Nonlinear analysis of doubly curved symmetrically laminated shallow shells with rectangular planform

Chia, C. Y.

doi:10.1007/bf00535935

Cited by 36 publications

(11 citation statements)

References 22 publications

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“…This panel was previously studied by Leissa and Kadi [2] and Chia [3]. Young's modulus E = 206 x 10^ Pa, mass density p = 7800 kg/m^ and Poisson ratio v = 0.3.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Leissa and Kadi [2] studied linear and nonlinear free vibrations of shallow shell panels, simply supported at the four edges without in-plane restraints. Chia [3] investigated doubly-curved panels with rectangular base by using Donnell's nonlinear shallow-shell theory and a single-mode expansion in all the numerical calculations, for both vibration shape and initial imperfection. A single mode expansion of the transverse displacement was used.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear vibrations of circular cylindrical panels

Amabili¹,

Pellegrini²

2003

Computational Fluid and Solid Mechanics 2003

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Large-amplitude (geometrically nonlinear) vibrations of circular cylindrical panels subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated. Two different nonlinear, thin shell theories, namely Donnell's and Novozhilov's theories, are used to calculate the elastic strain energy. The formulation is also valid for orthotropic and symmetric cross-ply laminated composite shells; geometric imperfections are taken into account. Comparison of calculations to numerical results available in the literature is also performed. The nonlinear equations of motion are studied by using a code based on arclength continuation method that allows bifurcation analysis.

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“…This panel was previously studied by Leissa and Kadi [2] and Chia [3]. Young's modulus E = 206 x 10^ Pa, mass density p = 7800 kg/m^ and Poisson ratio v = 0.3.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear vibrations of circular cylindrical panels

Amabili¹,

Pellegrini²

2003

Computational Fluid and Solid Mechanics 2003

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“…Chia [8] investigated doubly curved panels with rectangular base by using Donnell's non-linear shallow-shell theory and a single-mode expansion in all the numerical calculations, for both vibration shape and initial imperfection. Only the backbone curves, relative to free vibrations, were obtained.…”

Section: Introductionmentioning

confidence: 99%

Non-linear vibrations of doubly curved shallow shells

Amabili

2005

International Journal of Non-Linear Mechanics

117

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“…It is now necessary to transform all the non-linear stiffness matrices in Equations (11) and (12) (17) […”

Section: Equations In Modal Co-ordinatesmentioning

confidence: 99%

Non-linear random response of laminated composite shallow shells using finite element modal method

Guo

Lee

Mei

2006

Int. J. Numer. Meth. Engng

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SUMMARYThis paper investigates the large-amplitude multi-mode random response of thin shallow shells with rectangular planform at elevated temperatures using a finite element non-linear modal formulation. A thin laminated composite shallow shell element and the system equations of motion are developed. The system equations in structural node degrees-of-freedom (DOF) are transformed into modal coordinates, and the non-linear stiffness matrices are transformed into non-linear modal stiffness matrices. The number of modal equations is much smaller than the number of equations in structural node DOF. A numerical integration is employed to determine the random response. Thermal buckling deflections are obtained to explain the intermittent snap-through phenomenon. The natural frequencies of the infinitesimal vibration about the thermally buckled equilibrium positions (BEPs) are studied, and it is found that there is great difference between the frequencies about the primary (positive) and the secondary (negative) BEPs. All three types of motion: (i) linear random vibration about the primary BEP, (ii) intermittent snap-through between the two BEPs, and (iii) non-linear large-amplitude random vibration over the two BEPs, can be predicted.

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Nonlinear analysis of doubly curved symmetrically laminated shallow shells with rectangular planform

Cited by 36 publications

References 22 publications

Nonlinear vibrations of circular cylindrical panels

Nonlinear vibrations of circular cylindrical panels

Non-linear vibrations of doubly curved shallow shells

Non-linear random response of laminated composite shallow shells using finite element modal method

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