• Title/Summary/Keyword: plate equation

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Structural Behavior of RC Beam Strengthened with Steel Plate (강판 휨보강된 철근 콘크리트보의 구조적 거동)

  • 오병환;강동욱;조재열;채성태;이명규
    • Proceedings of the Korea Concrete Institute Conference
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    • 1997.04a
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    • pp.598-604
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    • 1997
  • In recent years, strengthening by epoxy-bonded steel plates, carbon fiber sheets, aramid fiber sheets and so on, is spotlighted. Among them, the method using steel plates is most widely applied. Most studies have dealt with strengthening by epoxy-bonded steel plates. However the actual behavior of strengthened RC beams are not well established. Particularly, the studies on the separation load thar affects failure load of the beam are relatively insufficient. In this study, test parameters are the magnitude of pre-load, plate length, plate thickness, existence and spacing of anchor bolt, the number of plate layer and the height of side strengthening, 17reinforced concrete beams are strengthened by steel plates according to test parameters. Deflection, failure load, strains of reinforcing bar, concrete and plate are measured from tests(4 points loading). The failure mode, and separation load are analyzed from these measured data. The difference between Robert's theory and test results is discussed, and the prediction equation for separation load in the case of rip off is proposed.

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Theoretical Approach to Welding Out-of Plane Oeformations in Thin Plate Structures (박판구조물의 용접 면외변형에 대한 이론 해석적 접근)

  • Seo, Sung-Il
    • Journal of the Society of Naval Architects of Korea
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    • v.42 no.5 s.143
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    • pp.466-471
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    • 2005
  • The out-of-plane deformation in thin plate structure has been a serious qualify problem. It has been known that the out-of-plane deformation is caused by the angular deformation of welded joint. However, experimental results show that the conventional theory based on angular deformation is not appropriate for prediction of the out-of-plane deformation in thin plate structure. In this study, large deformation plate theory is introduced to clarify the effect of residual stress on the out-of-plane deformation. A simple equation is proposed to predict the out-of-plane deformation. The results by the proposed method show good agreement with the experimental results.

Investigating dynamic stability of metal foam nanoplates under periodic in-plane loads via a three-unknown plate theory

  • Fenjan, Raad M.;Ahmed, Ridha A.;Faleh, Nadhim M.
    • Advances in aircraft and spacecraft science
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    • v.6 no.4
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    • pp.297-314
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    • 2019
  • Dynamic stability of a porous metal foam nano-dimension plate on elastic substrate exposed to bi-axial time-dependent forces has been studied via a novel 3-variable plate theory. Various pore contents based on uniform and non-uniform models have been introduced. The presented plate model contains smaller number of field variables with shear deformation verification. Hamilton's principle will be utilized to deduce the governing equations. Next, the equations have been defined in the context of Mathieu-Hill equation. Correctness of presented methodology has been verified by comparison of derived results with previous data. Impacts of static and dynamical force coefficients, non-local coefficient, foundation coefficients, pore distributions and boundary edges on stability regions of metal foam nanoscale plates will be studied.

A size-dependent study on buckling and post-buckling behavior of imperfect piezo-flexomagnetic nano-plate strips

  • Momeni-Khabisi, Hamed;Tahani, Masoud
    • Advances in nano research
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    • v.12 no.4
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    • pp.427-440
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    • 2022
  • In the present study, the nonlocal strain gradient theory is used to predict the size-dependent buckling and post-buckling behavior of geometrically imperfect nano-scale piezo-flexomagnetic plate strips in two modes of direct and converse flexomagnetic effects. The first-order shear deformation plate theory is used to analyze analytically nano-strips with simply supported boundary conditions. The nonlinear governing equations of equilibrium and associated boundary conditions are derived using the principle of minimum total potential energy with consideration of the von Kármán-type of geometric nonlinearity. A closed-form solution of governing differential equation is obtained, which is easily usable for engineers and designers. To validate the presented formulations, whenever possible, a comparison with the results found in the open literature is reported for buckling loads. A parametric study is presented to examine the effect of scaling parameters, plate slenderness ratio, temperature, the mid-plane initial rise, flexomagnetic coefficient, different temperature distributions, and magnetic potential, in case of the converse flexomagnetic effect, on buckling and post-buckling loads in detail.

Thermoelastic analysis of rectangular plates with variable thickness made of FGM based on TSDT using DQ method

  • Amiri, Majid;Loghman, Abbas;Arefi, Mohammad
    • Geomechanics and Engineering
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    • v.29 no.6
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    • pp.667-681
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    • 2022
  • This paper presents a thermoelastic analysis of variable thickness plates made of functionally graded materials (FGM) subjected to mechanical and thermal loads. The thermal load is applied to the plate as a temperature difference between the top and bottom surfaces. Temperature distribution in the plate is obtained using the steady-state heat equation. Except for Poisson's ratio, all mechanical properties of the plate are assumed to vary linearly along the thickness direction based on the volume fractions of ceramic and metal. The plate is resting on an elastic foundation modeled based on the Winkler foundation model. The governing equations are derived based on the third-order shear deformation theory (TSDT) and are solved numerically for various boundary conditions using the differential quadrature method (DQM). The effects of various parameters on the stress distribution and deflection of the plate are investigated such as the value of thermal and mechanical loads, volume fractions of ceramic and metal, and the stiffness coefficients of the foundation.

