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.

scholarly journals Saint-Venant torsion of orthotropic piezoelectric elliptical bar

2021 ◽  
Author(s):  
István Ecsedi ◽  
Attila Baksa
Keyword(s):  
Piezoelectric Material ◽  
Cross Section ◽  
Torsional Rigidity ◽  
Elliptical Cross Section ◽  
Sectional Area ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Maximum Value ◽  
Applied Torque ◽  
Piezoelectric Solid

AbstractThe object of this paper is the Saint-Venant torsion of a solid elliptical cylinder made of orthotropic homogeneous piezoelectric material. We find the shape of the homogeneous orthotropic piezoelectric elliptical cross section which does not warp under the applied torque. The sizes of the orthotropic piezoelectric solid elliptical cross section, which has the maximum value of torsional rigidity for a given cross-sectional area, are also determined.

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 Load bearing capacity of thin-walled rectangular and I-shaped steel sections of short both empty and concrete-filled columns

2021 ◽  
Vol 15 (58) ◽  
pp. 77-85
Author(s):  
Amor Bouaricha ◽  
Naoual Handel ◽  
Aziza Boutouta ◽  
Sarah Djouimaa
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Load Capacity ◽  
Cross Sectional ◽  
Short Columns ◽  
Cross Section Area ◽  
Section Area ◽  
Specimen Height ◽  
Steel Sections ◽  
Thin Walled

In this experimental work, strength results obtained on short columns subjected to concentric loads are presented. The specimens used in the tests have made of cold-rolled, thin-walled steel. Twenty short columns of the same cross-section area and wall thickness have been tested as follows: 8 empty and 12 filled with ordinary concrete. In the aim to determine the column section geometry with the highest resistance, three different types of cross-sections have been compared: rectangular, I-shaped unreinforced and, reinforced with 100 mm spaced transversal links. The parameters studied are the specimen height and the cross-sectional steel geometry. The registered experimental results have been compared to the ultimate loads intended by Eurocode 3 for empty columns and by Eurocode 4 for compound columns. These results showed that a concrete-filled composite column had improved strength compared to the empty case. Among the three cross-section types, it has been found that I-section reinforced is the most resistant than the other two sections. Moreover, the load capacity and mode of failure have been influenced by the height of the column. Also, it had noted that the experimental strengths of the tested columns don’t agree well with the EC3 and EC4 results.

scholarly journals The torsion and flexure of shafting with keyways or cracks

1932 ◽  
Vol 138 (836) ◽  
pp. 607-634 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Transverse Load ◽  
Torsion Problem ◽  
Circular Section ◽  
Physical Conditions ◽  
The Cross ◽  
Straight Lines

The object of the paper is to investigate the properties of shafts of circular cross-section into which keyways or slits have been cut, first when subjected to torsion, and second when bent by a transverse load at one end. The torsion problem for similar cases has been treated by several writers. Filon has worked out an approximation to the case of a circular section with one or two keyways ; in his method the boundary of the cross-section was a nearly circular ellipse and the boundaries of the keyways were confocal hyperbolas. In particular he considered the case when the hyperbola degenerated into straight lines starting from the foci. The solution for a circular section with one keyway in the form of an orthogonal circle has been obtained by Gronwall. In each case the solution has been obtained by the use of a conformal trans­formation and this method is again used in this paper, the transformations used being ρ = k sn 2 t . ρ = k 1/2 sn t , ρ = k 1/2 sn 1/2 t where ρ = x + iy , t = ξ + i η. No work appears to have been done on the flexure problem which is here worked out for several cases of shafts with slits. 2. Summary of the Problems Treated . We first consider the torsional properties of shafts with one and with two indentations. In particular cases numerical results have been obtained for the stresses at particular points and for the torsional rigidity. The results for one indentation and for two indentations of the same width and approximately the same depth have been compared. We next consider the solution of the torsion problem for one, two or four equal slits of any depth from the surface towards the axis. The values of the stresses have not been worked out in these cases since the stress is infinite at the bottom of the slits. This in stress occurs because the physical conditions are not satisfied at the bottom of the slits, but as had been pointed out by Filon this does not affect the validity of the values of the torsional rigidity. We compare the effect on the torsional rigidity of the shaft of one, two and four slits of the same depth in particular cases. We also compare the results for one slit with those obtained by Filon by another method, and find very good agreement which is illustrated by a graph. The reduction in torsional rigidity due to a semicircular keyway is compared with that due to a slit of approximately the same depth. Finally the distortion of the cross-sections at right angles to the planes is investigated, and in this, several interesting and perhaps unexpected features appear. The relative shift of the two sides of the slits is calculated in several cases.

