• 제목/요약/키워드: plate equation

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NURBS-based isogeometric analysis for thin plate problems

  • Shojaee, S.;Valizadeh, N.
    • Structural Engineering and Mechanics
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    • 제41권5호
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    • pp.617-632
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    • 2012
  • An isogeometric approach is presented for static analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection, as for description of the geometry. The governing equation based on Kirchhoff plate theory, is discretized using the standard Galerkin method. The essential boundary conditions are enforced by the Lagrange multiplier method. Several typical examples of thin plate and thin plate on elastic foundation are solved and compared with the theoretical solutions and other numerical methods. The numerical results show the robustness and efficiency of the proposed approach.

Nonlinear seismic performance of code designed perforated steel plate shear walls

  • Barua, Kallol;Bhowmick, Anjan K.
    • Steel and Composite Structures
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    • 제31권1호
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    • pp.85-98
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    • 2019
  • Nonlinear seismic performances of code designed Perforated Steel Plate Shear Walls (P-SPSW) were studied. Three multi-storey (4-, 8-, and 12-storey) P-SPSWs were designed according to Canadian seismic provisions and their performance was evaluated using time history analysis for ground motions compatible with Vancouver response spectrum. The selected code designed P-SPSWs exhibited excellent seismic performance with high ductility and strength. The current code equation was found to provide a good estimation of the shear strength of the perforated infill plate, especially when the infill plate is yielded. The applicability of the strip model, originally proposed for solid infill plate, was also evaluated for P-SPSW and two different strip models were studied. It was observed that the strip model with strip widths equal to center to center diagonal distance between each perforation line could reasonably predict the inelastic behavior of unstiffened P-SPSWs. The strip model slightly underestimated the initial stiffness; however, the ultimate strength was predicted well. Furthermore, applicability of simple shear-flexure beam model for determination of fundamental periods of P-SPSWs was studied.

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

  • 김종택;서재형;정병완
    • 한국정밀공학회지
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    • 제12권3호
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    • pp.73-81
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    • 1995
  • To find a way for establishing work roll initial crown according to roll conditions, computer simutation for predicting plate crown in plate mill is done and effects of roll conditions on plate crown is analyzed. Toll gap rorfile and plate crown are measured to be compared to the calculated values. As a result, regression equation to establish work roll initial crown according to roll conditions such as backup roll diameter, backup roll crown and work roll diameter is obtained.

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Nonlinear vibration analysis of composite laminated trapezoidal plates

  • Jiang, Guoqing;Li, Fengming;Li, Xinwu
    • Steel and Composite Structures
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    • 제21권2호
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    • pp.395-409
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    • 2016
  • Nonlinear vibration characteristics of composite laminated trapezoidal plates are studied. The geometric nonlinearity of the plate based on the von Karman's large deformation theory is considered, and the finite element method (FEM) is proposed for the present nonlinear modeling. Hamilton's principle is used to establish the equation of motion of every element, and through assembling entire elements of the trapezoidal plate, the equation of motion of the composite laminated trapezoidal plate is established. The nonlinear static property and nonlinear vibration frequency ratios of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results published in the open literatures. Moreover, the effects of the ply angle and the length-high ratio on the nonlinear vibration frequency ratios of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are analyzed for the different ply angles and harmonic excitation forces.

필릿 용접 공정에서 온도 분포 예측을 위한 해석적 모델 (Analytical Solution for Transient Temperature Distribution in Fillet Arc Welding)

  • 정선국;조형석
    • Journal of Welding and Joining
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    • 제13권2호
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    • pp.68-81
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    • 1995
  • This paper presents an analytical solution to predict the transient temperature distribution in fillet arc welding. The analytical solution is obtained by solving a transient three -dimensional heat conduction equation with convection boundary conditions on the surfaces of an infinite plate with finite thicknesses, and mapping an infinite plate onto the fillet weld geometry with energy equation. The electric arc heat input on fillet weld and on infinite plate is assumed to have a traveling bivariate Gaussian distribution. To check the validity of the solution, GTA and FCA welding experiments were performed under various welding conditions. The actual isotherms of the weldment cross - sections at various distances from the arc start point are compared with those of simulation result. As the result shows a satisfactory accuracy, this analytical solution can be used to predict the transient temperature distribution in the fiIIet weld of finite thickness under a moving bivariate Gaussian distributed heat source. The simplicity and short calculation time of the analytical solution provides rationales to use the analytical solution for modeling the welding control systems or for an optimization tool of welding process parameters.

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Z-Quality 강재 적용에 대한 고찰 (A Study on the application for Z-Quality steel)

  • 박성준;하윤석
    • 대한조선학회 특별논문집
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    • 대한조선학회 2017년도 특별논문집
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    • pp.8-13
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    • 2017
  • The rolled carbon steel plate has anisotropic property in Z-direction(thickness direction). This is induced by cooling rate difference of Z-direction and sulfur which make non-metallic inclusion(MnS) at center line of thickness direction. Z-directional mechanical properties of normal steel plate are not generally specified and it is defined for Z-Quality steel only through tensile test in Z-direction. If Z-quality steel is not applied for cruciform joint, the lamella tearing will be occurred by tensile stress after welding & during operation of the structure. In this research, one equation estimating Z-directional(orthogonal to plate) stress was developed to prevent lamella tearing by welding. This equation deals with plate thickness & joint configuration(eccentricity, angle and curvature). Analyses were done by strain boundary method using sectional FE modeling and FE 3D models are also used for some cases. Designers can predict the possibility of lamella tearing by adequately applying the result and can appropriately minimize the application of Z-quality steel by revising welding design to some extent.

