• Title/Summary/Keyword: plate equation

Search Result 811, Processing Time 0.029 seconds

Pullout capacity of vertical plate anchors in cohesion-less soil

  • Kame, G.S.;Dewaikar, D.M.;Choudhury, Deepankar
    • Geomechanics and Engineering
    • /
    • v.4 no.2
    • /
    • pp.105-120
    • /
    • 2012
  • In this paper, the ultimate pullout capacity of a vertical plate strip anchors in cohesion-less soil is analyzed with the consideration of active and passive state of equilibrium in the soil. K$\ddot{o}$tter's equation is used to compute the active and passive thrusts (along with their point of application) which are subsequently used in the analysis in which, all the equation of equilibrium are properly interpreted. A comparison of the results with the experimental results vis-$\grave{a}$-vis available theoretical/empirical solutions shows that, the proposed analysis provides a better estimate of the pullout capacity.

Single-shot Transport-of-intensity Equation Using a Wollaston Prism for Biological Samples

  • Joseph Vermont Bunyi Bandoy;Cuong Manh Nguyen;An Nazmus Sakib;Suhyeon Kim;Hyuk-Sang Kwon
    • Current Optics and Photonics
    • /
    • v.8 no.5
    • /
    • pp.502-507
    • /
    • 2024
  • The Wollaston prism (WP) has shown promise in enabling single-shot transport-of-intensity equation (ssTIE) measurements, facilitating efficient phase retrieval in microscopy. The 1-degree prism which produces the minor beam-separation angle is used to prevent distortions. An optical-glass plate is employed in the duplicated beam path to introduce defocusing. This configuration is also advantageous when aligning the beams laterally caused by the refraction of the optical-glass plate, thus allowing another method for single-shot measurements. We applied the proposed method to image the red blood cells (RBCs), demonstrating that the proposed method could be useful in various biological and medical applications.

Forced vibrations of an elastic rectangular plate supported by a unilateral two-parameter foundation via the Chebyshev polynomials expansion

  • Zekai Celep;Zeki Ozcan
    • Structural Engineering and Mechanics
    • /
    • v.90 no.6
    • /
    • pp.551-568
    • /
    • 2024
  • The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

Development of Doubler Plate Design System for Ship Structure Subjected to In-plane Combined Loads and Lateral Pressure (면내조합하중과 횡압 하의 선박 이중판 설계시스템 구축)

  • Ham, Juh-Hyeok
    • Journal of Ocean Engineering and Technology
    • /
    • v.33 no.2
    • /
    • pp.146-152
    • /
    • 2019
  • A design system was developed for the doubler plate of a ship structure simultaneously subjected to in-plane loads and lateral pressure based on general dimensions and those of a representative ship structure. An equivalent design equation that considers various structural design parameters was derived by introducing the equivalent plate thickness theory, and the design of the doubler plate reinforcement of the ship structure was developed. A hybrid structural design system was established for a doubler plate simultaneously subjected to in-plane loads and lateral pressure consisting of two modules: an optimized design module and a double plate strength & design review module. The practical application of this design system was illustrated to show its usability. It was found that the design safety of the doubler plate was ensured, and this system could be used as an initial design guide to review the double plate reinforcement for a dent or corrosion of the ship plate members. Using the developed design system would make it possible to obtain a more reasonable doubler plate structure that considers the rational reinforcement of plate members of ship structures. In addition, a more reliable structural analysis using a strength evaluation process can be performed to verify the efficiency of the optimum structural design for the doubler plate structure.

Robust Design for Showerhead Thermal Deformation

  • Gong, Dae-Wi;Kim, Ho-Jun;Lee, Seung-Mu;Won, Je-Hyeong
    • Proceedings of the Korean Vacuum Society Conference
    • /
    • 2014.02a
    • /
    • pp.150.1-150.1
    • /
    • 2014
  • Showerhead is used as a main part in the semiconductor equipment. The face plate flatness should remain constant and the cleaning performance must be gained to keep the uniformity level of etching or deposition in chemical vapor deposition process. High operating temperature or long period of thermal loading could lead the showerhead to be deformed thermally. In some case, the thermal deformation appears very sensitive to showerhead performance. This paper describes the methods for robust design using computational fluid dynamics. To reveal the influence of the post distribution on flow pattern in the showerhead cavity, numerical simulation was performed for several post distributions. The flow structure appears similar to an impinging flow near a centered baffle in showerhead cavity. We took the structure as an index to estimate diffusion path. A robust design to reduce the thermal deformation of showerhead can be achieved using post number increase without ill effect on flow. To prevent the showerhead deformation by heat loading, its face plate thickness was determined additionally using numerical simulation. The face plate has thousands of impinging holes. The design key is to keep pressure drop distribution on the showerhead face plate with the holes. This study reads the methodology to apply to a showerhead hole design. A Hagen-Poiseuille equation gives the pressure drop in a fluid flowing through such hole. The assumptions of the equation are the fluid is viscous-incompressible and the flow is laminar fully developed in a through hole. An equation can be expressed with radius R and length L related to the volume flow rate Q from the Hagen-Poiseuille equation, $Q={\pi}R4{\Delta}p/8{\mu}L$, where ${\mu}$ is the viscosity and ${\Delta}p$ is the pressure drop. In present case, each hole has steps at both the inlet and the outlet, and the fluid appears compressible. So we simplify the equation as $Q=C(R,L){\Delta}p$. A series of performance curves for a through hole with geometric parameters were obtained using two-dimensional numerical simulation. We obtained a relation between the hole diameter and hole length from the test cases to determine hole diameter at fixed hole length. A numerical simulation has been performed as a tool for enhancing showerhead robust design from flow structure. Geometric parameters for the design were post distribution and face plate thickness. The reinforced showerhead has been installed and its effective deposition profile is being shown in factory.

