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S Pradyumna - One of the best experts on this subject based on the ideXlab platform.

  • a Finite Element Formulation for thermally induced vibrations of functionally graded material sandwich plates and shell panels
    Composite Structures, 2017
    Co-Authors: Shashank Pandey, S Pradyumna
    Abstract:

    Abstract A Finite Element Formulation based on a higher-order layerwise theory is presented for the first time to investigate thermally induced vibrations of functionally graded material (FGM) sandwich plates and shell panels. The properties of FGM sandwich are assumed to be position and temperature dependent. The upper and lower layers of the sandwich panel are considered to be made of pure ceramic and metal, respectively and the elastic properties of FGM core are varied according to a power-law function. The top surface is exposed to a thermal shock and the bottom surface of the panel is either kept at a reference temperature or thermally insulated. The one-dimensional transient heat conduction equation is solved using a central difference scheme in conjunction with the Crank-Nicolson method. A higher-order layerwise theory is used for FGM sandwich panels, in which a higher-order displacement field for the FGM core and a first-order displacement field for the facesheets are assumed. The governing equations are solved using Newmark average acceleration method. It is shown that the proposed layerwise Finite Element Formulation is simple and can easily be applied to investigate FGM sandwich plates and shell panels subjected to rapid heating.

  • a new c0 higher order layerwise Finite Element Formulation for the analysis of laminated and sandwich plates
    Composite Structures, 2015
    Co-Authors: Shashank Pandey, S Pradyumna
    Abstract:

    Abstract In this paper, a new layerwise plate Formulation based on a C 0 higher-order Finite Element model is presented for static and free vibration analyses of laminated composite and sandwich plates. The proposed layerwise theory which is developed for a three layered composite plates, assumes higher-order displacement field for middle layer and first-order displacement field for top and bottom layers. Compatibility conditions are imposed at the layer interface to satisfy the interlaminar displacement continuity. An eight-noded isoparametric Element is used to model the plate. The accuracy of the proposed Formulation is assessed for linear static and free vibration analyses by comparing the authors’ results with available 3D elasticity, Finite Element and analytical solutions. It has been shown here that the present Finite Element Formulation is much simpler, straightforward and accurate for static and free vibration analyses of laminated composite and sandwich plates.

  • free vibration analysis of functionally graded curved panels using a higher order Finite Element Formulation
    Journal of Sound and Vibration, 2008
    Co-Authors: S Pradyumna, J N Bandyopadhyay
    Abstract:

    Free vibration analysis of functionally graded curved panels is carried out using a higher-order Formulation. A C0 Finite Element Formulation is used to carry out the analysis. The Element consists of nine degrees of freedom per node with higher-order terms in the Taylor's-series expansion, which represents the higher-order transverse cross-sectional deformation modes. The Formulation includes Sanders’ approximation for doubly curved shells considering the effects of rotary inertia and transverse shear. A realistic parabolic distribution of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided. Material properties are assumed to be temperature independent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Heat conduction between ceramic and metal constituents is neglected. The accuracy of the Formulation is validated by comparing the results with those available in the literature. Effects of panel geometry parameters and boundary conditions are studied.

  • free vibration analysis of functionally graded curved panels using a higher order Finite Element Formulation
    Journal of Sound and Vibration, 2008
    Co-Authors: S Pradyumna, J N Bandyopadhyay
    Abstract:

    Free vibration analysis of functionally graded curved panels is carried out using a higher-order Formulation. A C0 Finite Element Formulation is used to carry out the analysis. The Element consists of nine degrees of freedom per node with higher-order terms in the Taylor's-series expansion, which represents the higher-order transverse cross-sectional deformation modes. The Formulation includes Sanders’ approximation for doubly curved shells considering the effects of rotary inertia and transverse shear. A realistic parabolic distribution of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided. Material properties are assumed to be temperature independent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Heat conduction between ceramic and metal constituents is neglected. The accuracy of the Formulation is validated by comparing the results with those available in the literature. Effects of panel geometry parameters and boundary conditions are studied.

