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.

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.

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.

A New Method of Measuring the Cross-Sectional Area of Connective Tissue Structures

1988 ◽  
Vol 110 (2) ◽  
pp. 104-109 ◽  
Author(s):  
N. G. Shrive ◽  
T. C. Lam ◽  
E. Damson ◽  
C. B. Frank
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Connective Tissues ◽  
Maximum Width ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
The Cross

There appears to be no generally accepted method of measuring in-situ the cross-sectional area of connective tissues, particularly small ones, before mechanical testing. An instrument has therefore been devised to measure the cross-sectional area of one such tissue, the rabbit medial collateral ligament, directly and nondestructively. However, the methodology is general and could be applied to other tissues with appropriate changes in detail. The concept employed in the instrument is to measure the thickness of the tissue as a function of position along the width of the tissue. The plot obtained of thickness versus width position is integrated to provide the cross-sectional area. This area is accurate to within 5 percent, depending mainly on alignment of the instrument and pre-load of the ligament. Results on the mid-substance of the rabbit medial collateral ligaments are repeatable and reproducible. Values of maximum width and thickness are less variable than those obtained with a vernier caliper. The measured area is considerably less than that estimated assuming rectangular cross-section and slightly less than that estimated on the assumption of elliptical cross-section.

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.

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.

The Effect of Thermoelastic Stresses on Injection Well Fracturing

1985 ◽  
Vol 25 (01) ◽  
pp. 78-88 ◽  
Author(s):  
T.K. Perkins ◽  
J.A. Gonzalez
Keyword(s):  
Hydraulic Fracturing ◽  
Cross Section ◽  
Hydraulic Fracture ◽  
Outer Boundary ◽  
Elliptical Cross Section ◽  
Injection Well ◽  
Plan View ◽  
Elliptical Cross ◽  
Thermoelastic Stresses ◽  
Line Crack

Abstract When a cool fluid such as water is injected into a hot reservoir, a growing region of cooled rock is established around the injection well. The rock matrix within the cooled region contracts, and a thermoelastic stress field is induced around the well. For typical waterflooding of a moderately deep reservoir, horizontal earth stresses may be reduced by several hundred psi. If the injection pressure is too high or if suspended solids in the water plug the formation face at the perforations, the formation will be fractured hydraulically. As the fracture grows, the flow system evolves from an essentially circular geometry in the plan view to one characterized more nearly as elliptical. This paper considers thermoelastic stresses that would result from cooled regions of fixed thickness and of elliptical cross section. The stresses for an infinitely thick reservoir have been deduced from information available in public literature. A numerical method has been developed to calculate thermoelastic stresses induced within elliptically shaped regions of finite thickness. Results of these two approaches were combined, and empirical equations were developed to give an approximate but convenient, explicit method for estimating induced stresses. An example problem is given that shows how this theory can be applied to calculate the fracture lengths, bottomhole pressures (BHP's), and elliptical shapes of the flood front as the injection process progresses. Introduction When fluids are injected into a well, such as during waterflooding or other secondary or tertiary recovery processes, the temperatures of the injected fluids are typically cooler than the in-situ reservoir temperatures. A region of cooled rock forms around each injection well, and this region grows as additional fluid is injected. Formation rock within the cooled region contracts, and this leads to a decrease in horizontal earth stress near the injection well. In Ref. 1, the magnitude of the reduction in horizontal earth stress was given for the case of a radially symmetrical cooled region. Another factor, which may occur simultaneously, is the plugging of formation rock by injected solids. There is extensive literature indicating that waters normally available for injection contain suspended solids. Laboratory tests demonstrate that these waters, when injected into formation rocks, can plug the face of the rock or severely limit injectivity. In field operations, injection often simply continues at a BHP that is high enough to initiate and extend hydraulic fractures." The injected fluid then can leak off readily through the large fracture face area. Because of the lowering of horizontal earth stresses that results from cold fluid injection, hydraulic fracturing pressures can be much lower than would be expected for an ordinary low-leakoff hydraulic fracturing treatment. For this reason, the well operator may not be aware that injected fluid is being distributed through an extensive hydraulic fracture. If injection conditions are such that a hydraulic fracture is created, then the flow system will evolve from an essentially circular geometry in the plan view to one characterized more nearly as elliptical. In this paper, thermoelastic stresses for cooled regions of fixed thickness and of elliptical cross section are determined, and a theory of hydraulic fracturing of injection wells is developed. Conditions under which secondary fractures (perpendicular to the primary, main fracture) will open also are discussed. Finally, an example problem is given to illustrate how this theory can be applied to calculate fracture lengths, BHP'S, and elliptical shapes of the flood front as the injection process progresses. Thermoelastic Stresses in Regions of Elliptical Cross Section If fluid of constant viscosity is injected into a line crack (representing a two-wing, vertical hydraulic fracture), the flood front will progress outward. so its outer boundary at any time can be described approximately as an ellipse that is confocal with the line crack. If the injected fluid is at a temperature different from the formation temperature, a region of changed rock temperature with fairly sharply defined boundaries will progress outward from the injection well but lag behind the flood front. The outer boundary of the region of changed temperature also will be elliptical in its plan view and confocal with the line crack (see Fig. 1). Stresses within the region of altered temperature, as well as stress in the surrounding rock, which remains at its initial temperature, will be changed because of the expansion or contraction of the rock within the region of altered temperature. The thermoelastic stresses within an infinitely tall cylinder of elliptical cross section can be determined from information available in the literature. 10 The interior thermoelastic stresses perpendicular and parallel to the major axes of the ellipse are given by Eqs. 1 and 2, respectively. SPEJ P. 78^

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