A circular elastic cylinder under its own weight

Tarn, Jiann-Quo; Tseng, W.-D.; Chang, Hsi-Hung

doi:10.1016/j.ijsolstr.2009.03.016

Cited by 27 publications

(21 citation statements)

References 12 publications

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“…Recently, we have applied it to exact analysis of the deformation and stress field in a finite circular elastic cylinder under its own weight [18]. Extension to problems in three dimensions will be reported in a future publication.…”

Section: Discussionmentioning

confidence: 99%

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Axisymmetric Deformation of a Transversely Isotropic Cylindrical Body: A Hamiltonian State-Space Approach

2009

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A state-space approach for exact analysis of axisymmetric deformation and stress distribution in a circular cylindrical body of transversely isotropic material is developed. By means of Hamiltonian variational formulation via Legendre's transformation, the basic equations in cylindrical coordinates are formulated into a state-space framework in which the unknown state vector comprises the displacements and associated stress components as the dual variables and the system matrix possesses the symplectic characteristics of a Hamiltonian system. Upon delineating the symplecticity of the formulation, a viable solution approach using eigenfunction expansion is developed. For illustration, an exact analysis of a finite thick-walled circular cylinder under internal and external pressures is presented, with emphasis on the end effects.

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Section: Discussionmentioning

confidence: 99%

“…Equations (17) and (18) reveal that if μ is an eigenvalue of the system, so is −μ. It follows that μ = 0 must be a repeated eigenvalue.…”

Section: Hamiltonian Characteristicsmentioning

confidence: 99%

Axisymmetric Deformation of a Transversely Isotropic Cylindrical Body: A Hamiltonian State-Space Approach

2009

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“…Hasheminejad and Rajabi (2008) performed an exact analysis for 3D scattering of a time-harmonic plane-progressive sound wave obliquely incident upon an arbitrarily thick bilaminated circular hollow cylinder of infinite extent. Tarn et al (2009) carried out an exact analysis of a deformation and stress field in a finite circular elastic cylinder under its own weight. Alibeigloo and Liew (2014) presented an exact 3D free vibration solution for sandwich cylindrical panels with an FGM core.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells

Liang

Kou

Liu

et al. 2015

J. Zhejiang Univ. Sci. A

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Abstract:A good understanding of the mechanical behavior of functionally graded material (FGM) cylindrical shells is necessary for designers and researchers. However, the 3D transient response of FGM cylindrical shells under various boundary conditions has not yet been analyzed. In this paper, the problem is addressed by proposing an approach integrating the state space method, differential quadrature method, and Durbin's numerical inversion method of Laplace transform. The laminate model is used to obtain the transient solution in the radial direction. At the edges, four kinds of boundary conditions are considered: Clamped-Clamped, Clamped-Simply supported, Clamped-Free, and Simply supported-Simply supported. The results of the proposed method and finite element (FE) method agree with each other excellently. Convergence studies show that the proposed method has a fast convergence rate. The natural frequencies obtained by the proposed method, experiment, and other theoretical methods are in close agreement with each other. The effects of the load frequency and duration, length/outer radius ratio, and the (outer radius−inner radius)/outer radius ratio on the transient response of FGM shells are investigated. Two laws of variation of material properties along the radial direction are considered: the first has material properties varying according to an exponential law along the radial direction, while the second has material properties varying according to a power law. The effect of a functionally graded index on the transient response of FGM shells is investigated in both cases. The results obtained in this paper can serve as benchmark data for further research.

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“…During the past two decades, the symplectic method has been introduced into various fields of engineering applications successfully. In elasticity, a great amount of symplectic techniques can be found in literature including the work on free vibration, thin plate bending, and circular cylindrical problems [9][10][11]. Moreover, the symplectic elasticity approach has been recently extended to problems with complex material properties and structures.…”

Section: Introductionmentioning

confidence: 99%

The Symplectic Method in Polar Coordinates for Linear Viscoelastic Materials

Zhang¹,

Bai²

2015

TOMSJ

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Abstract:In this study, the symplectic method is applied to a two-dimensional annular-sector viscoelastic domain under the polar coordinate system. By applying variable separation approach, all fundamental solutions are derived in analytical form. Furthermore, using the method of variable substitution, lateral conditions are transformed into finding a particular solution for the governing equations, and this particular solution is derived with the use of eigensolution expansion. In the numerical example, the boundary condition problem is discussed in detail to analyze the stress response of viscoelastic solids.

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A circular elastic cylinder under its own weight

Cited by 27 publications

References 12 publications

Axisymmetric Deformation of a Transversely Isotropic Cylindrical Body: A Hamiltonian State-Space Approach

Axisymmetric Deformation of a Transversely Isotropic Cylindrical Body: A Hamiltonian State-Space Approach

A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells

The Symplectic Method in Polar Coordinates for Linear Viscoelastic Materials

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