Gregory M Hulbert - One of the best experts on this subject based on the ideXlab platform.

  • piecewise shear deformation theory and Finite Element Formulation for vibration analysis of laminated composite and sandwich plates in thermal environments
    Composite Structures, 2017
    Co-Authors: Rui Zhao, Gregory M Hulbert
    Abstract:

    Abstract In this paper, a piecewise shear deformation theory for laminated composite and sandwich plates is presented by integrating the advantages of the layerwise theory and equivalent single layer theory. A C0 continuous four-noded quadrilateral isoparametric plate Element based on this theory is developed for free and forced vibration analysis of laminated composite and sandwich plates in thermal environments. The accuracy and effectiveness of piecewise shear deformation theory and Finite Element Formulation are validated by comparing the numerical results obtained by the present Finite Element Formulation with the analytical and exact results available in literatures as well as the numerical results computed by MSC.Nastran software. It is demonstrated that the piecewise shear deformation theory and Finite Element Formulation are suitable for the vibration analysis of thin and thick laminated composite and sandwich plates. As compared with the layerwise theory, high-order zigzag theory and high-order equivalent single layer theory, the piecewise shear deformation theory is able to produce a sufficiently accurate result at a very low computational cost. The work reported in this paper provides an efficient modeling approach for thermal vibration analysis of laminated composite and sandwich plates in practical engineering.

Hansjorg Diersch - One of the best experts on this subject based on the ideXlab platform.

  • a Finite Element Formulation of the outlet gradient boundary condition for convective diffusive transport problems
    arXiv: Fluid Dynamics, 2011
    Co-Authors: Fabien Cornaton, Pierre Perrochet, Hansjorg Diersch
    Abstract:

    A simple Finite Element Formulation of the outlet gradient boundary condition is presented in the general context of convective-diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent variable gradient along open boundaries. Boundary normal unit vectors and gradient operators are evaluated using covariant bases and metric tensors, which allow handling Finite Elements of mixed dimensions. Even though the presented method has implications for many fields where diffusion processes are involved, discussion and illustrative examples address more particularly the framework of contaminant transport in porous media, in which the outlet gradient concentration is classically, but wrongly assumed to be zero.

  • a Finite Element Formulation of the outlet gradient boundary condition for convective diffusive transport problems
    International Journal for Numerical Methods in Engineering, 2004
    Co-Authors: Fabien Cornaton, Pierre Perrochet, Hansjorg Diersch
    Abstract:

    A simple Finite Element Formulation of the outlet gradient boundary condition is presented in the general context of convective–diffusive transport processes. Basically, the method is based on an upstream evaluation of the dependent variable gradient along open boundaries. Boundary normal unit vectors and gradient operators are evaluated using covariant bases and metric tensors, which allow handling Finite Elements of mixed dimensions. Even though the presented method has implications for many fields where diffusion processes are involved, discussion and illustrative examples address more particularly the framework of contaminant transport in porous media, in which the outlet gradient concentration is classically, but wrongly assumed to be zero. Copyright © 2004 John Wiley & Sons, Ltd.

Venkateswara G Rao - One of the best experts on this subject based on the ideXlab platform.

  • large deflection analysis of buckled compound cantilever columns under axial compressive uniformly distributed load weighted residual Finite Element Formulation
    Social Science Research Network, 2016
    Co-Authors: Durga K Rao, T V Karthikeyan, Manzoor M Hussain, Venkateswara G Rao
    Abstract:

    The large deflections of compound cantilever columns subjected to a uniformly distributed axial compressive load are investigated by using a weighted residual Finite Element Formulation, the simplest one being the Galerkin Finite Element Formulation. The compound column consists of two segments of different materials having different lengths, where the Young’s modulii of these materials are E1and E2 at the fixed and free end segments. The basic advantages of using the compound cantilever column and its production techniques (welding) are discussed. The solution of the problem in the Cartesian coordinate system is more complex and hence the ƒaƒzƒn S coordinate system is used to obtain a simpler second order nonlinear differential equation for the problem considered. The Galerkin Finite Element Formulation is used to obtain solution to the problem, and the difficulty involved in the assembly of the Element matrices, where the two segments with different materials are joined, is presented. The numerical results for uniform compound cantilever columns when compared with the existing solutions, where ever possible, match very well. The same for the compound cantilever columns are acceptable, as these do not violate any physical principles and logical reasoning.

