Torsion of an isotropic shaft of arbitrary cross-section embedded with multicoated or graded circular cylinders of cylindrically orthotropic materials

A method has been presented recently by Venkat and Spaulding to solve the nonlinear boundary-value problem of oscillating two-dimensional cylinders of arbitrary cross section on the free surface of a fluid. The method relies on a second-order finite-difference technique with a modified Euler method for the time domain and a successive over-relaxation procedure for the spatial domain. The authors compare their numerical results with those of other authors (theoretical and experimental), as they have published data for specialized forms like a wedge, circular cylinders, and ship-like sections in forced heave motion (references [4] to [7] and [22], [23] of the paper).

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Deformation Equations for Non-Circular Cylinders

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100073909 ◽

1960 ◽

Vol 64 (600) ◽

pp. 765-766 ◽

Cited By ~ 1

Author(s):

D. S. Houghton ◽

D. J. Johns

Keyword(s):

Cylindrical Shell ◽

Cross Section ◽

Explicit Solution ◽

Lateral Pressure ◽

Arbitrary Cross Section ◽

Circular Cylinders ◽

Pressure Loading ◽

Elastic Shells ◽

Linear Problems ◽

Arbitrary Curvature

As far as is known, no explicit solution exists in the literature for the displacement equations in u, v and w, for a uniform cylinder of arbitrary cross section subjected to a lateral pressure loading. However, the advent of Ref. 1 now makes available an admirable treatise devoted entirely to the analysis of thin elastic shells. The equations developed in this reference apply only to linear problems, i.e. the displacements are assumed to be small in comparison with the thickness of the shell, but they are general enough to include all shells of arbitrary curvature. Unfortunately the generality of these equations inhibits their immediate use to cylindrical shell problems, and it is the purpose of this note to present the essential features of the theory for non-circular cylinders.

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A Correlation Theory for Steady Natural Convective Heat Transport in Horizontal Annuli

Journal of Heat Transfer ◽

10.1115/1.3245533 ◽

1983 ◽

Vol 105 (1) ◽

pp. 144-150 ◽

Cited By ~ 8

Author(s):

R. D. Boyd

Keyword(s):

Rayleigh Number ◽

Aspect Ratio ◽

Heat Transport ◽

Cross Section ◽

Convective Heat ◽

Arbitrary Cross Section ◽

Circular Cylinders ◽

Curvature Effects ◽

Correlation Theory ◽

Horizontal Annuli

A correlation theory for two-dimensional natural convective heat transport data for horizontal annuli of arbitrary cross section has been developed and applied to two configurations: (i) concentric circular cylinders and (ii) annuli formed by an inner hexagonal cylinder and an outer circular cylinder. Also embodied in the theory is the capability to predict local as well as mean heat transfer. Thermal boundary conditions of the form T′xm can be accommodated. Data for the Rayleigh number (RaR) varied from 10 to 107, Prandtl number (Pr) varied from 0.7 to 3100, and the aspect ratio (Δ′/r′, maximum annulus gap/minimum radius of inner annulus) varied from 0.5 to 2.0. Even with these large variations, the present correlation theory collapses all the experimental data for the annular geometries to a signle line. The physical problem appears to be completely specified by a single equation when the following is known: thermal boundary condition (i.e., m), the fluid (i.e., Pr), the aspect ratio, the Rayleigh number, and the geometry. This work demonstrates that the present theory is applicable to annuli of arbitrary cross section, and therefore the theory will be extended to include curvature effects and axisymmetric geometry.

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