Dynamic Detection and Analysis of Raw Silk’s Flatness

2011 ◽  
Vol 175-176 ◽  
pp. 385-388
Author(s):  
Xin Zhang ◽  
Yi Quan Xu ◽  
Kai Meng ◽  
Qing Guan Chen
Keyword(s):  
Cross Section ◽  
Axial Length ◽  
Minor Axis ◽  
Cross Sectional Area ◽  
Elliptical Cross Section ◽  
Sectional Area ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Photoelectric Sensor ◽  
Dynamic Detection

The shape of most raw silk’s cross-section can be regarded as ellipse approximately. Axial length of the raw silk’s cross-section was detected and recorded dynamically by photoelectric sensor combined with the software of LabVIEW. Two photoelectric sensors were located orthogonally to measure axial lengths of the ellipse. The major and minor values can be considered as the major and minor axis values of the raw silk’s elliptical cross-section respectively. Thereby, the flatness and the area of raw silk’s cross-section can be calculated according to the values of major and minor axes. In addition, the raw silk’s evenness was characterized based on the variation of the cross-sectional area.

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.

scholarly journals Numerical simulation of a stabilizing Poiseuille-type polymer fluid flow in the channel with elliptical cross-section

2021 ◽  
Vol 2099 (1) ◽  
pp. 012014
Author(s):  
A Blokhin ◽  
B Semisalov
Keyword(s):  
Fluid Flow ◽  
Cross Section ◽  
Stationary Problem ◽  
Elliptical Cross Section ◽  
Elliptical Cross ◽  
Polymer Fluid ◽  
Flow Stabilization ◽  
The One ◽  
Pseudo Spectral Method ◽  
Pseudo Spectral

Abstract This work is devoted to the numerical analysis of stabilization of the incompressible viscoelastic polymer fluid flow in the channel with elliptical cross-section. To describe the flow, mesoscopic rheological relations are used, and resolving non-stationary equations are derived. For solving them a special pseudo-spectral method is developed and implemented. As time increases, under certain conditions on the parameters of flow the solution to the non-stationary problem stabilizes and converges to the one of three branches of the solution to the corresponding stationary problem. It is shown that the variation of the parameters describing polymer microstructure leads to the switch of stabilized solution between these branches. The work provides the results of simulation of the flow stabilization and the analysis of the threshold values of parameters at which the switching occurs.

Converting Helicopter Rotor Blades From D-Spar to C-Spar: Allowing for Aeromorphing Structures

2014 ◽  
Author(s):  
Nathan S. Hosking ◽  
Zahra Sotoudeh
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Leading Edge ◽  
Honeycomb Structure ◽  
Rotor Blades ◽  
Cross Sectional ◽  
Helicopter Blades ◽  
Helicopter Rotor Blades ◽  
Thin Walled ◽  
The Cross

Modern helicopter blades are designed as thin-walled hollow structures in form of either C-spar or D-spar cross-sections. With the advent of new materials hollow designs have been implemented to reduce the overall weight of the structure. A D-spar is a rotor blade cross-section that is hollow in nature with a single vertical spar used to carry a large portion of the stresses otherwise carried by the skin [1]. The vertical spar is normally located between the leading edge and half of the chord length. The remaining volume aft of the vertical spar can either be hollow or filled with a honeycomb structure. The honeycomb structure increases the cross-sectional stiffness. Figure 1. shows an example of a common D-spar with a honeycomb structure aft of the vertical spar [2]. Due to new manufacturing methods the D-spar has now become common place in helicopter design [3]. A C-spar cross-section is very similar to the D-spar cross-section in design and construction. The C-spar cross-section does not have the honeycomb structure and the spar. The structural load is offset by more lamina layers towards the leading edge of the cross-section [4,5]. The thin-walled structure is comprised of many layers of composite materials such as fiberglass or carbon fibers. There has been extensive research into D-spar cross-section while there is a lack of studies for C-spar cross-sections [1,3,4].

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