  • large amplitude free vibration analysis of timoshenko beams using a relatively simple Finite Element Formulation
    International Journal of Mechanical Sciences, 2010
    Co-Authors: Jagadish Babu Gunda, R K Gupta, Ranga G Janardhan, Venkateswara G Rao
    Abstract:

    Free vibration analysis of uniform isotropic Timoshenko beams with geometric nonlinearity is investigated through a relatively simple Finite Element Formulation, applicable to homogenous cubic nonlinear temporal equation (homogenous Duffing equation). Geometric nonlinearity is considered using von-Karman strain displacement relations. The Finite Element Formulation begins with the assumption of the simple harmonic motion and is subsequently corrected using the harmonic balance method. Empirical formulas for the non-linear to linear radian frequency ratios, for the boundary conditions considered, are presented using the least square fit from the solutions of the same obtained for various central amplitude ratios. Numerical results using the empirical formulas compare very well with the results available from the literature for the classical boundary conditions such as the hinged-hinged, clamped-clamped and clamped-hinged beams. Numerical results for the beams with non-classical boundary conditions such as the hinged-guided and clamped-guided, hitherto not studied, are also presented.

Shashank Pandey - One of the best experts on this subject based on the ideXlab platform.

  • a Finite Element Formulation for thermally induced vibrations of functionally graded material sandwich plates and shell panels
    Composite Structures, 2017
    Co-Authors: Shashank Pandey, S Pradyumna
    Abstract:

    Abstract A Finite Element Formulation based on a higher-order layerwise theory is presented for the first time to investigate thermally induced vibrations of functionally graded material (FGM) sandwich plates and shell panels. The properties of FGM sandwich are assumed to be position and temperature dependent. The upper and lower layers of the sandwich panel are considered to be made of pure ceramic and metal, respectively and the elastic properties of FGM core are varied according to a power-law function. The top surface is exposed to a thermal shock and the bottom surface of the panel is either kept at a reference temperature or thermally insulated. The one-dimensional transient heat conduction equation is solved using a central difference scheme in conjunction with the Crank-Nicolson method. A higher-order layerwise theory is used for FGM sandwich panels, in which a higher-order displacement field for the FGM core and a first-order displacement field for the facesheets are assumed. The governing equations are solved using Newmark average acceleration method. It is shown that the proposed layerwise Finite Element Formulation is simple and can easily be applied to investigate FGM sandwich plates and shell panels subjected to rapid heating.

  • a new c0 higher order layerwise Finite Element Formulation for the analysis of laminated and sandwich plates
    Composite Structures, 2015
    Co-Authors: Shashank Pandey, S Pradyumna
    Abstract:

    Abstract In this paper, a new layerwise plate Formulation based on a C 0 higher-order Finite Element model is presented for static and free vibration analyses of laminated composite and sandwich plates. The proposed layerwise theory which is developed for a three layered composite plates, assumes higher-order displacement field for middle layer and first-order displacement field for top and bottom layers. Compatibility conditions are imposed at the layer interface to satisfy the interlaminar displacement continuity. An eight-noded isoparametric Element is used to model the plate. The accuracy of the proposed Formulation is assessed for linear static and free vibration analyses by comparing the authors’ results with available 3D elasticity, Finite Element and analytical solutions. It has been shown here that the present Finite Element Formulation is much simpler, straightforward and accurate for static and free vibration analyses of laminated composite and sandwich plates.