  • PDF

Establishment of Initial Work Roll Crown in Finishing Plate Mill (후판 압연에서 작업롤 초기 크라운 설정)

  • 김종택;서재형;정병완
    • Proceedings of the Korean Society of Precision Engineering Conference
    • /
    • 1993.10a
    • /
    • pp.499-504
    • /
    • 1993
  • To find a way for establishing work roll initial crown according to roll conditions, computer simulation for predicting plate crown in plate mill is done and effects of roll conditions on plate crown is analysed. Roll gap profile and plate crown are measured to be compared to the calculated values. As a result,a regression equation to establish work roll initial crown according to roll cooditions such as backup roll diameter, backup roll crown and work roll crown is obtained.

  • PDF

Characteristics of Anchorage Length for Reinforced Concrete Beam Strengthened by CFRP Plate (탄소섬유보강판으로 보강된 철근콘크리트 보의 정착길이 특성)

  • 한상훈;최만용;조홍동;박중열;황선일;권용길
    • Proceedings of the Korea Concrete Institute Conference
    • /
    • 2002.05a
    • /
    • pp.405-410
    • /
    • 2002
  • This paper deals with the flexural behavior of RC hems strengthened with CFRP plate and the estimation on anchorage length of CFRP Plate. Experimental variables included concrete strength, reinforcement ratio, cover thickness of concrete and length ratio of CFRP plate for a pure span. A failure load, failure mode, deflection and strain response at different distances from a cut-off point of CFRP plate were observed and anchorage length was determined through strain distribution of CFRP plate. Herein, anchorage length is defined the length between CFRP plate end and the beginning point of full composite behavior. Also, the anchorage length observed from the experiment was compared with Nguyen's equation and BS specification.

  • PDF

Experimental and Computational Studies of the Pulse Wave Impinging upon a Vertical Flat Plate (수직평판에 충돌하는 펄스파에 관한 실험적/수치해석적 연구)

  • 이동훈;김희동;강성황
    • Journal of KSNVE
    • /
    • v.11 no.2
    • /
    • pp.285-291
    • /
    • 2001
  • The impingement of a weak shock wane discharged from the open end of a shock tube upon a flat plate was investigated using shock tube experiments and numerical simulations. Harten-Yee Total Variation Diminishing method was used to solve axisymmetric, unsteady, compressible flow governing equations. Experiments were carried out to validate the present computations. The effects of the flat plate and baffle plate sizes on the impinging flow field over the flat plate were investigated. Shock Mach number was varied in the range from 1.05 to 1.20. The distance between the plate and shock tube was changed to investigate the effect on the peak pressure. From both the results of experiments and computations we obtained a good empirical equation to predict the peak pressure on the flat plate.

  • PDF

A Study on the Characteristics of the Pulse Wave Impinging upon a Flat Plate (평판에 충돌하는 펄스파의 특성에 관한 연구)

  • Kim, H.D.;Lee, D.H.
    • Proceedings of the KSME Conference
    • /
    • 2000.11b
    • /
    • pp.562-567
    • /
    • 2000
  • The Impingement of a weak shock wave discharged from the open end of a shock tube upon a flat plate was investigated using shock tube experiments and numerical simulations. Harten-Yee Total Variation Diminishing method was used to solve axisymmetric, unsteady, compressible flow governing equations. Experiments were carried out to validate the present computations. The effects of the flat plate and baffle plate sizes on the impinging flow field over the flat plate were investigated. Shock Mach number was vaned in the range from 1.05 to 1.20. The distance between the plate and shock tube was changed to investigate the effect on the peak pressure. From both the results of experiments and computations we obtained a good empirical equation to predict the peak pressure on the flat plate.

  • PDF

Free Vibration Analysis of an Annular Plate by the Independent Coordinate Coupling Method (독립좌표연성법을 이용한 원환판의 자유진동해석)

  • Heo, Seok;Kwak, Moon-K.
    • Transactions of the Korean Society for Noise and Vibration Engineering
    • /
    • v.18 no.5
    • /
    • pp.564-571
    • /
    • 2008
  • This paper is concerned with the free vibration analysis of an annular plate with boundary conditions of simply supported-free, clamped-free and free-free, respectively. Exact solutions for the natural frequency and mode of an annular plate can be obtained by solving the differential equation but other methods such as the Rayleigh-Ritz method and the finite element method can be also used. In this research, we applied the Independent Coordinate Coupling Method(ICCM) to the annular plate and prove that the ICCM can accurately predict the natural frequency and mode shape of the annular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of plate with a hole compared to the Rayleigh-Ritz method and the finite element method.