• Title/Summary/Keyword: plate equation

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Flexural performances of deep-deck plate slabs: Experimental and numerical approaches

  • Inwook Heo;Sun-Jin Han;Khaliunaa Darkhanbat;Seung-Ho Choi;Sung Bae Kim;Kang Su Kim
    • Steel and Composite Structures
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    • v.52 no.3
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    • pp.313-325
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    • 2024
  • This work presents experimental and numerical investigations on the flexural performances of composite deep-deck plate slabs. Seven deep-deck plate slab specimens with topping concrete were fabricated; the height of the topping slab as well as presence and type of shear connector were set as the main variables to perform bending experiments. The flexural behaviors of the specimens and composite behaviors of the deck plate and concrete were analyzed in detail. The contributions of the deck plate to the flexural stiffness and strength of the slab were identified through finite element (FE) analysis. FE analysis was carried out using the validated FE model by considering the varying bond strengths of the deck plates and concrete, thickness of the deck plate, and types and spacings of the shear connectors. Based on the results, the degree of composite of the deep-deck plate was examined, and a flexural strength equation for the composite deck plate slabs was proposed.

Thermal vibration analysis of thick laminated plates by the moving least squares differential quadrature method

  • Wu, Lanhe
    • Structural Engineering and Mechanics
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    • v.22 no.3
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    • pp.331-349
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    • 2006
  • The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

Analysis for Lubrication between a Rotating Cylinder and a Translating Plate (회전하는 원통과 병진운동하는 평판사이의 윤활유동해석)

  • 정호열;정재택
    • Tribology and Lubricants
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    • v.18 no.6
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    • pp.411-417
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    • 2002
  • Two dimensional slow viscous flow between a rotating cylinder and a translating plate is investigated using Stokes' approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns are shown and the pressure distribution in the flow field is determined. By integrating the stress distributions on the cylinder, the farce and the moment exerted on the cylinder are calculated. The flow rate through the gap between the cylinder and the plate is also determined as a function of the distance between the cylinder and the plate. Special attention is directed to the case of very small distance between the cylinder and the plate concerned with the lubrication theory and the minimum pressure is calculated to explain a possible cavitation.

Stability analysis of transversely isotropic laminated Mindlin plates with piezoelectric layers using a Levy-type solution

  • Ghasemabadian, M.A.;Saidi, A.R.
    • Structural Engineering and Mechanics
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    • v.62 no.6
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    • pp.675-693
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    • 2017
  • In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

Stress Intensity Factor for the Cracked Sheet Subjected to Normal Stress and Reinforced with a Plate by Spot Welding (점용접에 의하여 판재로 보강된 균열판의 수직응력에 의한 응력세기계수)

  • 이강용;김옥환
    • Journal of Welding and Joining
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    • v.15 no.1
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    • pp.55-65
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    • 1997
  • The stress intensity factor has been calculated for the cracked plate subjected to remote normal stress and reinforced with a plate by symmetric spot welding. The solution was based on displacement compatibility condition between the cracked sheet and the reinforcement plate. It is shown that the results from the derived equation for stress intensity factor were agreed with previous solutions. The reinforcement effect gets better as a joining spot is closer to the crack tip and the other joining spots become nearer to the crack surface.

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Stiffness Reduction Factor for Post-Tensioned Flat Plate Slabs (포스트 텐션 플랫 플레이트 해석을 위한 강성감소계수)

  • Park, Young-Mi;Park, Jin-Ah;Han, Sang-Whan
    • Proceedings of the Korea Concrete Institute Conference
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    • 2009.05a
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    • pp.125-126
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    • 2009
  • Effective beam width model (EBWM) has been used for analysis of post-tensioned (PT) flat plate slab frames under lateral loads. For analyzing PT flat plate slab structure under lateral loads with good precision, reduction in slab stiffness has to be accurately estimated for Effective beam width model(EBWM). For this purpose, this study collected test results of PT flat plate system conducted by former researches. And this study reduced the width of slab so that the stiffness of the EBWM converged into the lateral stiffness of each test specimens by trial and error. By conducting nonlinear regression analysis, an equation for calculating stiffness reduction factor for the PT flat plate is proposed.

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Free Vibration Analysis of Rectangular Plate with Multiple Circular Cutouts by Independent Coordinate Coupling Method (독립좌표연성법을 이용한 여러 개의 원형 구멍을 갖는 직사각형 평판의 자유진동해석)

  • Kwak, Moon K.;Song, Myung-Ho
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.11
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    • pp.1086-1092
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    • 2007
  • This paper is concerned with the vibration analysis of a rectangular plate with multiple circular holes. On the contrary to the case of rectangular plate with multiple rectangular holes, it is very difficult to perform qualitative analysis on natural vibration characteristics because of geometrical inconsistency. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a circular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

A Study on the Vibration Characteristics of Steel and Plain Weave Composite Cylindrical Shells Combined with Internal Plate Structures (내부판 구조물이 결합된 강 및 평직 복합재료 원통셸의 구조진동 특성 연구)

  • 이영신;최명환
    • Journal of KSNVE
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    • v.9 no.1
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    • pp.149-162
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    • 1999
  • A method for the analysis of free vibrations of steel and plain weave composite cylindrical shells with a longitudinal, interior rectangular plate is developed by using the receptance method. This method is based on the ratio of a deflection (or slope) response to a harmonic force(or moment) at the joint. In this study, after getting the free vibration characteristics of the simply supported plate and shell, the frequency equation of the combined system is obtained by considering the continuity condition at the joint between the plate and the shell. The numerical results are compared with published results and experiment results in order to show the validate of the formulation, and shown that the analytical results agreed with those from other methods. The effects of the location and the thickness of the plate on the natural frequencies are also investigated.

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The Impingement of a Weak Shock Wave Discharged from a Tube Exit upon a Flat Plate (관 출구로부터 방출하는 약한 충격파의 평판충돌에 관한 연구)

  • 이동훈;김희동;강성황
    • Journal of KSNVE
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    • v.10 no.6
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    • pp.1035-1040
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    • 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. Computations predicted the experimented results with a good accuracy. The peak pressure on the flat plate was not strongly dependent of the shock wave Mach number in the present range of Mach Number 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.

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Scaling and Dynamic Effects on the Plate Cutting Response (판의 찢김 응답에 대한 치수 및 동적 효과)

  • 백점기;이탁기
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.3
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    • pp.48-55
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    • 1996
  • The aim of the present study is to investigate the scaling and dynamic erects on the plate cutting response. A series of cutting tests for unstiffened and longitudinally stiffened steel plate specimens in a quasi-static condition were carried out, varying the plate thickness. Based on the previous as well as the present test results, the scaling effect of Plate thickness on the cutting response is investigated. Dynamic erects are also clarified from the devious theoretical and experimental results. The Cowper-Symonds constitutive equation originally derived for mild steel is modified to consider the influence of strain-rate sensitivity on yield strength of high tensile steel.

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