A Study on Plate Bending Analysis Using Boundary Element Method

  • Son, Jae-hyeon;Kim, Yooil
    • Journal of Ocean Engineering and Technology
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    • v.36 no.4
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    • pp.232-242
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    • 2022
  • This study presents a method for level ice-structure interaction analysis to estimate the fatigue damage of arctic structures by applying plate theory to the behavior of level ice. The boundary element method (BEM), which incurs a lower computational cost than the finite element method (FEM), was introduced to solve the plate bending problem. The BEM formulation was performed by applying the BEM to plate theory. Finally, to check the validity of the proposed method, the BEM results and FEM results obtained using the ABAQUS commercial software were compared. The response results of the BEM analysis agreed well with those of the FEM analysis. Based on the results of the analysis, the BEM approach is considered to be very powerful in level ice-structure interaction analysis for estimating level ice-induced fatigue damage. Further work is being conducted to perform level ice fracture analysis based on the stress field calculated using the boundary element method.

Free Vibration Analysis of Simply-Supported Rectangular Plate with a Circular Cutout by Independent Coordinate Coupling Method (독립좌표연성법을 이용한 원형 구멍을 갖는 단순지지 직사각형 평판의 자유진동해석)

  • Kwak, Moon-K.;Han, Sang-Bo
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2006.05a
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    • pp.1177-1182
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    • 2006
  • This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have be en many methods developed for the free vibration of the rectangular plate with a rectangular cutout., very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian co ordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

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Wave Models and Experimental Studies of Beam-plate-beam Coupled Systems for a Mid-frequency Analysis (중주파수 대역 해석을 위한 Beam-plate-beam 연성 구조물의 웨이브 모형 연구와 시험적 규명)

  • Yoo, Ji-Woo;Thompson, D.J.;Ferguson, N.S.
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.2 s.119
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    • pp.121-129
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    • 2007
  • There has been much effort to find suitable methods for structural analysis in the mid-frequency region where traditional low frequency methods have increasing uncertainties whilst statistical energy analysis is not strictly applicable. Systems consisting of relatively stiff beams coupled to flexible plates have a particularly broad mid-frequency region where the beams support only a few modes whilst the plate has a high modal density and modal overlap. A system of two parallel beams coupled to a plate is investigated based on the wave method, which is an approximate method. Muller's method is utilised for obtaining complex roots of a dispersion wave equation, which does not converge in the conventional wave method based on a simple iteration. The wave model is extended from a single-beam-plate system, to a plate with two identical beams which is modelled using a symmetric-antisymmetric technique. The important hypothesis that the coupled beam wavenumber is sufficiently smaller than the plate free wavenumber is experimentally verified. Finally, experimental results such as powers and energy ratios show the validity of the analytical wave models.

Ultimate strength of simply supported plate with opening under uniaxial compression

  • Yu, Chang-Li;Lee, Joo-Sung
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.4 no.4
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    • pp.423-436
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    • 2012
  • Unstiffened plates are integral part of all kinds of structures such as ship and offshore oil platforms. Openings are unavoidable and absolutely reduce the ultimate strength of structures. In this study, the finite element analysis package, ABAQUS, is used to analyze the behavior of unstiffened plate with rectangular opening. The rectangular opening form is divided into two cases. In case1, opening depth is constant, but opening width is varied. Meanwhile, in case2 opening width is fixed and opening depth is varied. Besides, for the two different form opening, the effect of plate slenderness parameter (${\beta}$), opening area ratio (AR) and opening position ratio (PR) on the ultimate strength of plate with opening under axial compression are presented. It has been found that the ultimate strength of plate ofcase1is much more sensitive to the plate slenderness parameter (${\beta}$) and opening area ratio (AR) than that of case2. However, for case1, opening position (PR) almost has no effect on the ultimate strength, whereas, regardingcase2, the influence of opening position (PR) depends on the plate slenderness parameter (${\beta}$). Based on nonlinear regression analysis, three design formulae are not only developed but also approved reasonably for the practical engineering design.

Free Vibration Analysis of Simply-supported Rectangular Plate with a Circular Cutout by Independent Coordinate Coupling Method (독립좌표연성법을 이용한 원형 구멍을 갖는 단순지지 직사각형 평판의 자유진동해석)

  • Kwak, Moon-K.;Han, Sang-Bo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.6 s.111
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    • pp.643-650
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    • 2006
  • This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have been many methods developed for the free vibration of the rectangular plate with a rectangular cutout, very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian coordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.