scholarly journals Discussion: “Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage” (Clark, R. A., Gilroy, T. I., and Reissner, E., 1952, ASME J. Appl. Mech., 19, pp. 37–48)

1952 ◽  
Vol 19 (4) ◽  
pp. 565-566
Author(s):  
Walter Wuest
Keyword(s):  
Cross Section ◽  
Elliptical Cross Section ◽  
Elliptical Cross ◽  
Toroidal Shells

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

Saint–Venant torsion of anisotropic elliptical bar

2017 ◽  
Vol 45 (3) ◽  
pp. 286-294 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Elliptical Cross Section ◽  
Elliptical Cross

The object of this article is the Saint–Venant torsion of anisotropic, homogeneous bar with solid elliptical cross section. A general solution of the Saint–Venant torsion for anisotropic elliptical cross section is presented and some known results are reformulated. The case of non-warping cross section is analysed.

scholarly journals The Tidal Potential of a Homogeneous Torus with an Elliptical Section of the Sleeve

2016 ◽  
Vol 25 (3) ◽  
Author(s):  
B. P. Kondratyev ◽  
N. G. Trubitsyna
Keyword(s):  
Cross Section ◽  
Kuiper Belt ◽  
Analytical Form ◽  
Elliptical Cross Section ◽  
External Region ◽  
Elliptical Cross ◽  
Tidal Potential ◽  
Gravitational Model ◽  
Elliptical Section

AbstractIn this paper the problem of the tidal potential of a homogeneous gravitating torus with an elliptical cross-section sleeve is solved. In particular, the potentials in analytical form in the vicinity of the center of the torus and its external region are found. This torus can serve as a gravitational model of the Kuiper belt.

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