scholarly journals Geometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfaces

2020 ◽  
Vol 16 (1) ◽  
pp. 38-44
Author(s):  
Vyacheslav N. Ivanov ◽  
Alisa A. Shmeleva
Keyword(s):  
Differential Geometry ◽  
Coordinate System ◽  
Thin Shell ◽  
Tensor Analysis ◽  
Vector Analysis ◽  
Thin Shells ◽  
Orthogonal Coordinate System ◽  
Deformation State ◽  
The Common ◽  
To Receive

The aim of this work is to receive the geometrical equations of strains of shells at the common orthogonal not conjugated coordinate system. At the most articles, textbooks and monographs on the theory and analysis of the thin shell there are considered the shells the coordinate system of which is given at the lines of main curvatures. Derivation of the geometric equations of the deformed state of the thin shells in the lines of main curvatures is given, specifically, at monographs of the theory of the thin shells of V.V. Novozhilov, K.F. Chernih, A.P. Filin and other Russian and foreign scientists. The standard methods of mathematic analyses, vector analysis and differential geometry are used to receive them. The method of tensor analysis is used for receiving the common equations of deformation of non orthogonal coordinate system of the middle shell surface of thin shell. The equations of deformation of the shells in common orthogonal coordinate system (not in the lines of main curvatures) are received on the base of this equation. Derivation of the geometric equations of deformations of thin shells in orthogonal not conjugated coordinate system on the base of differential geometry and vector analysis (without using of tensor analysis) is given at the article. This access may be used at textbooks as far as at most technical institutes the base of tensor analysis is not given.

Membrane Solution of Fiber-Reinforced Corrugated Shells of Revolution

1967 ◽  
Vol 1 (4) ◽  
pp. 382-388 ◽  
Author(s):  
Harold G. Franklin
Keyword(s):  
Coordinate System ◽  
Thin Shell ◽  
Middle Surface ◽  
Loading Conditions ◽  
Fiber Reinforced ◽  
Shells Of Revolution ◽  
Torsional Loading ◽  
Explicit Formulas ◽  
Orthogonal Coordinate System ◽  
Corrugated Shells

A membrane solution of fiber-reinforced corrugated shells of revolution under axial and torsional loading is determined from the equations of a thin shell whose middle surface is referred to an orthogonal coordinate system. Explicit formulas for the stress resultants are determined and the displacements are stated in terms of simple quadratures without specifying the shape of the profile of the shell. It is found that the displacements are coupled under both loading conditions except when the orientation of the fibers are at the two extremes.

Appendixes

1997 ◽  
Author(s):  
David Jon Furbish
Keyword(s):  
Fluid Mechanics ◽  
Coordinate System ◽  
Vector Analysis ◽  
College Level ◽  
Coordinate Systems ◽  
Cartesian Coordinates ◽  
Orthogonal Coordinate System ◽  
Unit Vectors ◽  
Orthogonal Coordinates

Definitions and formulae used at various points in the text to manipulate vectors are listed below. Additional useful formulae, including geometrical and physical interpretations complementary to those provided in this text, can be found in standard texts on vector analysis and in mathematical handbooks. The Standard Mathematical Tables published by CRC Press (Boca Raton, Florida) is a particularly handy resource, and most college-level calculus texts cover introductory vector analysis as part of the material intended for a third-semester course. Appendix A in Bird, Stewart, and Lightfoot (1960) is a very good summary of vector and tensor notation presented in the context of fluid mechanics. Section 17.1.1 begins with several basic definitions of vector quantities that generally apply to any orthogonal coordinate system. The notation for unit vectors in Cartesian coordinates, i, j, and k, are used in this section, but it is understood that this notation may be directly replaced with symbols for unit vectors associated with other orthogonal coordinates. Section 17.1.2 then covers differential operations for Cartesian coordinates. Although the notation used for these differential operations in Cartesian coordinates is the same as that for other coordinate systems, the actual operations connoted by the notation are different, and must be defined separately (Appendix 17.2). Let S and T denote scalar functions, and let U, V, and W denote vectors. If U = 〈U1, U2, U3〉, then . . . U = U1i + U2j + U3k . . . . . . (17.1) . . .

Edges of Regression and Limit Normal Point of Conjugate Surfaces1

1998 ◽  
Vol 122 (4) ◽  
pp. 419-425 ◽  
Author(s):  
Ningxin Chen
Keyword(s):  
Differential Geometry ◽  
Contact Boundary ◽  
Boundary Line ◽  
Tangent Point ◽  
Common Tangent ◽  
Numerical Examples ◽  
Envelope Surface ◽  
The Common ◽  
Conjugate Surfaces ◽  
Definition Of

The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges of regression of the envelope surfaces are the undercutting line and the contact boundary line in theory of gearing respectively, and (2) the limit normal point is the common tangent point of the two edges of regression of the conjugate surfaces. New equations for the undercutting line, the contact boundary line and the limit normal point of the conjugate surfaces are developed based on the definition of the edges of regression. Numerical examples are taken for illustration of the above-mentioned concepts and equations. [S1050-0472(00)00104-5]

Three‐component sonde orientation in a deviated well

Geophysics ◽  
1990 ◽  
Vol 55 (10) ◽  
pp. 1386-1388 ◽  
Author(s):  
M. Becquey ◽  
M. Dubesset
Keyword(s):  
Hydraulic Fracturing ◽  
Coordinate System ◽  
Vertical Plane ◽  
Vertical Axis ◽  
Horizontal Axis ◽  
Orthogonal Coordinate System ◽  
Coordinate Rotation ◽  
Orthogonal Components ◽  
Particle Velocities

