elastic foundation parameter on dynamic response. The relations between Winkler and Pasternak elastic foundation parameter are discussed by numerical results. Also, the effects of static load factor, power-law index and side-to-thickness ratio on dynamic instability analysis are investigated and discussed. In order to validate the present solutions, the reference solutions are used and discussed. The theoretical development as well as numerical solutions presented herein should serve as reference for the dynamic instability study of S-FGM plates.

Effect on measurements of anemometers due to a passing high-speed train

  • Zhang, Jie;Gao, Guangjun;Huang, Sha;Liu, Tanghong
    • Wind and Structures
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    • v.20 no.4
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    • pp.549-564
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    • 2015
  • The three-dimensional unsteady incompressible Reynolds-averaged Navier-Stokes equations and k-${\varepsilon}$ double equations turbulent model were used to investigate the effect on the measurements of anemometers due to a passing high-speed train. Sliding mesh technology in Fluent was utilized to treat the moving boundary problem. The high-speed train considered in this paper was with bogies and inter-carriage gaps. Combined with the results of the wind tunnel test in a published paper, the accuracy of the present numerical method was validated to be used for further study. In addition, the difference of slipstream between three-car and eight-car grouping models was analyzed, and a series of numerical simulations were carried out to study the influences of the anemometer heights, the train speeds, the crosswind speeds and the directions of the induced slipstream on the measurements of the anemometers. The results show that the influence factors of the train-induced slipstream are the passing head car and tail car. Using the three-car grouping model to analyze the train-induced flow is reasonable. The maxima of horizontal slipstream velocity tend to reduce as the height of the anemometer increases. With the train speed increasing, the relationship between $V_{train}$ and $V_{induced\;slipstream}$ can be expressed with linear increment. In the absence of natural wind conditions, from the head car arriving to the tail car leaving, the induced wind direction changes about $330^{\circ}$, while under the crosswind condition the wind direction fluctuates around $-90^{\circ}$. With the crosswind speed increasing, the peaks of $V_X,{\mid}V_{XY}-V_{wind}{\mid}$ of the head car and that of $V_X$ of the tail car tend to enlarge. Thus, when anemometers are installed along high-speed railways, it is important to study the effect on the measurements of anemometers due to the train-induced slipstream.

Numerical Analysis on Wave Characteristics around Submerged Breakwater in Wave and Current Coexisting Field by OLAFOAM (파-흐름 공존장내 잠제 주변에서 OLAFOAM에 의한 파랑특성의 수치해석)

  • Lee, Kwang-Ho;Bae, Ju-Hyun;An, Sung-Wook;Kim, Do-Sam;Bae, Kee Seung
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.28 no.6
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    • pp.332-349
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    • 2016
  • OLAFOAM is the powerful CFD code and is an expanded version of $OpenFOAM^{(R)}$, for wave mechanics simulation. The $OpenFOAM^{(R)}$ does provide many solvers to correspond to each object of the numerical calculation in a variety of fields. OLAFOAM's governing equation bases on VARANS (Volume-Averaged Reynolds-Averaged Navier-Stokes) equation, and the finite volume method is applied to numerical techniques. The program is coded in C++ and run on the Linux operating system. First of all, in this study, OLAFOAM was validated for 1) wave transformation inside porous structure under bore and regular wave conditions, 2) wave transformation by submerged breakwater under regular wave condition, and 3) regular wave transformation and resultant vertical velocity distribution under current by comparison with existing laboratory measurements. Hereafter, this study, which is almost no examination carried out until now, analyzed closely variation characteristics of water surface level, wave height, frequency spectrum, breaking waves, averaged velocity and turbulent kinetic energy around porous submerged breakwater in the wave and current coexisting field for the case of permeable or impermeable rear beach. It was revealed that the wave height fluctuation according to current direction(following or opposing) was closely related to the turbulent kinetic energy, and others.

Development of a High Performance Ocean Model using Julia Language (줄리아 언어를 이용한 고성능 해양모델의 개발)

  • KWON, MIN-SUN;KIM, JONG GU
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.24 no.2
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    • pp.187-207
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    • 2019
  • In order to develop a high performance ocean model, we used Julia, a Just-In-Time compile language, and to obtain the solution of the momentum equation, we made the code to solve the Poisson equation by the Successive Over-Relaxation method. And then we made two models to test Julia calculation codes. First, a simple channel form is modeled to test constant source/sink conditions. Second, the simplified Yellow Sea was modeled to test tidal forcing, Coriolis forces, and the effect of vertical eddy diffusivity coefficients. The model has been tested with a total of eight cases in the two scenarios. As a result of the test, the depth-averaged current speed of the three cases in Scenario 1 converged perfectly to the theoretical value, and that showed well a vertical flow velocity gradient due to the bottom friction. Also, the result of Scenario 2 represented well the amphidromic points of Yellow Sea and the tidal characteristics of mid-western and southwestern coast of Korea. Therefore, it is considered that the ocean model using Julia language has developed successfully, this suggests that the ocean model has come to the stage of successful transition from a classical compile language to a Just-In-Time compile language.