• Title/Summary/Keyword: Parabolic problem

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Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models

  • Bouiadjra, Rabbab Bachir;Mahmoudi, Abdelkader;Benyoucef, Samir;Tounsi, Abdelouahed;Bernard, Fabrice
    • Structural Engineering and Mechanics
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    • v.66 no.3
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    • pp.317-328
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    • 2018
  • In this paper, a new refined quasi-three-dimensional (3D) shear deformation theory for the bending analysis of functionally graded plate is presented. The number of unknown functions involved in this theory is only four against five or more in the case of the other shear and normal deformation theories. Due to its quasi-3D nature, the stretching effect is taken into account in the formulation of governing equations. In addition, the effect of different micromechanical models on the bending response of these plates is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG plates whose properties vary continuously across the thickness according to a simple power law. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of displacements across the thickness, and the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The problem is solved for a plate simply supported on its edges and the Navier solution is used. The results of the present method are compared with others from the literature where a good agreement has been found. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG plates.

Study of a Searchlight Lens to Improve Optical Performance and Fabricability (광학 성능 및 제작성 향상을 위한 탐조등 렌즈 연구)

  • Jo, Ye-Ji;Jung, Mee-Suk
    • Korean Journal of Optics and Photonics
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    • v.31 no.2
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    • pp.81-87
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    • 2020
  • This study examines the design technology of searchlight optics featuring narrow beam angles and high luminous intensities. Halogen and xenon lamps, which are conventional searchlight sources, are vulnerable to vibration and shock, and are large and heavy, making them difficult to transport. In addition, the parabolic mirror located at the rear of the searchlight has the disadvantages of poor performance and low light efficiency, due to the assembly error produced during manufacturing. To solve this problem, a 1-kW halogen lamp is replaced by a 150-W high-power COB LED, and a high-efficiency TIR lens is designed to meet the target performance. Afterward, the TIR lens array is proposed to solve the surface error generated during optical injection. After a prototype is manufactured based on the designed optical system, the optical performance is confirmed to be excellent, by comparing it to that of a commercial halogen-lamp searchlight.

Effect of tapered-end shape of FRP sheets on stress concentration in strengthened beams under thermal load

  • El Mahi, Benaoumeur;Kouider Halim, Benrahou;Sofiane, Amziane;Khalil, Belakhdar;Abdelouahed, Tounsi;Adda Bedia, El Abbes
    • Steel and Composite Structures
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    • v.17 no.5
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    • pp.601-621
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    • 2014
  • Repairing and strengthening structural members by bonding composite materials have received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs under various types of loading. In this paper, a numerical solution using finite - difference method (FDM) is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends under thermal loading. Different thinning profiles are investigated since the later can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. The shear correction factor for I-section beams is also included in the solution. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

The Modeling and Simulation for Pseudospectral Time-Domain Method Synthetic Environment Underwater Acoustics Channel applied to Underwater Environment Noise Model (수중 환경 소음 모델이 적용된 의사 스펙트럼 시간영역 법 합성환경 수중음향채널 모델링 및 시뮬레이션)

  • Kim, Jang-Eun;Kim, Dong-Gil;Han, Dong-Seog
    • Journal of the Korea Society for Simulation
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    • v.25 no.3
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    • pp.15-28
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    • 2016
  • It is necessary to analyze underwater acoustics channel(UAC) modeling and simulation for underwater weapon system development and acquisition. In order to analyze UAC, there are underwater acoustics propagation numerical analysis models(Ray theory, Parabolic equation, Normal-mode, Wavenumber integration). However, If these models are used for multiple frequency signal analysis, they are inaccurate to calculate result of analysis effectiveness and restricted for signal processing and analysis. In this paper, to overcome this problem, we propose simple/multiple frequency signal analysis model of the Pseudospectral Time-Domain Method synthetic environment UAC applied to underwater environment noise model as like as realistic underwater environment. In order to confirm the validation of the model, we performed the 9 scenarios simulation(4 scenarios of single frequency signal, 4 scenarios of multiple frequency signal, 1 scenario of single/multiple frequency signal like submarine radiated noise) for validation and confirmed the validation of this model through the simulation model.

A Study of Lens Design Technique for Proximity Exposure Using a UVA LED (UVA LED를 이용한 근접 노광용 렌즈 설계 기술 연구)

  • Lee, Jeong-Su;Jo, Ye-Ji;Lee, Hyun-Hwa;Kong, Mi-Seon;Kang, Dong-Hwa;Jung, Mee-Suk
    • Korean Journal of Optics and Photonics
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    • v.30 no.4
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    • pp.146-153
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    • 2019
  • The exposure system is a device that transfers a circuit pattern to a desired location. To display patterns on a substrate without deforming the optical characteristics, the characteristics of the optical exposure system are very important. Therefore, to form a microcircuit pattern, a small divergence angle should impinge on the irradiation area. Also, since the light from the source must react uniformly with the photosensitizer, it must have high luminance efficiency and uniformity of illumination. In this paper a parabolic reflector and an aspherical lens were designed to solve the problem of narrow-angle implementation, and it was confirmed by simulation analysis after their arrangement that the beam angle, uniformity, and maximum illuminance satisfied the target performance.

