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Dhanjoo N Ghista - One of the best experts on this subject based on the ideXlab platform.

  • applications of point interpolation method for spatial general Shells Structures
    Computer Methods in Applied Mechanics and Engineering, 2007
    Co-Authors: L Liu, L P Chua, Dhanjoo N Ghista
    Abstract:

    The meshfree point interpolation method (PIM) based on polynomial function is presented for the static analysis of spatial general shell Structures. The formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible Shells based on the Cosserat surface. The PIM technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property. Hence, the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method. An improved matrix triangularization algorithm (MTA) is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis. It is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non-conforming PIM (NPIM) when the energy principles are used to formulate PIM. To obtain compatible shape functions, the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell-based nodal selection is utilized, which lead to conforming PIM (CPIM). Both NPIM and CPIM are evaluated in the paper. Several benchmark problems for Shells are analyzed to demonstrate the validity and efficiency of the NPIM and CPIM. The phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy. The convergences and performances are investigated for both conforming and non-conforming PIMs. It is also shown that the NPIM and CPIM with the improved MTA are very easy to implement and very efficient in constructing shape functions in comparison with the Element-Free Galerkin method.

Laurent Dumas - One of the best experts on this subject based on the ideXlab platform.

Calogero Orlando - One of the best experts on this subject based on the ideXlab platform.

  • sound transmission analysis of viscoelastic composite multilayered Shells Structures
    Aerospace, 2019
    Co-Authors: Stefano Valvano, A Alaimo, Calogero Orlando
    Abstract:

    In the development of aircraft comfort, one of the main issues is the sound transmission analysis to estimate the insulation capability of aeronautical panels. In this work, a higher-order shell finite element is proposed for the passive noise insulation analysis of composite laminated Structures embedding viscoelastic layers. Starting from the Principle of Virtual Displacements, the present Finite Elements are obtained by making use of higher-order Layer-Wise theories, employing the Mixed Interpolated Tensorial Components (MITC) method to avoid the shear locking effect and taking into account the frequency dependence of the viscoelastic material through the use of a fractional derivative model. The Rayleigh integral method is considered for the evaluation of the acoustic insulation of the panels. Numerical studies are carried out to demonstrate that the present shell finite element is an efficient and accurate tool for the sound transmission analysis. Different lamination sequences, different boundary conditions and various radius to thickness ratios are taken into account.

L Liu - One of the best experts on this subject based on the ideXlab platform.

  • applications of point interpolation method for spatial general Shells Structures
    Computer Methods in Applied Mechanics and Engineering, 2007
    Co-Authors: L Liu, L P Chua, Dhanjoo N Ghista
    Abstract:

    The meshfree point interpolation method (PIM) based on polynomial function is presented for the static analysis of spatial general shell Structures. The formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible Shells based on the Cosserat surface. The PIM technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property. Hence, the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method. An improved matrix triangularization algorithm (MTA) is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis. It is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non-conforming PIM (NPIM) when the energy principles are used to formulate PIM. To obtain compatible shape functions, the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell-based nodal selection is utilized, which lead to conforming PIM (CPIM). Both NPIM and CPIM are evaluated in the paper. Several benchmark problems for Shells are analyzed to demonstrate the validity and efficiency of the NPIM and CPIM. The phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy. The convergences and performances are investigated for both conforming and non-conforming PIMs. It is also shown that the NPIM and CPIM with the improved MTA are very easy to implement and very efficient in constructing shape functions in comparison with the Element-Free Galerkin method.

L P Chua - One of the best experts on this subject based on the ideXlab platform.

  • applications of point interpolation method for spatial general Shells Structures
    Computer Methods in Applied Mechanics and Engineering, 2007
    Co-Authors: L Liu, L P Chua, Dhanjoo N Ghista
    Abstract:

    The meshfree point interpolation method (PIM) based on polynomial function is presented for the static analysis of spatial general shell Structures. The formulation of the discrete system equations is derived from stress resultant geometrically exact shell theory of shear flexible Shells based on the Cosserat surface. The PIM technique constructs its interpolation functions through a set of arbitrarily distributed points in the problem domain and its shape function has the delta function property. Hence, the implementation of essential boundary conditions can be imposed with ease as in conventional finite element method. An improved matrix triangularization algorithm (MTA) is proposed to obtain proper node enclosure and basis selection in order to overcome the singularity problem in the point interpolation method using a polynomial basis. It is found that the shape functions are generally not compatible to ensure the compatibility of the solution and lead to non-conforming PIM (NPIM) when the energy principles are used to formulate PIM. To obtain compatible shape functions, the enforcement of compatibility is needed along the common edges of the background cells in the problem domain and a background cell-based nodal selection is utilized, which lead to conforming PIM (CPIM). Both NPIM and CPIM are evaluated in the paper. Several benchmark problems for Shells are analyzed to demonstrate the validity and efficiency of the NPIM and CPIM. The phenomena of shear locking and membrane locking are illustrated by showing the membrane and shear energies as fractions of the total energy. The convergences and performances are investigated for both conforming and non-conforming PIMs. It is also shown that the NPIM and CPIM with the improved MTA are very easy to implement and very efficient in constructing shape functions in comparison with the Element-Free Galerkin method.