• Title/Summary/Keyword: Governing equation

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Micromechanical failure analysis of composite materials subjected to biaxial and off-axis loading

  • Ahmadi, Isa
    • Structural Engineering and Mechanics
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    • v.62 no.1
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    • pp.43-54
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    • 2017
  • In this study, the failure behavior of composite material in the biaxial and off-axis loading is studied based on a computational micromechanical model. The model is developed so that the combination of mechanical and thermal loading conditions can be considered in the analysis. The modified generalized plane strain assumption of the theory of elasticity is used for formulation of the micromechanical modeling of the problem. A truly meshless method is employed to solve the governing equation and predict the distribution of micro-stresses in the selected RVE of composite. The fiber matrix interface is assumed to be perfect until the interface failure occurs. The biaxial and off-axis loading of the SiC/Ti and Kevlar/Epoxy composite is studied. The failure envelopes of SiC/Ti and Kevlar/Epoxy composite in off-axis loading, biaxial transverse-transverse and axial-transverse loading are predicted based on the micromechanical approach. Various failure criteria are considered for fiber, matrix and fiber-matrix interface. Comparison of results with the available results in the litreture shows excellent agreement with experimental studies.

Closed-form solutions for non-uniform axially loaded Rayleigh cantilever beams

  • Sarkar, Korak;Ganguli, Ranjan;Elishakoff, Isaac
    • Structural Engineering and Mechanics
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    • v.60 no.3
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    • pp.455-470
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    • 2016
  • In this paper, we investigate the free vibration of axially loaded non-uniform Rayleigh cantilever beams. The Rayleigh beams account for the rotary inertia effect which is ignored in Euler-Bernoulli beam theory. Using an inverse problem approach we show, that for certain polynomial variations of the mass per unit length and the flexural stiffness, there exists a fundamental closed form solution to the fourth order governing differential equation for Rayleigh beams. The derived property variation can serve as test functions for numerical methods. For the rotating beam case, the results have been compared with those derived using the Euler-Bernoulli beam theory.

Large amplitude free vibration analysis of laminated composite spherical shells embedded with piezoelectric layers

  • Singh, Vijay K.;Panda, Subrata K.
    • Smart Structures and Systems
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    • v.16 no.5
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    • pp.853-872
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    • 2015
  • Numerical analysis of large amplitude free vibration behaviour of laminated composite spherical shell panel embedded with the piezoelectric layer is presented in this article. For the investigation purpose, a general nonlinear mathematical model has been developed using higher order shear deformation mid-plane kinematics and Green-Lagrange nonlinearity. In addition, all the nonlinear higher order terms are included in the present mathematical model to achieve any general case. The nonlinear governing equation of freely vibrated shell panel is obtained using Hamilton's principle and discretised using isoparametric finite element steps. The desired nonlinear solutions are computed numerically through a direct iterative method. The validity of present nonlinear model has been checked by comparing the responses to those available published literature. In order to examine the efficacy and applicability of the present developed model, few numerical examples are solved for different geometrical parameters (fibre orientation, thickness ratio, aspect ratio, curvature ratio, support conditions and amplitude ratio) with and/or without piezo embedded layers and discussed in details.

Analysis of flow through dam foundation by FEM and ANN models Case study: Shahid Abbaspour Dam

  • Shahrbanouzadeh, Mehrdad;Barani, Gholam Abbas;Shojaee, Saeed
    • Geomechanics and Engineering
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    • v.9 no.4
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    • pp.465-481
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    • 2015
  • Three-dimensional simulation of flow through dam foundation is performed using finite element (Seep3D model) and artificial neural network (ANN) models. The governing and discretized equation for seepage is obtained using the Galerkin method in heterogeneous and anisotropic porous media. The ANN is a feedforward four layer network employing the sigmoid function as an activator and the back-propagation algorithm for the network learning, using the water level elevations of the upstream and downstream of the dam, as input variables and the piezometric heads as the target outputs. The obtained results are compared with the piezometric data of Shahid Abbaspour's Dam. Both calculated data show a good agreement with available measurements that demonstrate the effectiveness and accuracy of purposed methods.

Response of orthotropic Kelvin modeling for single-walled carbon nanotubes: Frequency analysis

  • Hussain, Muzamal;Naeem, Muhammad N.;Tounsi, Abdelouahed
    • Advances in nano research
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    • v.8 no.3
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    • pp.229-244
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    • 2020
  • In this paper, modified Kelvin's model has been used to analyze the orthotropic vibration frequencies of single walled carbon nanotubes with clamped-clamped and clamped-free boundary conditions. For this system the governing equation is developed with wave propagation approach. Armchair, zigzag and chiral structures are considered for the vibrational analysis to investigate the effect of different modes, in-plane rigidity and mass density per unit lateral area. Throughout the computations, on decreasing the length-to-diameter ratios, the frequencies of said structure increases. In addition, by increasing three different value of in-plane rigidity resulting frequencies also increase and frequencies decrease on increasing mass density per unit lateral area. The results generated using computer software MATLAB to furnish the evidence regarding applicability of present model and also verified by available published literature.