A computational investigation on flexural response of laminated composite plates using a simple quasi-3D HSDT

  • Draiche, Kada;Selim, Mahmoud M.;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Bourada, Fouad;Tounsi, Abdeldjebbar;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.41 no.5
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    • pp.697-711
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    • 2021
  • In this work, a simple quasi 3-D parabolic shear deformation theory is developed to examine the bending response of antisymmetric cross-ply laminated composite plates under different types of mechanical loading. The main feature of this theory is that, in addition to including the transverse shear deformation and thickness stretching effects, it has only five-unknown variables in the displacement field modeling like Mindlin's theory (FSDT), yet satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without requiring a shear correction factor. The static version of principle of virtual work was employed to derive the governing equations, while the bending problem for simply supported antisymmetric cross-ply laminated plates was solved by a Navier-type closed-form solution procedure. The adequacy of the proposed model is handled by considering the impact of side-to-thickness ratio on bending response of plate through several illustrative examples. Comparison of the obtained numerical results with the other shear deformation theories leads to the conclusion that the present model is more accurate and efficient in predicting the displacements and stresses of laminated composite plates.

Mechanical behaviour analysis of FGM plates on elastic foundation using a new exponential-trigonometric HSDT

  • Fatima Z. Zaoui;Djamel Ouinas;Abdelouahed Tounsi;Belkacem Achour;Jaime A. Vina Olay;Tayyab A. Butt
    • Steel and Composite Structures
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    • v.47 no.5
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    • pp.551-568
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    • 2023
  • In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.

THREE-SITE PHOTOMETRIC MONITORING OF THE δ SCT-TYPE PULSATING STAR V1162 ORIONIS : PERIOD CHANGE AND ITS IMPLICATIONS FOR PRE-MAIN SEQUENCE EVOLUTION

  • KIM, SEUNG-LEE;CHA, SANG-MOK;LIM, BEOMDU;LEE, JAE WOO;LEE, CHUNG-UK;LEE, YONGSEOK;KIM, DONG-JIN;LEE, DONG-JOO;KOO, JAE-RIM;HONG, KYEONGSOO;RYU, YOON-HYUN;PARK, BYEONG-GON
    • Journal of The Korean Astronomical Society
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    • v.49 no.5
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    • pp.199-208
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    • 2016
  • We present photometric results of the δ Sct star V1162 Ori, which is extensively monitored for a total of 49 nights from mid-December 2014 to early-March 2015. The observations are made with three KMTNet (Korea Microlensing Telescope Network) 1.6 m telescopes installed in Chile, South Africa, and Australia. Multiple frequency analysis is applied to the data and resulted in clear detection of seven frequencies without an alias problem: five known frequencies and two new ones with small amplitudes of 1.2-1.7 mmag. The amplitudes of all but one frequency are significantly different from previous results, confirming the existence of long-term amplitude changes. We examine the variations in pulsation timings of V1162 Ori for about 30 years by using the times of maximum light obtained from our data and collected from the literatures. The O − C (Observed minus Calculated) timing diagram shows a combination of a downward parabolic variation with a period decreasing rate of (1/P)dP/dt = −4.22 × 10−6 year−1 and a cyclic change with a period of about 2780 days. The most probable explanation for this cyclic variation is the light-travel-time effect caused by an unknown binary companion, which has a minimum mass of 0.69 M. V1162 Ori is the first δ Sct-type pulsating star of which the observed fast period decrease can be interpreted as an evolutionary effect of a pre-main sequence star, considering its membership of the Orion OB 1c association.

Development of 3-D Nonlinear Wave Driver Using SPH (SPH을 활용한 3차원 비선형 파랑모형 개발)

  • Cho, Yong Jun;Kim, Gweon Soo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.28 no.5B
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    • pp.559-573
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    • 2008
  • In this study, we newly proposed 3-D nonlinear wave driver utilizing the Navier-Stokes Eq. the numerical integration of which is carried out using SPH (Smoothed Particle Hydrodynamics), an internal wave generation with the source function of Gaussian distribution and an energy absorbing layer. For the verification of new 3-D nonlinear wave driver, we numerically simulate the sloshing problem within a parabolic water basin triggered by a Gaussian hump and uniformly inclined water surface by Thacker (1981). It turns out that the qualitative behavior of sloshing caused by relaxing the external force which makes a free surface convex or uniformly inclined is successfully simulated even though phase error is visible and an inundation height shrinks as numerical simulation more proceeds. For the more severe test, we also simulate the nonlinear shoaling and refraction over uniform beach of wedge shape. It is shown that numerically simulated waves are less refracted than the linear counterpart by Hamiltonian ray theory due to nonlinearity, energy dissipation at the bottom and side walls, energy loss induced by breaking, and the hydraulic jump occurring when breaking waves encounter a down-rush by the preceding wave.