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빙해수조 모형빙판의 유효탄성계수 산출 (The Effective Young's Modulus of Model Ice Sheet in Ice Basin)

  • 이재환;최봉균;김태완;이춘주
    • 대한조선학회논문집
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    • 제52권4호
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    • pp.315-322
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    • 2015
  • In this paper, the theory of rectangular plate on the elastic foundation is used to get the relation equation between the effective Young’s modulus and the ice sheet deflection by applying the characteristic length concept, since the model ice sheet is rectangular shape in KRISO (Korea Research Institute for Ships and Ocean Engineering) ice basin. The obtained relation equation is equal to that of using the circular plate theory. A device is made and used to measure the deflection of ice plate using LVDT (Linear Variable Differential Transformer) for several loading cases and the procedure of experiments measuring the deflection used for getting the Young’s modulus is explained. In addition, the flexural strength value obtained through flexural strength experiments is compared with that of finite element analysis using the obtained effective Young’s modulus. Also, a nonlinear FEA (Finite Element Analysis) of cantilever ice beam is done with eroding effect and LS-DYNA result shows the fracture of brittle ice under 1 mm/s velocity load.

시스템식별과 최적제어를 이용한 지능형 복합적층판의 다중보드 진동제어 (Multi-modal Vibration Control of Intelligent Laminated Composite Plates Using System Identification and Optimal Control)

  • 김정수;강영규;박현철
    • 한국소음진동공학회논문집
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    • 제12권1호
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    • pp.5-11
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    • 2002
  • Active vibration control of intelligent laminated composite plates is performed experimental1y Laminated composite place is modeled by the system identification method. For the system identification process, the laminated composite place is excited by two piezoelectric actuators with PRBS signals. At the same time, the displacement of the laminated composite plate is measured by a gap sensor. From these excited PRBS signals and the measured displacement sequence, system parameters of the laminated composite plate are estimated using a recursive prediction error method. Model of the laminated composite plate with two piezoeletric actuators is assumed to be the form of ARMAX. From the estimated ARHMAX model, a state space equation of the observable canonical form is obtained. With this state space equation, a controller and an observer for active vibration control is designed using the optimal control method. Controller and observer are implemented on a digital system. Experiments on the vibration control are Performed with changing the outer layer fiber orientation of intelligent composite plates.

등방성 및 복합재 플레이트용 16절점 요소의 강성행렬 계산 (Evaluation of Stiffness Matrix of 3-Dimensional Elements for Isotropic and Composite Plates)

  • 윤태혁;김정운;이재복
    • 대한기계학회논문집
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    • 제18권10호
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    • pp.2640-2652
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    • 1994
  • The stiffness of 6-node isotropic element is stiffer than that of 8-node isotropic element of same configuration. This phenomenon was called 'Relative Stiffness Stiffening Phenomenon'. In this paper, an equation of sampling point modification which correct this phenomenon was derived for the composite plate, as well as an equation for an isotropic plate. The relative stiffness stiffening phenomena of an isotropic plate element could be corrected by modifying Gauss sampling points in the numerical integration of stiffness matrix. This technique could also be successfully applied to the static analyses of composite plate modeled by the 3-dimensional 16-node elements. We predicted theoretical errors of stiffness versus the number of layers that result from the reduction of numerical integration order. These errors coincide very well with the actual errors of stiffness. Therefore, we can choose full integration of reduced integration based upon the permissible error criterion and the number of layers by using the thoretically predicted error.

Attenuation of quasi-Lamb waves in a hydroelastic system "elastic plate+compressible viscous fluid+rigid wall"

  • Akbarov, Surkay D.;Negin, Mesut
    • Structural Engineering and Mechanics
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    • 제81권4호
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    • pp.443-459
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    • 2022
  • The paper studies the dispersion and attenuation of propagating waves in the "plate+compressible viscous fluid layer" system in the case where the fluid layer flow is restricted with a rigid wall, and in the case where the fluid layer has a free face. The motion of the plate is described by the exact equations of elastodynamics and the flow of the fluid by the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluids. Analytical expressions are obtained for the amplitudes of the sought values, and the dispersion equation is derived using the corresponding boundary and compatibility conditions. To find the complex roots of the dispersion equation, an algorithm based on equating the modulus of the dispersion determinant to zero is developed. Numerical results on the dispersion and attenuation curves for various pairs of plate and fluid materials under different fluid layer face conditions are presented and discussed. Corresponding conclusions on the influence of the problem parameters on the dispersion and attenuation curves are made and, in particular, it is established that the change of the free face boundary condition with the impermeability condition can influence the dispersion and attenuation curves not only in the quantitative, but also in the qualitative sense.