Improved Momentum Exchange Theory for Incompressible Regenerative Turbomachines (I) - Hydraulic Model - (비압축성 재생형 기계에 대한 개선된 운동량 교환 이론 (I) - 수력학적 모델 -)

  • Park Mu Ryong;Chung Myung Kyoon;Yoo Il Su
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.28 no.10
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    • pp.1238-1246
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    • 2004
  • Momentum exchange theory has been generally used for an analysis of the regenerative turbomachines due to its direct description of the complicate circulatory flow. However, because its application is limited only to linear region and its model equations are incomplete on three variables, it needs further refinements. In the present study it is improved by introducing a central pivot of circulatory flow. Also, by assuming linear circulatory velocity distribution, mean radii of inlet and outlet flows through the impeller are newly suggested. By applying control volume analysis to both linear region and the acceleration region, the governing equation on the circulatory velocity is derived. As a result, systematic performance analysis on the entire region of the incompressible regenerative turbomachines can be carried out based on the proposed model equations.

Effect of viscous damping force subjected to a rotating flexible disk (점성감쇠력이 회전탄성원판에 미치는 영향)

  • Kong, Dae-Wee;Joo, Won-Gu
    • Proceedings of the KSME Conference
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    • 2001.06e
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    • pp.185-190
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    • 2001
  • Rotating disks are used in various machines such as floppy disks, hard disk, turbines and circular sawblades. The problems of vibrations of rotating disks are important in improving these machines. Many investigators have dealt with these problem. Specially, vibrations of a rotating flexible disk taking into account the effect of air is difficult problem in simulation. The governing equation of a rotating flexible disk coupled to the surrounding fluid is investigated by a simple mathematical model. And several important parameters concerned with the stability of a rotating flexible disk are defined. Coupling strength between air and rotating flexible disk is proportional to square of disk radius directly and square root of the all of bending rigidity, disk density and thickness inversely. Lift-to-damping coefficient has relation to the onset of disk flutter.

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Flow analysis and design optimization of a mixed-flow fan (사류송풍기의 유동해석 및 최적설계)

  • Seo, Seoung-Jin;Jun, Jae-Wook;Kim, Kwang-Yong
    • Proceedings of the KSME Conference
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    • 2001.06e
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    • pp.684-689
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    • 2001
  • In this study, three-dimensional viscous flow analysis and optimization are presented for the design of a mixed-flow fan. Steady, imcompressible, three-dimensional Reynolds averaged Navier-Stokes equations are used as governing equations, and standard $k-{\varepsilon}$ turbulence model is chosen as a turbulence model. Governimg equations are discretized using finite volume method. Upwind difference scheme is used for the discretization of the convective term and SIMPLEC algorithm is used as a velocity-pressure correction procedure. The computational results are compared with the results obtained by TASCflow. For the numerical optimization of the design, objective function is defined as a ratio of generation of the turbulent energy to pressure head. Sweep angles are used as design variables.

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Aha, CST and CFD !

  • Kim, S.J.;Kim, M.K.;Moon, J.K.
    • 한국전산유체공학회:학술대회논문집
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    • 2009.04a
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    • pp.9-18
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    • 2009
  • This paper presents the state of the art of computational structures technology(CST) and comparison of two computational mechanics - CST and CFD, to the CFD engineers. Classical mechanics is based on the five classical axioms which describe the motion and behaviors of the continuum materials like solid structures and fluids. Computational structures technology uses the finite element method to solve the governing equation, whereas finite volume method is generally used in CFD. A few famous commercial structural analysis programs and DIAMOND/IPSAP will be introduced. DIAMOND/IPSAP is the efficient parallel structural analysis package developed by our research team. DIAMOND/IPSAP shows the better performance than the commercial structural analysis software not only in the parallel computing environments but also in a single computer.

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Position Control of ER Valve-Cylinder System Via Neural Control Technique (신경 제어 기법을 이용한 ER 밸브-실린더 시스템의 위치 제어)

  • 정재민;최승복;정재천
    • Transactions of the Korean Society of Automotive Engineers
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    • v.4 no.6
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    • pp.52-64
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    • 1996
  • This paper presents an active position control of a single-rod cylinder system featuring an electrorheological(ER) fluid-based valve. The ER fluid consisting of silicone oil and chemically treated particles is firstly composed and its Bingham property is tested as a function of imposed electric field. A multi-channel plate type of ER valve is then designed and manufactured on the basis of the field-dependent Bingham model. Performance test of the ER valve is undertaken by evaluating pressure drop with respect to the number of electrode as well as the intensity of the electric field. Subsequently, the ER valve-cylinder system is constructed and its governing equation of motion is derived. A neural control scheme for position control of the cylinder is formulated by incorporating proportional-plus-derivative(PD) controller and implemented. Experimental results of both regulating and tracking control responses are presented in order to demonstrate the efficacy of the proposed ER valve-cylinder control system.

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