In well seismics, when operating with a three‐component tool, particle velocities are measured in the sonde coordinate system but are often needed in other systems (e.g., source‐bound or geographic). When the well is vertical, a change from the three orthogonal components of the sonde to another orthogonal coordinate system can be performed through one rotation around the vertical axis and, if necessary, another one around a horizontal axis (Hardage, 1983). If the well is deviated, the change of coordinate system remains easy in the case when the source is located at the vertical of the sonde, or in the case when the source stands in the vertical plane defined by the local well axis. In the general case (offset VSPs or walkaways) or when looking for unknown sources (such as microseismic emissions induced by hydraulic fracturing), coordinate rotation may still be performed, provided that we first get back to a situation in which one of the axes is vertical.

On the Dynamic Stability of Fluid-Conveying Pipes

1973 ◽  
Vol 40 (1) ◽  
pp. 48-52 ◽  
Author(s):  
D. S. Weaver ◽  
T. E. Unny
Keyword(s):  
Potential Theory ◽  
Dynamic Stability ◽  
Thin Shell ◽  
Critical Flow ◽  
Thin Shells ◽  
Classical Potential ◽  
Classical Potential Theory ◽  
Limiting Case ◽  
Beam Mode ◽  
Fluid Conveying Pipes

This paper presents a general analysis of the dynamic stability of a finite-length, fluid-conveying pipe. The Flu¨gge-Kempner equation is used in conjunction with classical potential theory so that circumferential modes as well as the usual beam modes may be considered. The cylinders are found to become unstable statically at first but flutter is predicted for higher velocities. The critical flow velocities for short, thin shells are associated with a number of circumferential waves. This number reduces for thicker and longer shells until the instability is in a beam mode. When the limiting case of a long thin shell is taken, it is found to agree with previous results obtained using a simpler beam approach.

Parenteral Hydration in Patients with Advanced Cancer (DRAFT)

2018 ◽  
Author(s):  
Carlos Eduardo Paiva ◽  
Bianca Sakamoto Ribeiro Paiva
Keyword(s):  
Quality Of Life ◽  
Advanced Cancer ◽  
Clinical Case ◽  
Fluid Intake ◽  
Hospice Care ◽  
Important Study ◽  
The Common ◽  
To Receive

There has been much debate about the role of parenteral hydration in the last weeks and days of life. In this important study, 129 patients with advanced cancer receiving hospice care with mild to moderate dehydration who were no longer able to maintain adequate fluid intake were randomized to receive parenteral hydration of either 1 L or 100 ml of normal saline per day subcutaneously. Parenteral hydration did not significantly improve the symptoms related to dehydration, the occurrence of delirium, fatigue, quality of life, and overall survival. At the end of the chapter, a clinical case leads readers to consider the common practice of parenteral hydration.

ON THE DYNAMICS OF A CLASS OF EINSTEIN–VLASOV SHELLS

2011 ◽  
Vol 20 (05) ◽  
pp. 661-674
Author(s):  
REINALDO J. GLEISER ◽  
MARCOS A. RAMIREZ
Keyword(s):  
Angular Momentum ◽  
Thin Shell ◽  
Continuous Distribution ◽  
Related Result ◽  
Thin Shells ◽  
Spherically Symmetric ◽  
Vlasov Equations ◽  
Finite Set ◽  
Thick Shells ◽  
Symmetric Systems

The Einstein–Vlasov equations govern the dynamics of systems of self-gravitating collisionless particles in the framework of general relativity. Here we review some recent results obtained by restricting to spherically symmetric systems and imposing the simplifying restrictions that the conserved angular momentum of the particles can take values only on a discrete, finite set. The first set of results is restricted to the existence of thin shells, their dynamics and stability. A second set is concerned with the existence of thick shells satisfying the same restrictions and the conditions under which they admit, in general, a thin shell limit. In a related result it is shown that the so called Einstein shells have a unique thin shell limit where the particle's angular momentum has a continuous distribution.

scholarly journals INFIDELS IN ENGLISH LEGAL THOUGHT: CONQUEST, COMMERCE AND SLAVERY IN THE COMMON LAW FROM COKE TO MANSFIELD, 1603–1793

2017 ◽  
Vol 16 (02) ◽  
pp. 375-409
Author(s):  
EDWARD CAVANAGH
Keyword(s):  
Intellectual History ◽  
Political Change ◽  
Common Law ◽  
Legal Thought ◽  
Starting Point ◽  
The Common ◽  
Law Reports ◽  
To Receive

English common law reports are dense with ideas. Yet they remain mostly untapped by intellectual historians. This article reveals how intellectual history can engage with law and jurisprudence by following the notion that “infidels” (specifically non-Christian individuals) deserved to receive exceptional treatment within England and across the globe. The starting point is Sir Edward Coke: he suggested that infidels could be conquered and constitutionally nullified, that they could be traded with only at the discretion of the monarch, and he confirmed their incapacity to enjoy full access to the common law. This article uncovers how each of these assertions influenced the development of the imperial constitution in the seventeenth and eighteenth centuries, when it came to war, trade and slavery. Identifying each of the major moves away from Coke's prejudices, this article argues that sometimes common lawyers responded to political change, but at other times anticipated it.

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