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.

scholarly journals Saint-Venant’s torsion of thin-walled nonhomogeneous open elliptical cross section

2021 ◽  
Vol 11 (5) ◽  
pp. 151-158
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel ◽  
Attila Baksa ◽  
Dávid Gönczi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Elliptical Cross Section ◽  
Curvilinear Coordinates ◽  
Torsion Problem ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Thin Walled ◽  
The One

This paper deals with the Saint-Venant’s torsion of thin-walled isotropic nonhomogeneous open elliptical cross section whose shear modulus depends on the one of the curvilinear coordinates which define the cross-sectional area of the beam. The approximate solution of torsion problem is obtained by variational method. The usual simplification assumptions are used to solve the uniform torsion problem of bars with thin-walled elliptical cross-sections. An example illustrates the application of the derived formulae of shearing stress and torsional rigidity.

Optimization of Arrays of Rectangular Longitudinal Fins and Circular or Elliptical Cross-Section Spines

2010 ◽  
Author(s):  
P. Razelos ◽  
S. Das
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Heat Dissipation ◽  
Thermal Characteristics ◽  
Elliptical Cross Section ◽  
Elliptical Cross ◽  
Practical Applications ◽  
Pin Fins ◽  
Optimum Heat ◽  
Heat Released

The purpose of this study is to illustrate a method for obtaining the thermal performance and optimum dimensions of arrays consisting of rectangular longitudinal fins, cylindrical and elliptical cross-section spines. Since the majority of fin problems in an array have constant boundary temperatures, our endeavor is focused on the analysis and optimization of these types of fins. The temperature distribution, heat released to the environment, and the fins’ optimum dimensions in the array have been determined. Our analysis is based on a new set of dimensionless parameters, which are more suitable than those frequently used in fin analyses in the available literature. The effects of the boundary temperature ratio on the temperature variation in the fin have been examined and the results are shown graphically. Three salient results are derived regarding the thermal characteristics of these types of fins. They are: (1) the fin’s heat dissipation is expressed exactly with the same expression which describes the optimum heat dissipated by a fin with insulated tip, having half the fin’s dimensionless height. (2) The optimum fins’ dimensionless height and thickness are identical with those obtained for a fin with adiabatic tip of twice the dimensionless height (3) The optimum semi-axes ratio of elliptical-cross section spines is uniquely defined. In addition, it is shown that this approach can be successfully applied to solve problems in several practical applications, including pin fins having elliptic-cross sections. Two examples serve to illustrate the usefulness of our method.

Theoretical and Experimental Study on the Crimp Mechanism of Bi-Component Filament

2012 ◽  
Vol 476-478 ◽  
pp. 2209-2212
Author(s):  
Yuan Fang ◽  
Cheng Hu Wang ◽  
Hui Fang Liang ◽  
Li Li Bao ◽  
Xiao Hong Zhou
Keyword(s):  
Experimental Study ◽  
Cross Section ◽  
Cross Sections ◽  
Elliptical Cross Section ◽  
Elliptical Cross ◽  
The Cross ◽  
The Relationship

Based on two typical cross-sections such as the circular and the near-elliptical of PTT/PET bi-component filament, the crimp modeling was established. It can be used to describe the relationship among the crimp morphology in Longitudinal, the cross-section characteristics and the shrinkage difference of two components. The cross section characteristics of PTT/PET bi-component filament with nearly circular and elliptical cross section were obtained. The average ρ∆ of T400 made by Dupont is 17.46μm and that made by Huvis is 11.09μm.

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